{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The HFM library - A fast marching solver with adaptive stencils\n", "\n", "## Part : Non holonomic metrics and curvature penalization\n", "## Chapter : Curvature penalized planar paths.\n", "\n", "In this notebook, we demonstrate the computation of globally optimal curvature penalized minimal paths, as described in the paper:\n", "\n", " [Mir17c]\tJ.-M. Mirebeau, “Fast Marching methods for Curvature Penalized Shortest Paths,” JMIV. 2018. [link](https://hal.archives-ouvertes.fr/hal-01538482)\n", "\n", "More precisely, to each path $x : [0,T] \\to {\\mathbb R}^2$, parametrized at *unit euclidean speed*, we attach a cost of the form\n", "\\begin{equation*}\n", "\\mathcal E(x(\\cdot)) = \\int_0^T c(x(t),x'(t)) \\, {\\mathcal C}( \\|x''(t)\\| ) \\, \\mathrm d t.\n", "\\end{equation*}\n", "The integrated path cost is the product of two factors: a first term $c(x,\\dot x)$ depending on the current position and orientation, and a second term ${\\mathcal C}(\\|\\ddot x\\|)$ depending on the curvature. \n", "Recall, indeed, that for a path parametrized at unit euclidean speed, acceleration is curvature.\n", "\n", "The first term $c : \\mathbb R^2 \\times \\mathbb S^1 \\to ]0,\\infty[$ is arbitrary and provided by the user. \n", "The second must be chosen among the following cost functions $\\mathcal C(\\kappa)$\n", "\n", "Model name | Reeds-Shepp | Euler-Mumford elastica| Dubins car\n", "--- | :---: | :---: | :---:\n", "$\\mathcal C(\\kappa)$ | $\\sqrt{1+(\\xi\\kappa)^2}$ | $1+(\\xi\\kappa)^2$ | $\\begin{cases} 1 & |\\xi\\kappa| \\leq 1 \\\\ \\infty & \\text{else} \\end{cases}$\n", "\n", "The parameter $\\xi>0$ has the dimension of a radius of curvature, and is chosen by the user. (It is unrelated with the similarly named parameter appearing in the discussion of sensitivity analysis.)\n", "The Reeds-Shepp, Euler-Mumford elastica, and Dubins car costs penalize large curvatures in an increasingly strong manner: respectively (approximately) linear, quadratic, and absolute (the path is rejected).\n", "\n", "The Reeds-Shepp cost is used to define two distinct models, referred to as *Reeds-Shepp* (the classical, sub-riemannian model), and *Reeds-Shepp forward*. In the former case, the car may shift into reverse gear, which introduces *cusp points* where the path orientation is reversed. This behaviour is forbidden in the *Reeds-Shepp forward* model, as well as in the Euler-Mumford elastica and the Dubins car models.\n", "\n", "Consider a two dimensional domain $U \\subset \\mathbb R^2$, and some initial and final points $x_*,x^* \\in U$, and tangents $n_*, n^* \\in \\mathbb S^1$. \n", "The HFM software is able to find the path $x : [0,T] \\to U$, parametrized at unit speed and where the terminal time $T$ is free, obeying the prescribed constraints and globally minimizing the cost $\\mathcal E(x(\\cdot))$. In other words it solves\n", "\\begin{align*}\n", "&\\min_{T,c} \\mathcal E(x()) &\\text{ subject to } \\ x:[0,T] \\to U,\\, x(0)=x_*,\\ x'(0)=n_*,\\ x(T)=x^*,\\ x'(T)=n^*, \\text{ and }\\forall t, \\|x'(t)\\|=1.\n", "\\end{align*}\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[**Summary**](Summary.ipynb) of volume Fast Marching Methods, this series of notebooks.\n", "\n", "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n", "\tbook of notebooks, including the other volumes.\n", "\n", "# Table of contents\n", " * [1. Defining the domain](#1.-Defining-the-domain)\n", " * [2. Specifying the metric](#2.-Specifying-the-metric)\n", " * [3. Calling the software, and displaying the results.](#3.-Calling-the-software,-and-displaying-the-results.)\n", " * [4. Comparison of the different models.](#4.-Comparison-of-the-different-models.)\n", " * [4.1 The Reeds-Shepp car (with reverse gear)](#4.1-The-Reeds-Shepp-car-(with-reverse-gear))\n", " * [4.2 The Reeds-Shepp forward model (without reverse gear)](#4.2-The-Reeds-Shepp-forward-model-(without-reverse-gear))\n", " * [4.3 Euler-Mumford elastica curves](#4.3-Euler-Mumford-elastica-curves)\n", " * [4.4 The Dubins car](#4.4-The-Dubins-car)\n", " * [5. Varying the cost function](#5.-Varying-the-cost-function)\n", " * [5.1 Cost depending on the physical position](#5.1-Cost-depending-on-the-physical-position)\n", " * [5.2 Orientation dependent speed](#5.2-Orientation-dependent-speed)\n", " * [6. Generalized models with non-uniform curvature penalization](#6.-Generalized-models-with-non-uniform-curvature-penalization)\n", " * [6.1 Position dependent radius of curvature](#6.1-Position-dependent-radius-of-curvature)\n", " * [6.2 Distinct bound on the radius of curvature for right and left turns.](#6.2-Distinct-bound-on-the-radius-of-curvature-for-right-and-left-turns.)\n", " * [7. Additional functionality](#7.-Additional-functionality)\n", " * [7.1 Euclidean length of geodesics](#7.1-Euclidean-length-of-geodesics)\n", " * [7.2 Minimal geodesic joining two seeds.](#7.2-Minimal-geodesic-joining-two-seeds.)\n", "\n", "\n", "\n", "This Python® notebook is intended as documentation and testing for the [HamiltonFastMarching (HFM) library](https://github.com/mirebeau/HamiltonFastMarching), which also has interfaces to the Matlab® and Mathematica® languages. \n", "More information on the HFM library in the manuscript:\n", "* Jean-Marie Mirebeau, Jorg Portegies, \"Hamiltonian Fast Marching: A numerical solver for anisotropic and non-holonomic eikonal PDEs\", 2019 [(link)](https://hal.archives-ouvertes.fr/hal-01778322)\n", "\n", "Copyright Jean-Marie Mirebeau, University Paris-Sud, CNRS, University Paris-Saclay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Importing the required libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.061280Z", "iopub.status.busy": "2024-04-30T08:51:28.060537Z", "iopub.status.idle": "2024-04-30T08:51:28.077716Z", "shell.execute_reply": "2024-04-30T08:51:28.076684Z" } }, "outputs": [], "source": [ "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n", "#from Miscellaneous import TocTools; print(TocTools.displayTOC('Curvature','FMM'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.080218Z", "iopub.status.busy": "2024-04-30T08:51:28.080100Z", "iopub.status.idle": "2024-04-30T08:51:28.334535Z", "shell.execute_reply": "2024-04-30T08:51:28.334228Z" } }, "outputs": [], "source": [ "from agd import Eikonal\n", "from agd.Plotting import savefig, SetTitle3D; #savefig.dirName = 'Figures/Curvature/'" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.336290Z", "iopub.status.busy": "2024-04-30T08:51:28.336167Z", "iopub.status.idle": "2024-04-30T08:51:28.338106Z", "shell.execute_reply": "2024-04-30T08:51:28.337875Z" } }, "outputs": [], "source": [ "import numpy as np; xp=np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D # Plots 3D paths\n", "\n", "useMayavi = False\n", "if useMayavi:\n", " from mayavi import mlab # Plots implicit surfaces" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0.1 Optional configuration\n", "Uncomment the following line to use the GPU eikonal solver." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.339508Z", "iopub.status.busy": "2024-04-30T08:51:28.339408Z", "iopub.status.idle": "2024-04-30T08:51:28.340973Z", "shell.execute_reply": "2024-04-30T08:51:28.340748Z" }, "tags": [ "EikonalGPU_config" ] }, "outputs": [], "source": [ "#from agd import AutomaticDifferentiation as ad; xp,plt,Eikonal = map(ad.cupy_friendly,(xp,plt,Eikonal))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following command allows, when it works, to make matplotlib interactive - in particular, 3D plots can be rotated around. However, it is also somewhat buggy, and plots may not show up at all. Uncomment it for a try." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.342385Z", "iopub.status.busy": "2024-04-30T08:51:28.342306Z", "iopub.status.idle": "2024-04-30T08:51:28.343868Z", "shell.execute_reply": "2024-04-30T08:51:28.343635Z" } }, "outputs": [], "source": [ "#%matplotlib notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Defining the domain\n", "\n", "In order to compute paths minimizing curvature dependent energies, we use a technique referred to as dimension lifting. It involves the three dimensional product domain \n", "\\begin{equation*}\n", "\\Omega := U \\times \\mathbb S^1\n", "\\end{equation*}\n", "where $U \\subset \\mathbb R^2$ is the physical domain, and $\\mathbb S^1 = [0,2\\pi[$ is the angular domain, with periodic boundary conditions. The HFM software extracts a three dimensional path $\\gamma : [0,T] \\to U \\times \\mathbb S^1$, featuring directional information \n", "\\begin{equation*}\n", "\\gamma(t) = (x(t), \\theta(t)).\n", "\\end{equation*}\n", "The physical velocity and the angular orientation are tied by the relation\n", "where $x'(t) = \\|x'(t)\\| (\\cos \\theta(t), \\sin \\theta(t))$. In the case of the Reeds Shepp model, which has a reverse gear, the constraint is relaxed into $x'(t) = \\pm \\|x'(t)\\| (\\cos \\theta(t), \\sin \\theta(t))$.\n", "\n", "\n", "The physical domain $U$ is discretized using a cartesian grid, which dimensions, origin, a spacing are specified similarly to the Isotropic and Riemannian models.\n", "\n", "For the angular domain use a uniform sampling $\\{0,h_\\theta, \\cdots, (n_\\theta-1) h_\\theta\\}\\subset [0,2 \\pi[$ is used, where $n_\\theta$ is the number of discretization points and $h_\\theta := 2\\pi/n_\\theta$ is the corresponding angular resolution. We often use $n_\\theta = 60$, and in general we suggest choosing $60 \\lesssim n_\\theta \\lesssim 120$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.345334Z", "iopub.status.busy": "2024-04-30T08:51:28.345244Z", "iopub.status.idle": "2024-04-30T08:51:28.347244Z", "shell.execute_reply": "2024-04-30T08:51:28.347025Z" } }, "outputs": [], "source": [ "# Define the physical domain, by specifying (bottom,left) and (top,right) corners\n", "n = 100; nTheta=60\n", "hfmIn = Eikonal.dictIn({'model':'Elastica2'}) # Has (position , orientation) domain\n", "hfmIn.SetRect(sides=[[-1,1],[0,1]],gridScale=1./n) # Position space\n", "hfmIn.nTheta=nTheta # Angular domain sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us insert in the domain some seeds, from which the front is propagated, and tips, from which geodesics are backtracked. Seeds $p_* = (x_*,\\theta_*)$ and tips $p^*=(x^*,\\theta^*)$ are elements of the three dimensional product space $\\Omega = U \\times \\mathbb S^1$.\n", "\n", "We also offer the possibility to introduce some \"unoriented seeds\" $x_*\\in U$, from which the front is propagated in all directions $(x_*,\\theta)$, $\\theta \\in \\mathbb S^1$. \"Unoriented tips\" $x^*\\in U$ can also be specified, in which case the shortest geodesic is returned, among all those starting from $(x^*,\\theta)$, $\\theta \\in \\mathbb S^1$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.348587Z", "iopub.status.busy": "2024-04-30T08:51:28.348509Z", "iopub.status.idle": "2024-04-30T08:51:28.350931Z", "shell.execute_reply": "2024-04-30T08:51:28.350680Z" } }, "outputs": [], "source": [ "hfmIn.update({\n", " # Declare the seeds, from which the front is propagated\n", " 'seed':[-0.5,0.5,0],\n", " 'seed_Unoriented':[0.5,0.5],\n", " \n", " # Optionally declare the boundary conditions at the seeds (default is 0)\n", " 'seedValue':0.,\n", " 'seedValue_Unoriented':0.3,\n", "})\n", "\n", "# Declare the tips, from which the geodesics are backtracked\n", "hfmIn['tips'] = [[x,y,np.pi/4] \n", " for x in Eikonal.CenteredLinspace(-1,1,6) \n", " for y in Eikonal.CenteredLinspace(0,1,4)]\n", "hfmIn['tips_Unoriented'] = hfmIn['tips'][:,0:2] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Finally, we construct a coordinate system, for constructing the synthetic data used in our examples. Actually, we build two: First, a three dimensional coordinate system, as could be expected. Second, a system adapted to the construction of fields depending only on the position, or only on the orientation. The latter one is enough for many examples, and somewhat reduces the memory usage. \n", "\n", "\n", "Let us immediately ackowledge a potential conflict of notations: the letter $x$ refers to a point of the physical domain in the mathematical paragraphs. However, in the python codes, the capital letters X and Y refer to the horizontal and vertical coordinates in the physical domain." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.352291Z", "iopub.status.busy": "2024-04-30T08:51:28.352213Z", "iopub.status.idle": "2024-04-30T08:51:28.356837Z", "shell.execute_reply": "2024-04-30T08:51:28.356555Z" } }, "outputs": [], "source": [ "# Genuine three dimensional coordinate system.\n", "X,Y,Theta = hfmIn.Grid()\n", "\n", "# System built of two dimensional arrays X2,Y2, and of a one dimensional array Theta2\n", "X2,Y2 = X[:,:,0], Y[:,:,0]\n", "Theta2 = Theta[0,0,:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Specifying the metric\n", "\n", "In this paragraph, we briefly expose how the computation of curvature penalized minimal paths is addressed using fast marching techniques, although this is not strictly necessary for using the HFM software. Our objective is to minimize a second order energy $\\mathcal E(x(\\cdot))$, where $x : [0,T] \\to U$ is a planar path. For that purpose, this energy is encoded as the path length $L_F(\\gamma)$ of a [lifted path](#sec_domain) $\\gamma : [0,T] \\to \\Omega = U \\times \\mathbb S^1$. The metric $F$, which is singular, is defined in the next paragraph.\n", "\n", "\n", "We introduce a metric $F$ on the tangent space to the lifted domain. For any point $p = (x,\\theta) \\in \\Omega$ and any tangent vector $\\dot p = (\\dot x, \\dot \\theta) \\in \\mathbb R^2 \\times \\mathbb R$ with unit physical speed $\\|\\dot x\\| = 1$, it is defined by \n", "\\begin{equation*}\n", "F_{(x,\\theta)}(\\dot x, \\dot \\theta) = c(x,\\theta)\n", "\\begin{cases}\n", "\\mathcal C(\\dot \\theta) & \\text{ if } \\dot x = (\\cos \\theta, \\sin \\theta),\\\\\n", "+\\infty & \\text{ else}.\n", "\\end{cases}\n", "\\end{equation*}\n", "The colinearity constraint is changed into $\\dot x = \\pm (\\cos \\theta, \\sin \\theta)$ is the case of the classical Reeds-Shepp model, which has a reverse gear.\n", "We extend the metric by $1$-homogeneity: $F_p(\\lambda \\dot p) = \\lambda F_p(\\dot p)$, $\\lambda >0$, in the case $\\|\\dot x\\| \\neq 1$ of a non-unit physical speed. Thanks to this, the length of a path, as measured by the metric $F$ is parametrization invariant.\n", "\n", "Denote by $u(p)$, where $p = (x,\\theta) \\in \\Omega$ is a point of the lifted domain, the minimal length of a path $\\gamma:[0,1] \\to \\overline \\Omega$ from $\\partial \\Omega$ to $p$. Length is measured using the metric $F$, and takes into account the boundary conditions $\\sigma : \\partial \\Omega \\to ]-\\infty,\\infty]$\n", "\\begin{equation*}\n", "u(p) := \\min_{\\substack{\\gamma(0) \\in \\partial \\Omega\\\\ \\gamma(1)=p}} \\sigma(\\gamma(0)) + \\int_0^1 F_{\\gamma(t)}(\\gamma'(t))\\, \\mathrm dt.\n", "\\end{equation*}\n", "Then, under general assumptions, and similarly to the Isotropic and the Riemannian case, the arrival times $u : \\overline \\Omega \\to ]-\\infty,\\infty]$ are weak solutions to the generalized eikonal PDE \n", "\\begin{align*}\n", "\\forall p \\in \\Omega, F^*_p(\\nabla u(p)) &= 1, &\n", "\\forall p \\in \\partial \\Omega, u(p) = \\sigma(p).\n", "\\end{align*}\n", "The dual metric, involved in this equation, is defined at any point $p \\in \\Omega$ and for any co-tangent vector $\\hat p\\in R^2 \\times \\mathbb R$ by\n", "\\begin{equation*}\n", "F_p^*(\\hat p) := \\sup \\{ \\hat p \\cdot \\dot p;\\, \\dot p \\in R^2 \\times \\mathbb R, F_p(\\dot p) \\leq 1\\}.\n", "\\end{equation*}\n", "\n", "\n", "The HFM software numerically solves the generalized eikonal equation above, using a finite differences approximation of the quantity $F_p^*(\\nabla u(p))$. The explicit expression of the dual metric $F_p^*(\\nabla u(p))$, and the design of the discretization scheme, are described in [Mir17c](#cite_Mire17c) and in the IPOL submission. \n", "\n", "Our PDE discretization actually depends on a small parameter $\\varepsilon>0$, which reflects the relaxation of the non-holonomy constraint (In the Euler-Mumford elastica case there is also a integer parameter $K$ related to a quadrature formula). The default values $\\varepsilon = 0.1$ and $K=5$ are suitable for many applications, and we recommend not changing them unless one knows what he is doing. Let us nevertheless mention that:\n", "* reducing the value of $\\varepsilon$ enforces better the non-holonomy constraint, but a proportional increase in the physical and angular resolution is required.\n", "* using a larger $K$ may slightly enhance the accuracy of the Euler-Mumford discretization, but it increases the computational cost." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.358329Z", "iopub.status.busy": "2024-04-30T08:51:28.358247Z", "iopub.status.idle": "2024-04-30T08:51:28.360061Z", "shell.execute_reply": "2024-04-30T08:51:28.359821Z" } }, "outputs": [], "source": [ "# Select the model. Possible choices are : \n", "# * ReedsShepp2 - the classical Reeds-Shepp model with reverse gear\n", "# * ReedsSheppForward2 - likewise but without reverse gear\n", "# * Elastica2 - Euler-Mumford elastica, with quadrature parameter K=5. (Elastica2<9> is also implemented.)\n", "# * Dubins2 - Dubins car model\n", "hfmIn['model'] = 'Elastica2'\n", "\n", "# Choose the reference radius of curvature \n", "hfmIn['xi'] = 0.2\n", "\n", "# Optionally, choose the relaxation parameter related with the non-holonomy constraint (default is 0.1)\n", "#hfmInput['eps'] = 0.15 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cost function $c$ defined on $\\Omega = U \\times \\mathbb S^1$, may depend on both the physical coordinate $x \\in U$ and the angular coordinate $\\theta \\in \\mathbb S^1$. It may also be a constant, or depend on the physical coordinate only, or the angular coordinate only. \n", "\n", "The systems of coordinates (X,Y,Theta), and the sub-systems (X2,Y2) and Theta2 were built [here](#coords). Recall that the capital letters X and Y, or X2 and Y2, refer to the coordinates of the physical point $x \\in U$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.361413Z", "iopub.status.busy": "2024-04-30T08:51:28.361334Z", "iopub.status.idle": "2024-04-30T08:51:28.363006Z", "shell.execute_reply": "2024-04-30T08:51:28.362774Z" } }, "outputs": [], "source": [ "# Define the cost function c(x,theta). You may enter :\n", "hfmIn['cost'] = 1. # (i) A constant c=c_0\n", "#hfmInput['cost'] = 1.+(Y2<=0.5) # (ii) A field c=c(x) depending on the physical position only\n", "#hfmInput['cost'] = 1.+ 0.5*cos(Theta2) # (iii) A field c=c(theta) depending on theta only\n", "#hfmInput['cost'] = 1.+(Y<=0.5)+0.5*cos(Theta) # (iv) A general field c=c(x,theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next introduce walls in the domain, described by their indicator function. As for the cost function, walls may depend on the physical coordinates, angular coordinates, or both. We consider here the same obstacles used in the two dimensional isotropic examples, which depend on the physical position only." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.364325Z", "iopub.status.busy": "2024-04-30T08:51:28.364251Z", "iopub.status.idle": "2024-04-30T08:51:28.366479Z", "shell.execute_reply": "2024-04-30T08:51:28.366213Z" } }, "outputs": [], "source": [ "# Define the walls, which may depend on \n", "disk = (X2-0.3)**2 + (Y2-0.3)**2 <= 0.2**2\n", "barrier = np.logical_and(X2==X2[70,0], Y2>=0.4)\n", "hfmIn['walls']= np.logical_or(disk,barrier) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Calling the software, and displaying the results.\n", "\n", "Conventions for calling the HFM software, and displaying the resulting distance map and backtracked geodesics, is identical to the Isotropic or Riemannian cases. The main difference being that the models considered in this section are posed on the three dimensional, partly periodic, dimension lifted domain $\\Omega = U \\times \\mathbb S^1$. In practice, the angular coordinate is often discarded, by projecting onto the physical domain $U$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.367972Z", "iopub.status.busy": "2024-04-30T08:51:28.367890Z", "iopub.status.idle": "2024-04-30T08:51:28.369532Z", "shell.execute_reply": "2024-04-30T08:51:28.369312Z" } }, "outputs": [], "source": [ "hfmIn['exportValues'] = 1. # Export the arrival time values for inspection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Computation time is larger than for most of the examples considered in the previous sections, because the domain is three dimensional, and due to the complex stencil used for the discretization of the Euler-Mumford elastica model." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:28.370869Z", "iopub.status.busy": "2024-04-30T08:51:28.370787Z", "iopub.status.idle": "2024-04-30T08:51:31.867321Z", "shell.execute_reply": "2024-04-30T08:51:31.866988Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 3.36787 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n", "CPU times: user 4.59 ms, sys: 8.04 ms, total: 12.6 ms\n", "Wall time: 3.49 s\n" ] } ], "source": [ "%%time\n", "hfmOut = hfmIn.Run() # Warning : takes up to a minute." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first display the *planar projection* of the minimal geodesics, backtracked from the tips, which are points of the configuration space $\\Omega = U \\times \\mathbb S^1$.\n", "Note that, at their final tip, the velocity of the backtracked geodesics is colinear with the vector $(1,1)$.\n", "This was expected, in view of the angular coordinate $\\theta = \\pi/4$ of the tips. Note also that these paths are quite smooth, including around obstacles, thanks to the Euler-Mumford elastica model penalizing curvature.\n", "\n", "\n", "The geodesics start from either the left seed, or the right *unoriented* seed. Note that : \n", "* At the left seed, geodesics have an horizontal tangent as prescribed ($\\theta=0$).\n", "* At the right *unoriented* seed, geodesics have an arbitrary tangent." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:31.869053Z", "iopub.status.busy": "2024-04-30T08:51:31.868938Z", "iopub.status.idle": "2024-04-30T08:51:31.948309Z", "shell.execute_reply": "2024-04-30T08:51:31.948020Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[6,3]); plt.title(\"Euler-Elastica minimal paths\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the specified tips was located in the disk shaped obstacle. Obviously, no geodesic could be backtraced from this specific point." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:31.949897Z", "iopub.status.busy": "2024-04-30T08:51:31.949791Z", "iopub.status.idle": "2024-04-30T08:51:31.952132Z", "shell.execute_reply": "2024-04-30T08:51:31.951877Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0.16666667],\n", " [0.375 ],\n", " [0.78539816]])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hfmOut['geodesics'][13] # Backtracking failed since the tip was inside an obstacle. The tip alone is returned." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next display the minimal geodesics from the seed (left) and unoriented seed (right), to the *unoriented* tips. These geodesics end with an arbitrary tangent at their final tip, namely the most favourable orientation in terms of energy." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:31.953659Z", "iopub.status.busy": "2024-04-30T08:51:31.953552Z", "iopub.status.idle": "2024-04-30T08:51:32.021241Z", "shell.execute_reply": "2024-04-30T08:51:32.020955Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[6,3]); plt.title(\"Minimal Euler elasticas from the unoriented tips\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics_Unoriented']: plt.plot(geo[0],geo[1]) \n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The backtracked geodesics are actually three dimensional paths. In the following cell, they are shown as such, in other words their angular coordinate is not discarded. The seedpoint at the extremity of each geodesic is shown in bold. Three groups of geodesics can be distinguished\n", "* One ending on the vertical line $(0.5,0.5,\\theta)$, with an arbitrary angle $\\theta$, which corresponds to the *unoriented* seed $(0.5,0.5) \\in U$.\n", "* Another one ending at the position $(-0.5,0.5,0)$, which is a prescribed seed.\n", "* A last one ending at the position $(-0.5,0.5,2 \\pi)$, which is identical to the above one once periodic boundary conditions are applied on the angular third variable $\\theta\\in \\mathbb S^1$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:32.022854Z", "iopub.status.busy": "2024-04-30T08:51:32.022730Z", "iopub.status.idle": "2024-04-30T08:51:32.202548Z", "shell.execute_reply": "2024-04-30T08:51:32.202271Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(); ax = plt.axes(projection='3d'); SetTitle3D(ax,\"Minimal Euler elasticas\")\n", "for geodesic in hfmOut['geodesics']:\n", " if geodesic.shape[1]==1: continue # Eliminate the geodesic starting in an obstacle.\n", " plt.plot(*geodesic)\n", " if hfmIn.mode=='cpu':ax.scatter(*geodesic[:,-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we present a level surface of the arrival times function $u$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:32.204223Z", "iopub.status.busy": "2024-04-30T08:51:32.204105Z", "iopub.status.idle": "2024-04-30T08:51:32.205924Z", "shell.execute_reply": "2024-04-30T08:51:32.205680Z" } }, "outputs": [], "source": [ "if useMayavi:\n", " mlab.contour3d(hfmOutput['values'], contours=[1])\n", " mlab.show() # Displays in an external window." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is what the previous command should display.\n", "![Solution level set](https://dl.dropbox.com/s/f0a0l64sjjy8xmd/3_Elastica_Contour3D.png?dl=0)\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Comparison of the different models.\n", "\n", "In this section, we compare the qualitative features of the four main curvature penalized models implemented in the HFM library. Namely the Reeds-Shepp, Reeds-Shepp forward, Euler-Mumford elastica, and Dubins car models.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1 The Reeds-Shepp car (with reverse gear)\n", "\n", "The classical Reeds-Shepp model is adequate for describing slow vehicles, such as wheelchairs, equipped with a reverse gear. The model belongs to the field of sub-Riemannian geometry, a generalization of Riemannian geometry involving tensors with *infinite* eigenvalues. An alternative point of view is the eikonal equation is Riemannian-like, but involves rank deficient tensors. \n", "\n", "The precise definition of sub-Riemannian geometry involves additional controllability assumption which are outside of the scope of this document." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:32.207486Z", "iopub.status.busy": "2024-04-30T08:51:32.207370Z", "iopub.status.idle": "2024-04-30T08:51:32.209118Z", "shell.execute_reply": "2024-04-30T08:51:32.208881Z" } }, "outputs": [], "source": [ "hfmIn['model']='ReedsShepp2'\n", "hfmIn['xi']=0.3\n", "hfmIn['exportValues']=0\n", "hfmIn.pop('tips_Unoriented',None);" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:32.210427Z", "iopub.status.busy": "2024-04-30T08:51:32.210348Z", "iopub.status.idle": "2024-04-30T08:51:32.975783Z", "shell.execute_reply": "2024-04-30T08:51:32.975425Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field projective defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.723453 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A distinguishing feature of the planar projections of minimal paths for the Reeds-Shepp model is the presence of *cusps*, at the points where the vehicle shifts into reverse gear." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:32.977442Z", "iopub.status.busy": "2024-04-30T08:51:32.977324Z", "iopub.status.idle": "2024-04-30T08:51:33.044383Z", "shell.execute_reply": "2024-04-30T08:51:33.044103Z" } }, "outputs": [ { "data": { "image/png": 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ikSQJIUThE0kBP/zwAyaT6a77BG7q89tvv707I4thyZIlNG3atPD9b7/9htFoLIzSL40N/34as7W1vWfbAgMDGTNmDFu2bGHPnj2l3j8kJAR/f3+WLl3K+PHjC48lJyeH33//vXDlwd3w3yfPu6Fnz5588MEHuLu7l9nyQK1Wy9y5c+nYsSPTp0/n22+/pVu3bqhUKi5dunTbKZGQkBBq167N8ePH+eCDD247TqdOnVi9ejUJCQmFbnKTycSyZctuuY9SqaRly5bUrVuXJUuWcPToUQYMGFAoMv5LSkoKjo6OaDSamz47e/YsYPH0lIaSnot/s2TJEl599dXC90uXLgUospIFYMuWLcWej5o1a97SOwDQvXt3fvnlFxYuXHjLaYPirkMhBN9//32JjkHm/iALAplicXJyon379nzyySd4eHhQvXp1duzYwY8//ljEpVka2rRpg6urKy+++CLvv/8+arWaJUuWcPz48TKz+48//kClUtGlSxdOnTrFxIkTCQ8Pp1+/fqW2oUGDBgB89NFHdO/eHaVSScOGDYv9QS+OjIwMOnXqxKBBg6hbty6Ojo4cOnSI9evX3/KJ9XYoFAo+/vhjBg8eTM+ePXnhhRfQ6XR88sknpKen8+GHH5a6zwIKMhF+9913ODo6YmNjQ3Bw8G2fBP/L66+/zu+//0779u0ZO3YsDRs2xGw2c+3aNTZu3Mj//vc/WrZsWWrbOnToQI8ePViwYAFvvfUWwcHBTJ06lXfffZfLly/z6KOP4urqSkJCAgcPHsTe3p4pU6YAFqHXvXt3unXrxrBhw/D39yc1NZUzZ85w9OhRli9fDsB7773H6tWr6dy5M5MmTcLOzo65c+fetFzym2++YevWrTz22GMEBgaSn59f6BF55JFHbnsc27Zt47XXXmPw4MG0adMGd3d3EhMT+eWXX1i/fj1Dhgy57Y22OKpXr17icwGg0Wj47LPPyM7Opnnz5uzdu5fp06fTvXv3wqWuBXh4eNC5c2cmTpyIvb098+bN4+zZs3dcejhw4EAWLFjAiy++yLlz5+jUqRNms5kDBw4QGhrKgAED6NKlCxqNhoEDB/LGG2+Qn5/P119/TVpaWqmOX6aMsXZUo8z95VbLDv9LcasMYmJixFNPPSVcXV2Fo6OjePTRR0VkZKQICgoSQ4cOveMYxfW5d+9e0bp1a2FnZyc8PT3FqFGjxNGjR29aBnarJWi3oiCq/siRI6JXr17CwcFBODo6ioEDBxZZrlYaG3Q6nRg1apTw9PQUkiQViTYHxMsvv3yTHf8+N/n5+eLFF18UDRs2FE5OTsLW1laEhISI999/X+Tk5Nz2eIpbZVDAqlWrRMuWLYWNjY2wt7cXDz/8sNizZ0+x5+Pfy0PvxOzZs0VwcLBQKpVFzkWHDh1E/fr1b2o/dOhQERQUVGRbdna2eO+990RISIjQaDTC2dlZNGjQQIwdO7ZIxHpx3O5/fvLkSaFQKIosSVu1apXo1KmTcHJyElqtVgQFBYm+ffuKzZs3F9n3+PHjol+/fsLLy0uo1Wrh4+MjOnfuLL755psi7fbs2SNatWoltFqt8PHxERMmTBDfffddkf/7vn37xJNPPimCgoKEVqsV7u7uokOHDmL16tW3PTYhhIiOjhbvvfeeaNu2rfDx8REqlUo4OjqKli1bijlz5gij0VjYtjTXVEnPRcH5PXHihOjYsaOwtbUVbm5u4qWXXhLZ2dlF+iv4fs+bN0/UrFlTqNVqUbduXbFkyZI7HqcQQuTl5YlJkyaJ2rVrC41GI9zd3UXnzp3F3r17C9v89ddfIjw8XNjY2Ah/f38xYcIE8ffff990fLf6/smUPZIQQpS7CpGRKWMmT57MlClTSEpKKtFctYzMg8awYcNYsWIF2dnZd2wrSRIvv/wyX331VTlYJlNRkJcdysjIyMjIyMiCQEZGRkZGRgbkKQMZGRkZGRkZ2UMgIyMjIyMjIwsCGRkZGRkZGWRBICMjIyMjI0MlSUxkNpuJjY3F0dFRTmEpIyMjIyNTCoQQZGVl3bHGRKUQBLGxsQQEBFjbDBkZGRkZmUpLdHT0bbNhVgpBUFBi9uLFi0XKzcrIlCdHjhzh448/5uTJk/Tt25fHH3+8SN0EGRkZmYpIVlYWtWrVuuP9s1IIgoJpAkdHx1KXw5WRKSvs7e1RqVQoFAq0Wi329vby91FGRqbScKcpdzmoUEZGRkZGRkYWBDIyMjIyMjKyIJCRkZGRkZFBFgQyMjIyMjIyyIJARkZGRkZGBlkQyMjIyMjIyCALAhkZGRkZGRlkQSAjIyMjIyODLAhkZGRkZGRkkAWBjIyMjIyMDLIgkJGRkZGRkUEWBDIyMjIyMjLIgkBGRkZGRkYGWRDIyMjIyMjIIAsCGRkZGRkZGWRBICMjIyMjI4MsCGRkZGRkZGSQBYGMjIyMjIwMsiCQkZF5gEiLvc6aWR8QcybS2qbIyFQ4VNY2QEZGRqY8MBkNLH37NQCMOh3VQsOsbJGMTMVC9hDIyMg8EBz4/dd/3igk6xkiI1NBkQWBjIxMlSfq6CEi1v1Z+N7e2dWK1sjIVEzkKQMZmcpMdgKKhEik5LNIyeeRcpKQ8lIgNwVJlwXCBMIMKluExgG0jgitE8I5AJyqIZwDEM4BmF0CwakaSFXvyTn23Gk2zPvc2mbIyFR4ZEFwD5jz8lDY2lrbjEqHwWBArVZb24zKhyEPVFoU1/ahOLsaxdVdKFIvlWxffQ5SbvJtmwhbN8y+jTH7NUH4N8fs3ww09mVguPXISIjnz4+mYjYZqd6oGb4hoexb9jMCYW3TZKogQghEfn6lvS/IguAu0UdFEf/c87iN/x8Ojz5qbXMqDTExMaxcuZJevXpRvXp1a5tTaVAeX4z67//dtF1ICoRbLYRnXcyeoeDoh7BzQ9i6gdYJFCrLU78h1yIKdFmQl4aUGY2UEYOUEf3PKy8V5eUtKC9vsfStUCF8G2EObIupVheEbxNQKMv70O+JxW+MAcDWyZluL4/l/L7dAORnZVnTrAqNzmzmo2tJHM3K44vafgTZaKxtUqVAGI0kT5+OMeY63nO/QqHVWtukUiMLgrvAmJxMwstjMCUnk7n0F+y7dEFSVq4fSmuQmprK77//Tl5eHhEREbIgKCkmfRExILROmEJ6Yq7dDXNAa7BxLnFXt3wuNuqQEk+hiItAEXsERfR+pMzrSNcPo7h+GNW+LxB2HphqPoI55DHMwR1BWbFvFHmZGYV/e9esjUqjxcXHF4D0+DhrmVXhidUZmR+XBsClPL0sCEqAMBhIfONNcrdtA4UC3dEIbFu3srZZpUYWBKXElJpKwstjMMbGogoIwHv257IYKAE6nY4VK1aQl5eHr68vPXv2tLZJlQchMAe0RhG9D33PuZjr9gSVTdmOodIi/Jpg8muCqelIEAIp4xqKa3tRRG1DcXkrUm4yqpO/wslfEVpnTCE9MIc+iTmorcUTUcHQ2NlTs3lrVBoNDz9n8RS4+PgBkJWShFGvR6WRb3b/5ZvYlMK/O7hU7imj8kCYTCRNnETutm1IGg2eH31YKcUAyIKgVBjj4oh/8SUMV6+icHXFZ+5XKN3crG1WhUcIwd9//01qaiqOjo707dtXjiEoDSot+sGryndMSUK4BGFyCcLUcCCYDCii96O4sB7lub+QshNQnfgFTvyCsHPHFPokpvBBCK/65WvnbVCqVDw6pug0i62TM1p7B3Q52SRHX8GnZh0rWVcxicrTsyLR4ln5PSwIZRUMMi1LhMlE8rRp5KxfDyoVXp99il27dtY2666Rlx2WEP2lS8QOHYbh6lWUPj74LpiPOjDQ2mZVCiIiIjh79iwKhYInnngCe3v5qaPSoVRjrt4OY5cZ6EZHoBu0EmPjoQhbd6TcFFRHfkA7vzOahd1QRvwE+ZnWtrhYJEnCv249AGJOn7SyNRWPH+NSMQGdXexp6lg5A+PKC2E2kzx9Btmr/gSlEs8Z0yu1GABZEJQI3clI4kaMxJSYiLpGMH4LF6CR579LRHp6Otu2bQOgY8eO+Pv7W9kimXtGoUQEtsHY7WN0r5xA//RSTCG9EAo1ivhjqDe8gXZuOKoNbyIln7O2tTfhH9oAkAXBf8k0mliZZBFyo/xkz+ftEEKQ+sknZK9cCQoFnh/MwKFbN2ubdc/IUwZ3IG//fhLGjkPk5aENC8P7qzkoXVysbValQAjBunXrMBgMBAQE0Lx5c2ubJFPWKFSYaz6MuebDkJuMMnIFyuNLUKScRxWxEFXEQkw1HsbY+jVEQEtrWwtAtfoWQRB/4RwGXT5qbRnHY1RS/krJJMdsppathtZOdtY2p0KTNmcOmb9YMl96TJlcJcQAyB6C25KzaRPxY15B5OVh06oVPt99K4uBUnDq1CmuXbuGWq2mR48eSPJ8ZNXGzgNTixfRj9qJfuDvmOr0QEgKlJe3oF3SG82SJ1BEbQdh3RwArr7+OHl6YzIYiDp62Kq2VCTWJluWYj7t6Sxfq7ch/YcfyZi/AAD3d9/BsVcvK1tUdsiC4BZkrlhB4htvgtGIfZcu+Hz5BQo7WTWXFL1ez/bt2wFo06YNrq5yqtgHBknCHPQQhj4L0D+/D2P4M5bphOh9aJb1R/PToyjOrbNkULSKeRJ12ljmes/v22kVGyoaGUYTBzJzAeju7mhlayouGUuWkvbVVwC4jRuL09NPW9miskUWBP9BmEykfjWXlOkzQAgc+z6F54czkeTlSaXiwIEDZGdn4+LiIk8VPMAI1+oYu3+G7sWDGJs9j1DZoog/hmblcDQLuqC4tNkqHoM6rS2C4NrJY+Skp5X7+BWN3Rk5mIDathoC5bwDxZK9di2pn3wCgMsLL+A8ZIiVLSp7ZEHwL0zp6SSMeYWMH34AwHnUKNzffVfOM1BK8vLyOHToEGAJJFSp5FCVBx4nP4yPTEM3+rAlnkDjgCIxEs3ywWiW9EZxdU+5muPq6493zToIs5nIrRvLdeyKyJ4Mi3egnZx3oFhytm8n6f3JADg9MxiXF1+wrkH3CVkQ3EB3+jSxAweRt28fko0NnjNm4DbmZXku7S44cOAAer0eLy8vQkJCrG2OTEXCzgNjh3csHoMWoxEqGxQxB9H80gf1r08jxZ8oN1PCu1mSY0Vu3YBBpyu3cSsiR7PyAGjhKE+L/pe8AwdInPCGZfr4scdwGzeuyt4XHnhBIIQga+VK4oYNxxgXhyogAL9FP+HwWA9rm1YpycnJ4ciRIwC0a9euyl44MveInTvGzu+je+EAxibDEQo1yis70Szsimr9eLhDIaayoGazljh6eJGflcm5Pdvv+3gVlRyTmfO5FkHU2FFecfFvdCcjSXh9LBgM2D3yMJ5TJiMpqu5ts+oeWQkwJiSQ8NrrJE+ZitDrsevQHr8lS9DUkbOX3S2HDh3CYDDg4+NDrVq1rG2OTEXH0Qdj1w/RP78XU70nkRCojv2M9ts2KA//AGbjfRtaoVQS3u0xAI6tX4MwWyfI0dqcysnHDPhoVHhr5AyiBegvXCB+9GjLKrOWLfH64AOkKj79eVeCYN68eQQHB2NjY0PTpk3ZtWvXbdsvWbKE8PBw7Ozs8PX1Zfjw4aSkpNx2n/uJMJvJXL6cmD5PkbdzJ6hUuL4yBq/PP0fpJEfY3i16vZ6IiAjAsrJA9g7IlBThEoih9zfoBq/G7BWGpMtAvfldNPM7o7hy/1YChLbrjNbOnoyEOC4e2n/fxqnIXMzTAxBiV/mq890vDLGxxI9+GXNWFtrwcLw/n/VABJaXWhAsW7aM119/nXfffZeIiAjatWtH9+7duXbtWrHtd+/ezZAhQxg5ciSnTp1i+fLlHDp0iFGjRt2z8aVFCEHegQPEjRxFyowPEDk5aBs2wP/XX3EZObJKu4LKg9OnT6PT6XBxcZG9AzJ3hQhoiX7YRgzdPkHYuqFIPofm16dR/zECKb3435h7QWNrS8OulunBA78vxWQ0lPkYFZ2r+RZBECyvLgDAmJhI/HPPY0pKQl2jBt4P0JLzUt8BZ82axciRIxk1ahShoaHMnj2bgIAAvv7662Lb79+/n+rVq/Pqq68SHBzMQw89xAsvvMDhw+WXEESYzeRs3Ubcs0OIf+FFdBERSDY2uE2YgO+CBWhq1Sw3W6oqQojC/2nTpk1RyOJK5m5RKDE1HoLuhX0Ym45ESEqU59ei+aEdyv1flfk0QqNHe2Pr5ExGQjyntm0u074rA9H5FhEUaCNPF5gys0gYMwbj9euoAgLw+fprlM4lLy9e2SnVr7Zer+fIkSN07dq1yPauXbuyd+/eYvdp06YNMTExrFu3DiEECQkJrFixgscee+zurS4hwmwmY+lSrjRpSuK4cegiI5G0WpwGDqDaqpU4Dx4kLyksI6Kjo0lOTkaj0dCgQQNrmyNTFbBxwdjlA/TDN2MKbINkzEe9fRqan7ojJUSW2TAaW1taPNkPgEN/Lkefl1tmfVcGYnQWQeCvfbAFgTkvj4TXXkN//gJKDw98vvkalbeXtc0qV0olCJKTkzGZTHh7exfZ7u3tTXx8fLH7tGnThiVLltC/f380Gg0+Pj64uLgwZ86cW46j0+nIzMws8rob8vbuJfXjT4ps8/r0E9zeeAOVj89d9SlTPJGRlh/o0NBQbGzkSGWZskN41cMw8A8MPWYjtM4oEk5YViNsnw6GvDIZI7T9w7j4+pGflcnBVcvLpM/KQoLe4nHxe4ADCoXRSOKbb6GLiEDh4IDPvLmoH8BCbHfl1/1vsJgQ4pYBZKdPn+bVV19l0qRJHDlyhPXr1xMVFcWLL754y/5nzpyJs7Nz4SsgIOBuzMSmUSPs/+OJSHjlVWL7DyDrz9UIw4M3X3g/MBgMnD17FoCwsDArWyNTJZEkTA0HontuN6aQXkjChGr/HDTzOyNdK947WRqUKhUPDRoOwImNa0m6GnXPfVYGhBCkGU0AuKkfTG+pMJtJnjqNvJ07kbRavOfMeWBXmpVKEHh4eKBUKm/yBiQmJt7kNShg5syZtG3blgkTJtCwYUO6devGvHnzmD9/PnFxccXu8/bbb5ORkVH4io6OLo2ZhSgcHPCaMZ2gvXvw/Ogj7B/thqTVoj9/nuT33yem9+NkLF6COSvrrvqXsXDhwgX0ej3Ozs5Uq1bN2ubIVGUcvDA8+QP6PgsQDt4o0i6jXfokqg1vgj7nnroOatiYms1bI8xmdvz03QOxDDHPLNDfSB3tonowBUHq55+TvXo1KJV4ffwRNo0bWdskq1EqQaDRaGjatCmbNm0qsn3Tpk20adOm2H1yc3NvCjBT3pi3F7fIYa7VanFyciryuhcUdnY4dOuK14cfErBxA66vvYrS3R1jXBypn35KdM9eZPz8M+bcB2vusKwomC4ICwuTlxrKlAvmOj3QjdqFsdGzAKgiFlq8BTGH7qnfdoOHo7axJeHSBU5t33TnHSo5mTe8AyoJ7BQP3rWbsWgRmT8vBsDj/UnYdehgZYusS6mnDMaNG8cPP/zA/PnzOXPmDGPHjuXatWuFUwBvv/02Q/5V9KFXr1788ccffP3111y+fJk9e/bw6quv0qJFC/z8/MruSEqI0tkZl+HDqbZ2De7vvYs6OBhzRgapn80i5oknyVr1J8J4/5KhVDWys7OJirK4V+XpAplyxcYZ46Ofoh/wG8LRD0X6FTRLeltiC4x3l4rY3tWNVn0HArDvtyVkJieVpcUVjpwbXhBbheKBE/NZq1aROutzAFxffx3H3r2tbJH1KbUg6N+/P7Nnz2bq1Kk0atSInTt3sm7dOoKCggCIi4srkpNg2LBhzJo1i6+++oqwsDCefvppQkJC+OOPP8ruKO4ChY0NTn374r/8N9wnTkTl748pMZHkyZO53vdpcrZuvaUHQ+YfTp06hRACf39/ucSxjFUwV++AbuR2TGH9kITZElvw06NIiafuqr+wh7vhUysEfV4uW76bg9lsKluDKxA6s+U3zuYB8w7k7thB8tRpADgPGYLz0KpXufBuuKugwtGjR3PlyhV0Oh1Hjhyhffv2hZ8tXLiQ7du3F2n/yiuvcOrUKXJzc4mNjWXx4sX4V5AITkmlwumpPvj/vgK3sWNRuLhguHKFxHH/I/6559GdPWdtEys0/54ukJGxGjbOGHrOQf/kAoStO4qk02gWdkO574tS5y1QKJQ88sKrqG1siD13mmN/r75PRlsf/Q1BoHmABEF+xDES33gTzGYcevfGdezrD5x35FbI2WNuoLCxwXnoEALW/IXzqFFIWi35hw8TO3AgSVOmYrJiquWKSkJCAklJSSiVSkJDQ61tjowM5pAe6EZtx1T7USSzAfWOD9AseRwp9XKp+nH28uahwZZVBwd+X0bS1dLtX1ko8H0oeDBuiPpLl0h49VWETodt+/Z4TJooi4F/IQuC/6BwcMBtzMv4r/wD+25dQQiyV64kuvfjpC9YgNDrrW1iheHUKYtLtlatWnLuAZmKg70Xhj4LMfT4AqF1RHH9MJoFnVEeXQClmAYMbdeZ4CYtMJuMbJj7Obqce1vFUJF5EG6Jxvj4f+oTNGyI10cfVvliRaVFFgS3QO3nh9dHH1lSG9evj8jJIe2LL7nefwD5EcesbZ7VEUJw4cIFANk7IFPxkCRMDQegG7EdU9BDSIY81BvfQv3bAMiMLWEXEp1GvIiDuwcZCXFs/m5OFVyKaBFIVV0QmDIziR/9MqaEBNQ1gi31CWxtrW1WhUMWBHfApnEj/H5ehMf0aSjd3TFERRE3fDjJM2Zgynxw8xekpKSQlpaGUqkkODjY2ubIyBSPczUMA5ZjeGQ6QmWDMmo72h87ojj7V4l2t3V0ovsr41Gq1Vw5dpjDf/1+nw0ubyxSoCqHT5t1OhLHjsVw+TJKT0985s5F6eJibbMqJLIgKAGSQoFjz574//E7Dk88DkDW8hVc79OHnE1Vf61ycRR4B4KCgtBq5bKpMhUYSYGp2XPoh2/G7NsISZeBZtUoVOvGliiZkVdwLToMeQ6Agyt/48rxo/fb4nKj4AZQ1fweBQiTiaR33iH/yFEkBwd85n6FytfX2mZVWGRBUAqUzs54Tp6Mzw/fo65eHVNyMokT3iBp8mTM2dnWNq9cKRAEtWvXtrIlMjIlQ7jXRv/MGoytX0MgoTqxFM3CrkjxJ++4b2j7zoR17gZCsPmbL8hIKL52S2VDfSOgzmCuej4CIQSpn3xC7patoFbj/fnnD2xK4pIiC4K7wLZZM/x/W4bzyJEgSWSv+pOYp58m78ABa5tWLmRnZxMba5mHrVWrlpWtkZEpBUo1xg7vYBj4O8LRF0XqRTQ/90B56Ns7Bhw+NHgY3jXroMvNYe3sD8nPqfwPAQXLDfVVMOdKxk+LyPx1GUgSXjNmYNu8mbVNqvDIguAukTQa3F4Zg8/331mSGsXFE//iS6R98y3CVHUTmQBcvHgRAF9fXxwdHa1sjYxM6TEHtUU3Yium2t2RTHrUWyahXj4Ycm6dmVCpUtP9lfHYu7qRFhvD+jmfYjJW7gJpBQmJ8qtYsGT2ur9Jmz0bALdxY7Hv2sW6BlUSZEFwj9g2a4b/8t9wePJJEIL0b74h/uUxmFJTrW3afUOeLpCpEti6YeizAEPXjywBh5e3oJ3fCUXU9lvuYu/qRs9x76C2seH6mUi2L/i2Umc0tblRZybfLCr1cfybvEOHSJo0CQCnZwbj/OyzVrao8iALgjJAYWeH5/uT8Jg2FcnGhvz9+7k+YGCVXJ6o1+u5cuUKIAsCmSqAJGFqMgz90PWYPUKQcpLQLOuPattUMBWfc8QjsDrdRo9DUig4u3s7h/9cUc5Glx32SsstQGCpfFjZ0V+8SOLYcWA0Yt+lC27jxlnbpEqFLAjKEMdevfBb/LMl4DAxkbhRo8j4eXGVUd4AUVFRmEwmXFxc8PDwsLY5MjJlgvAMRT90A8YmluyEqgNz0fzcCyktqtj2QeFNaD9kFAAHVy7j7O7t5WVqmWL7r5TFOabKPW1gTEgg/uUxmLOz0TZujMf0aUgK+RZXGuSzVcZoatXCb8li7B/tBiYTqZ99RvKk9zHr7q76WkWjIH6gdu3acspPmaqF2hZj1w/R91mAsHFFEX8MzYJHUJz5s9jmYZ260riHZRny1h/nERVxuDytLRMUkoT9jZtmdiUWBKbMLMtUbUIC6uBgvGd/jkJeDl1qZEFwH1DY2+M5cyZuEyaAQkH2X38R/9xzGJMqdylVIQSXLl0CoGbNmla2Rkbm/mCu0wPdiK2Yq7VC0mej+fN5VBveBGP+TW1bPz2YOm3aI8xmNsydRezZ01aw+N5wUFZuQSD0ekvioYsXUXp64D33K5TOztY2q1IiC4L7hCRJOA8ehM/cuSgcHdGdOEns4GfQna58PxgFxMfHk5ubi0ajISAgwNrmyMjcP5z80A/6HWPr1wBQRSxEs+ixm4okSQoFnUeOpnqjZpgMetbO/rDSFUJyUSkByDBWvtVRwmwmaeJE8o8cQbK3x/urr1D7+VnbrEqLLAjuM7atW1niCoKDLXEFw0eQvX69tc26KwqmC6pXr45SqbSyNTIy9xmFCmOHd9D3+9VSUjkxEs3CLijOrCrSTKlS0e3lsfiF1EOfl8tfn0wnPb5k9RIqAs4qy20gvRIKgtTPPydnw0ZQqfCe9RnakBBrm1SpkQVBOaAOCsJv0U/YPvQQQqcj6a23SZ3zVaUrlCJPF8g8iJhrdEI3YgvmgNY3phBeQLXhjSJTCCqNlh6vv4lHUDB5WZn8+fFUslMrR8l0d7Wl4l+ywWhlS0pHxs+Lyfx5MQCeU6Zg27KllS2q/MiCoJxQODri/cVsnIcNAyDjxx9JHDcOcyUpqZqdnU18vCVdqywIZB44HH3RD1yBsc1YS9rjiJ/QLOpRZApBa2dPr/Hv4eLjR3ZKMqs/mUZ+dsUvgOZyw0OQYaw8DyjZGzaS+tlnALi+/joOj/WwskVVA1kQlCOSUonb669ZlsNoNORu30HskKEYYmKsbdoduXzZ8sPn4+ODg4ODla2RkbECChXG9m9h6P8rws4dReIpNAsfQXF6ZWETOydnek2YiIObO2mxMfz16Qx0uRVb9Hvc8BAkVRIPQd7hwyS99x4ATgMH4Dx0iJUtqjrIgsAKOPbsic+PP6D09MBw6RKxg58h79Aha5t1W+TpAhkZC+bgjuiGb8Uc0AZJn4Nm9YuoNr5dmMjIycOTXhMmYuPgSGLURf76dHqFFgUuaks8UGWIIdBfvETi62PBYMDu4c64jR8vL38uQ2RBYCVsGjTAb/ESNPXqYc7IIP6l0WT+9pu1zSoWk8lUmJ1QFgQyMoCjD/qByzG2eR0A1dH5aJY+CVlxALj5VaP3GxPR2juQcOkCf306HX1erhUNvjWVxUNgTEgk/uWXLYmHGjXCc8YMJDm4uUyRBYEVUXl74Tv/R+y7dwejkZQPZpI8YwbCULEKpsTExKDT6bCzs8NXriUuI2NBocLY/m30fX9GaJ1RXD+MdsEjSNf2AuAZVIPH35z0H1GQZ2Wjb8brhocgSV9xPQTm7GwSXvlX4qEvZqOwsbG2WVUOWRBYGYWNDZ4fzMD1tVdBkshavoL4F1/ClJZmbdMKKZguqFGjhuyek5H5D+ZaXdEP24jZqz5SbjKaX/qiPPA1CGERBW9MQmtnT/zF86z5bEaFEwWemortIRAGAwn/+x/68xdQurvj/ZWceOh+IQuCCoAkSbgMH473F7OR7O3JP3KE2MHPoD9/3tqmAXL8gIzMnRCu1dE/uwZT/aeRhAn1tsmo/3wedNl4Vq9B7xuiIO7CWdbMmoE+v+KIAu8bUwZZJnOFq2cghCB5yhTyDxxEsrXF+6s5qP3lxEP3C1kQVCDs2rfHb9FPqAICMMbGEjt0GDlbt1nVpvT0dFJSUpAkieDgYKvaIiNToVHbYeg5B0PXDxEKNcqzq9Es6o6UcgGv4Jr0mjARjZ0dcefP8tcn09BVkCXHjioldjeKHCXqK5aXIH3ePLLXrAWlEq9PP0EbGmptk6o0siCoYGhq1sRv8c/YtGyByMsjcdw40r7/3moVEwu8A9WqVcNGnrOTkbk9koSpyXD0g1ciHHxQpJxH81M3FGfX4F2jFr3HTyycPlj10WTysjKtbTEAXjemDRIr0LRB5ooVpH//AwAe776DXdu2Vrao6iMLggqI0tkZn6++wmngAADS584j6b2JCH3x9dnvJ/J0gYxM6RH+zdEN34Qp8MbSxFUjUW2bindwME+8PQVbRyeSr0ax8oNJ5KRbP17I68a0QXwF8RDk7t5NyswPAXB58UUc+/SxskUPBrIgqKBIajXub76J+3vvgVJJztq1xL3wYrkGG+r1eq5evQrIgkBGptTYe2EYsBxji9EAqA7MRf3r03i42/PkO9Owd3EjLTaGP2ZMJDPZupVQ/bRqAGJ11l/hpDtzhsQJb4DJhEPv3ri88Ly1TXpgkAVBBcep71P4zP0KhYMDuogIYocMRX8jJ8D95urVq5hMJpycnPDw8CiXMWVkqhQKFcbO76N/4geExh7ltb1oF3bBTcTx5LvTcPTwIjMxnpUzJpIeH2c1M6vdEATXrSwIDLGxJLzyKiIvD5uWLfGY+J68sqkckQVBJcC2VSt8f1qIys8PY3Q0cc8OIW/f/vs+bsF0Qa1ateSLUkbmHjDX7YV+yHrM7rWRsuLQLHkCt5i/6fPOVFx8/chOTeaPDyaSEnPNKvYVCIJr+dYTBKaMDBJeHoMpORlNndp4f/YpklptNXseRGRBUEkoCDbUhodjzsoifswYMpYuvW/BhmazmQsXLgAWQSAjI3NvCI866IesxxTSE8lsQL3xTVz3TeHJ8W/jHhBEXkY6Kz+YRGLUpXK3rUAQxOmtIwiEXk/iuHEYoqJQ+vjgPcfiFZUpX2RBUIlQurnh+/13OPTqBSYTqR9/QvLUafcls2FsbCw5OTlotVqCgoLKvH8ZmQcSrQOGJ37A0Ol9hKRAGfkbLqsH8+SLI/EKroUuJ5s/P5pC3Pmz5WqWj+bWQYX5+bFcvDiJrKzj92VsYTaT9N5E8o8cRXJwwOerOai8ve7LWDK3RxYElQxJo8Fj6hTcxo0FhYLslSuJe/4FTKmpZTrO+RtJkWrVqoVSzhcuI1N2SBKmlqMxDFheWDXRafkTPPl0O/xC6qHPy2X1J9OIPnWi3EwqCCrMMpnJ/FeRI50ujiNHu5CQ+Dvx8cvuy9hpX84hZ+NGUKnw/uxTNLJH0mrIgqASIkkSzkOG4P3lF0g3gg2vDx6M7uy5MulfCMG5c5a+6tSpUyZ9ysjIFMUc9BC6YZsx+zVF0mXg8NcInmhtS0D9hhj1OtZ+PpOoiMPlYoudUoGLynI7KAgszM+/TmTk8MI2Ts7Ny3zcrJUryVi4EADPqVOxbdmyzMeQKTmyILhLdCYd0w9NJz433mo22D30EH4/L0IVGIgpLp64YcPI2bTpnvtNTEwkIyMDlUpV5tkJzXlGslZFYc6tGOudKwtXUnKZvu4cOTr5vJWG1Ngc9q+MwmyyTmKvO+Lkh37wKoxNRgBge2A2jwecJji8ESaDgfVzPuHC/t3lYoqfpiCOwEhW1glOnBxIvi668HN3ty5lOl7uzl0kT58BgMvzz+HQo3uZ9m8NtkZvZdn5++NJKQ9kQXAXmIWZ9/e/z5+X/+TVHa9iMluvSpgmOBi/xT9j27o1Ij+fxAlvkDbva4T57nOSF0wXBAcHo9FoyspUzLlGMn46h+5YMlm/l3/gVGXFYDLz5h+nWHwwhul/V4z6FpWBrJR8NnxzmlM74ji2MfrOO1gLpQZj15noH5uDUNmgvbqNXtpV1GnUALPJxMZvviByy4b7bkaQjeVav5idRuSpERgMKYWfOTg0RKUquyA/3blzJL7xr1wDL71UZn1bix3Xd/DOvnf4NOJT9sTtsbY5d4XK2gZUNoQQfB7xOVtitqBWqHmjyRsoFdadY1c6OeE950tSv/iCzJ8Xk/7dd+gvXcRz2jQUdnal7q9AEJTldIHQm8hcfB5TfC6SvQr7LgFl1ndV54utlzl+PRMnGxWvdKxhbXMqBTnpOtbNPUVupsX9nRafy4ZvTqPPN2HQmTDqTRgNZhQKCYVKgVIlobVTYe+sxc5Fg4OrFjdfO9z87NDal8/SN3ODfui96qFeOQJ1+lV6KOejDe/PyeOX2bHoe/Kzs2ja+6n7tgTYX3uj6qFJS1Dga6Rn7MdG609c/BIc7MuuhoAxIZGE115H5Odj06pVlcg1sOLiCj45+glmYaZbYDdaebeytkl3xV0Jgnnz5vHJJ58QFxdH/fr1mT17Nu3atbtle51Ox9SpU1m8eDHx8fFUq1aNd999lxEjRty14dZACMGsiFn8euFXACa3nEwz72ZWtsqCpFLh/r//oalZi+QZM8jdspW46Gi8Pp9dqupgaWlpJCUlIUlSmS03FEYzmb9exBibg2SrwnloXVRetmXSd1Vnz6UUfthjyRY5vXcofi5yPYk7oc838evkI0W2XTle0qDbrJu22LtocK9mj3cNJ7yDnfAIsEepuj/OVeEdhn7YRtR/vYzy0ma6GH/Ctn4vDp5K58Afv5KfnUXbgUORFGU/foGH4FKeDt+gZ/D1Hcy5c+MAsLUtm6lDc04OCa+MwRQfjzooCK+PPqzUuQaMZiNzjs9h6fmlAPQK7sU7zd6x+kPi3VJqQbBs2TJef/115s2bR9u2bfn222/p3r07p0+fJjAwsNh9+vXrR0JCAj/++CO1atUiMTERo7FyzYWazCZmHp7Jn1F/AvBGkzfoGtjVylbdjOMTj6OuHkTi/8ajP3+B2GcG4/Xpp9g2bVqi/Qu8A4GBgdja3vtNWwhB9pqrGC5nglqB06DashgoITk6IxNXW5afDWzmT9d68lKskpCZVLS0cGCYK+7VHHBw0aCxU6HWKlFplKg0CoRZYDKaMRkE+TkGcjP05KTryEzWkRaXQ1aKjpx0PTnpeq5FWtKGK9UKvIIcqBbqSkB9V1y8bcv2CdfGBUPfnzHv+RzV7k9oZ/4L29rN2XHBhuMb15KfnUWnkaNRqsrWwVsgCKJ1hhvHI5Gvuw6A1sb/nvsXZjNJEyehP38Bpbs73vPmoXR2vud+rUVCbgIT908kIikCgBfDXmREvRGV2ttR6m/UrFmzGDlyJKNGjQJg9uzZbNiwga+//pqZM2fe1H79+vXs2LGDy5cv4+bmBkD16tXvzepyxmg2Mmn/JDZFb0IhKZjYfCI9g3ta26xbYtOoEX5LFpMwdhz6M2eIf+FF3N96C6e+T91x3wJBEBIScs92CCHI3RiN7lgySODUrxbqADnZSEmZvfUSsRn5+LvYMKFrbWubU2nwCHCg97gGKNUKXL3tkBR3/wOtzzOSGpdL0tUsEi5nkXA5k/wcI3EXM4m7mMmhv67i4KYloJ4rgfVd8a3tXDbeA0mB6aH/Ifwao179Es3yD2EbFMyGawGc27sTXW4OXUePQ63V3vtYN6hjW+Ah0JNrMmOnVKDXJwCg1fjcc/+ps2aRu3UrqNV4fT6rVJ7LioQQgo3XNvLx0Y/J1Gdir7LnvRbv8UjAI9Y27Z4p1TdXr9dz5MgRunYt+mTctWtX9u7dW+w+q1evplmzZnz88cf4+/tTp04dxo8fT15eXrHtwTLFkJmZWeRlLdJ16by681U2RW9CpVDxQesPKrQYKEDl44Pv/B+x79YVjEZSpk8neeaHt01ilJ2dzfXrlieC2rXv/QaUtzuOvH2WHxSHntXR1K68TwPlzbn4LBYfiAFgSs+62GkqpwvSWngGOuLma39PYgBAY6vCp4YTDTr588jIugya3pyn3m5E66eCqVbXBaVKIjtVx5nd8Wz49gy/TDrM7mWXiLuQgTDf+8oGc43O6IdtwuwTTn27KHr7n0KpVHDl2BH++mQa+dk3T3HcLT5aNa4qJWYgKl+PEGYMBotXRK25t1omGYuXkLl4CQCeU6Zg07DhvZprFeJz4hm/ezzv7X+PTH0moa6h/Nz15yohBqCUHoLk5GRMJhPe3t5Ftnt7exMfX/zyu8uXL7N7925sbGxYuXIlycnJjB49mtTUVObPn1/sPjNnzmTKlCmlMe2+cC7tHBN2TyAuNw5blS0z28ykrW/lqcmtsLXF88MP0dSuQ9pXX5G1bBmGqCi8Pv4IpYvLTe0LvAN+fn44Ojre09j5EcnkbrGIC/tHA7Bp6nlP/T1ofLzpIgLoXt+Lh2q5W9scmRtIkoSLtx0u3nbUa+eLQWci7kIG0afTuBqZSl6mgXP7Eji3LwE7Zw01GrtTo4knHgH2d+1KFi6B6J9ZjWrTu9Q6vpi+yghWXg8n7sJZ/pgxkV7j38PRvWyKjwXZqEnLNhGdbyBEawAsq5XUqrsX87l795E6axYArq+9VimXF+YZ81h0dhE/n/0ZnUmHSqFiZL2RDAsdhkpRdWLz78q39d8vthDill92s9mMJEksWbKEFi1a0KNHD2bNmsXChQtv6SV4++23ycjIKHxFR5fvkiGzMLP03FKGbR5GXK6lAtlr4a9hFmb2xu3lSOIRTqeeJjE3EaO5YsdCSJKEy6iReH0+C8nOjvyDB4l95ln0F29e9ldWqwt0p1PJXh0FgG0bH2xb3bu78UFi18UU9lxKRa2QGPewnLWtIqPWKgkMc6Ntv5oMmNyM7qPrUaeVFxpbJbkZeiK3x7F61glWzIjg6N/XyEzOv7uBVDYYu3+Gofvn+DvqGBBwBAeNibTYGH6f9k6ZFUXyLyiDrDdgNFo8s5KkQaG4u6kJSynjCWA24/DE4zgPG1omdpYXBpOBlZdW0mdtH3449QM6k44mnk34ucvPjKo/qkqJASilh8DDwwOlUnmTNyAxMfEmr0EBvr6++Pv74/yv4JHQ0FCEEMTExBTrmtZqtWjLcG6stEzaP4kN14qu+/3wyIfFtpWQcLVxJdAhkJrONanhXIOazjWp6VwTF61LOVhbMuw7dUK96CcSXnsdY0wMsUOG4PnBDOw7dgQgPz+fa9csPyr3Igj0UZlk/X4ZBGgbe2DXpVpZmP/AYDILPt5oKSo1uGUAAW5yAGZlQaGQ8Kvjgl8dF9r0rUHMmXQuHU3iWmQamcn5RGyIIWJDDP4hLtRt601gfTcUytJ5DUzhgzB71cNj5UgGKo/we3QDUtNSWTljIj1eexO/uvXu6RgKkhPF6AyYTJbpCJXK6a76MiYkWkoZ5+Rg06wZHu+8U2kC7oxmI+uurOPH0z8SmxMLgJ+9H6+Gv0rnap0rzXGUllIJAo1GQ9OmTdm0aRNPPvlk4fZNmzbx+OOPF7tP27ZtWb58OdnZ2TjcqF51/vx5FAoF1apVzJvF5czLRd47qh1x1jrjqHbELMzozXpyDDmk5KdgEiZS81NJzU/lWPKxIvsFOgbSyKMR4R7hNPJsRIBDgFW/SJpatfBbspjECW+Qf+gQia+PxXnkSFxfepGLFy9iNpvx8PAoDP4sLca4XLJ+vQgmgSbUFYde1avshXO/WHMynguJOTjbqHixXXVrmyNzlyhVCoIauBHUwA2DzsTVk6lcPJzE9XPphS87Zw0hrbyo08obB9eSPwAJ30bohm3EfvWLDFDsZVV0PWJzYfUn0+jy0mvUbHb3a+ADbSyCIDrfgMmUazkWZelFqTkvj4Sxr2NKTkZdqxben89CKsMkZ/eLXEMuqy6v4tfzvxZ6h91t3BlSdwh9a/VFo6z4x3AvlNrfMW7cOJ599lmaNWtG69at+e6777h27RovvvgiYHH3X79+nUWLFgEwaNAgpk2bxvDhw5kyZQrJyclMmDCBESNGlMmytvvB952/JyE3AWetM84a51u6hczCTJoujcTcRK5mXeVSxqXCV2xOLNeyrnEt6xqro1YD4KZ1I9wznEYejWjk2Yi6rnVRSOWbLFLp4oLPvLmkfvYZmb8uI+PHH9GdOMG5hzsDd+8dMCXnk/HzOYTOhCrIEcc+Ne45oOtBw2gyM2+HZaplZNsgXOwq7/psmX9Qa5XUauZJrWaeZCbnc25fAucPJJCboSdiQwzHNsYQUN+Vum18qFbXpWTXjZ07hn6/ot4xg777vmbt9bpcynZn/Vef0eHZUYQ93O2ubC2oemjxEOQAoFSWbmWQMJlIeust9KfPoHBxwXv25yjuMSbpfhOTHcOy88v468pf5Bgsx+1m48YzIc/Qt1ZfbFUV815V1pRaEPTv35+UlBSmTp1KXFwcYWFhrFu3rrBEblxcXKHrGcDBwYFNmzbxyiuv0KxZM9zd3enXrx/Tp08vu6MoY+zV9tRwvnNGOIWkwN3GHXcbd0LdimbyytBlcDLlJMeSj3E86TinUk+RqktlW8w2tsVsA8BV60prn9a09WtLS++WOGvLJwpfUqtxf+sttI0bkzxlKlkREVyuHgRK5V0JAlOmnozF5xC5RlS+djgNrIWklrNil5Y1JxO4mpqHi62awS0qpvdM5t5w8rChea8gmnQP4OqJVM7ujSfuYibXItO4FpmGg5uWum28qdPSC1vHOzyNKpQYO01C4VGXXn+PZ+t1PSfSfdmx6Huy01Jo+dTAUnvoQuwsnopLeXp0BksMQWkFQdrcueTu2Imk1eL9+eeoK6gn2GAysDtuN39c+oMD8QcQWFaFBDkGMThkMN2DumOjerASgd1VRMTo0aMZPXp0sZ8tvFG56t/UrVuXTWVQdKcy4ax15iG/h3jI7yHAUgzpbOpZjiUf41jyMSISI0jTpbHu6jrWXV2HQlIQ5hZGW7+2tPVtSx2XOvfd3e7QrRuamrXY/eGHmJRKHDMzsdm4CfHsMyUe25xrJHPxeczpehRuWpwG10FhU7UCbcoDo8nM1zsLvAOB2Gvlc1iVUaoU1GjiQY0mHqTH53J2XwIXDiaSnarj8JprHP07mqCGbtRv54tXsONtr0dzg34Ijzo8/Ptw7KOusi85iCN//UFWSjKdR76EUlVyT5O/Vo1aAr0QxOktNVqUypKnP89eu46M+QsA8Jg0EZvGjUq8b3kghOBs2lnWXlnL+qvrydBnFH7W2qc1A+sMpKVPy3L33FYU5F+dckKr1BLuGU64ZzhDGYrRbOR48nH2xu1lT9weLmVc4kTKCU6knODrk1/jbuNOG982tPW1eA8cNPcnoY+mVk2utWkNiYnUuHSZtHV/ozt6BI+pU1E63T6YSOhNZC49jykxD4WDGudnQ1A4yG7uu+GvG94BVzs1g5pXzCcqmfuDi48drZ4MptljgVyOSOHs3niSrmYTFZFCVEQKnkEONOjkR1AD91sGIQrfRuiHb6TVqudxPHmeTXG1Ob93JzlpqXR/dQJaO/sS2aKUJGraajmbqyMyX0UNQCGVbN48P+IYyTeWizuPGoXDY4+VaL/yIC4njo3XNvL31b+5lPHPCit3G3ceq/4YT9Z8kmoO8nUnCwIroVKoaOrVlKZeTXkl/BXic+LZG7eXvfF7OZhwkJT8FP6K+ou/ov5CKSlp6NGQtr5taefXjmCn4DLzHiQkJBCfmIhCoaBJ797kzp5N7vYdxPYfgOfHH2HToEGx+wnDjfoEMTlINkqchoSgLEVglMw/GE1mvi6IHWgTJHsHHlBUGiV1WnpRp6UXyTHZnNkdz8VDSSRdzWbrwvM4uGmp396XOq280dgUk6jK3hP9gN8I9Z6C4/blrL4eyvUzkfwx7R16jp9Y4lwFrZzsOJur43i+PTUASbrz99Fw/ToJ48Yi9HrsOnbA9aUXS3n0ZU9ibiJbY7ay8dpGTqacLNyuUWjo4N+Bx4Ifo6V3yyq3dPBekM9EBcHH3oc+tfrQp1Yf9CY9EUkRhd6Dq1lXiUiKICIpgq9OfIW/vT/t/NrR3r89jT0b39MX+vjx44AlmND7iSfQNWlM4htvYoyOJm74CNxeexWnZ4pOIQiTIGvFJbk+QRnx18kErqXd8A7IsQMygEc1B9oNqEWzxwI5szueM7vjyU7VcWDVFY6uj6Zua2/qtfe9eXWCUo3xken4+YTTf+UkVl6pRWrsdX6f/AY9J0zCI7D6HceueSOFcaLR4jZX3GHKwJyVReLYcZjT0tGEhuI5cyaS0jqZNWNzYtkes51tMds4nny8MC5AQqKpV1O6BHbhkYBHcNLc3VLKqo4sCCogGqWGlj4taenTkrGNxxKTHcPeuL3sjt3N4cTDXM+5zq8XfuXXC7/ioHagtU9r2vm1o41vm1IFJhoMBk6dOgVAeHg4ANrQUPyXLiF56jRyNm0i9bNZ5O3dh8eUyai8vBBmQfafUejPpYNKwmlQbdSBFTuCuCJjMgu+uRE7MKptkJyiWKYIto4amnQPpOHD/lw8nETk9jgyEvM4uS2WyB2xBDfyoEEnPzz+UyPEHPY0Lh4hDPxlFCtPu5OSCX9Me5vur71FQFj4bcf0UFu+gykmy+1Bqbh1YJ0wGkmY8Ab68+dRuLpaVhSU4+oxszBzPu08u2J3se36Ni6kXyjyeUP3hjwc8DBdA7viYVs22RyrMrIgqARUc6hGv9r96Fe7H7mGXA4kHGDn9Z3sidtDmi6NTdGbCgsvhXuE086vHe382hHkGHTbqYVz586h0+lwcnIqUnBK4ehomS5Y3swiCPbt43rfp3F78y0k6qE7kQISOD5dC02wrLTvhU1nErmamoezjYoBze69opxM1USlUVK3jQ8hrbyJPpNG5PZY4i5kcvloMpePJuNT04mwTn4E1nMtXLYofBqifWEd/X4bxZoD6UTnurDms+k88vxr1G790C3H8ruRrTDOaLmx3y5LYfr3P5C/fz+SjQ0+8+aiukWCurIkx5DDwYSD7Inbw67YXaTm/1PaWiEpaOzZmI7+HelYrSM+dnKW1NIgC4JKhp3ajk7VOtGpWidMZhOnUk+xK3YXu2J3cSnjUuHUwpfHv6SaQzXa+bXjIb+HaOzRGLWyaMBfRISlbGd4ePhNwkGSJJz69cOmWTOS3n0P/ZkzZC09gqa2RWU7PFkDbYhLuRxzVUUIwfe7rwIwuEU1OXZA5o5IConA+m4E1ncjOTqbyB1xXD6aTPylTOIvZeLkaUNYBz9qt/RCpVaAnQeKZ5bR220Cmzcd41ymFxu/mU3ylQu07D8EheJmj1SNG2WQU802ZOGApCg+UDhn4ybSv/sOAI9Jk9CGhhbb7l4RQhCdHc2euD2FqeMN5n+KtNmqbGnh3YIO/h1o59euQmWIrWzIv0CVGKXCEmzY0KMhLzd8mdicWHbH7mZX7C6OJB4hJjuGX87/wi/nf8FebV9kakGXruP69esoFIrC6YLi0NSoge9PC0n7cgMi26K2dedWYBv/CDTsUl6HWiXZH5XGqbgsbFQKnmkZYG1zZCoZHgEOdHymNs17BnJ6Vzxn98aTmZTP3hWXOb45hoaP+FOnhRcqjRZ6fUFX3++xX7qQo6l+HF2/lvTYa3R55S3L5//CUaWkmlZNjM5ANEHUKyaoMD8igsR33wUhcOzXr8wLFmXrszmYcJC98XvZH7+fhNyEIp8HOARYfs/829HUs+lNDzsyd4csCKoQfvZ+hVMLOYYcDiQcYHfsbvbE7iFVl8rm6M1sjt6MQlLQOaszzjjjH+yPvf3tlyTl7UkqFAPG+K3oz2wk8Y2N2G/pivtbb6F0dS2Pw6tyFHgH+jT2w82+aqdElbl/2Ltoad4riEZdq3H+QCInt14nJ13PvhVRHP07mtC2PtRr54Nt8+dp61Uf3wX/Y/0VPy6fOMnqaePp8eYH2DgUjQOqZashRmcgAR9UyqKf6S9eImHsODAYsOvcGfc337jnYzCajZxLO8eRxCPsjN1JZEokJmEq/FytUBPuEU5b37a09WtLdUc5Lfr9QBYEVRR7tT2dq3Wmc7XOmIWZUymn2B23m13Xd3E19Sr2yRYRsDhnMb+t/a0w7qCJZ5Miajtn23XydliKe9h3C8Cm2TjSv3ck/cf55GzYSN6hw3i89x72nTtZ5TgrK6fjsth7ORWlJDGiTaC1zZGpAqi1Suq39yWklRfn9idyakcsWSk6jm2M4eTW69Rs5kmDjo2pPnYFfRY8x+rjWuKuxfHHe2PoNfFTHN3/KVEecCOOIAEfFMp/ggpN6enEjxmDOT0dTf36eM6YflcrCoQQnE8/z4H4A5xIOcHRxKNkGbKKtAlyDKK1T2ta+7amiWeTBy5roDWQBcEDgEJS0MCjAQ08GvBSg5dYvX41p6+dxmBnIMMuA0OOgWUXlrHswjLsVfa08mnFQ74P0fpcCOJAOgB2Xaph29riJXAdPRq7Dh1ImjgJw+XLJI4bh13HjrhNGI/aXw6MKwk/7rF4Bx6t70U1V3nJpkzZodJYhEHoQz5cPZHCya2xJF3L5vz+RM4fSCS4kTuN+y7hac93WbU1hrQ0+OPdMTz25jQ8gi2py2vfSGEcTRBwI0jRaCTpnXcxxcejCgzEZ97cUq0oSMpL4kjiEY4lHWNX7C4S8xKLfO6kcaKhR0Pa+LThIb+H8LX3LZsTIlNiZEHwgJGens7ZE2cBeKbXM/yv2v84mHCQXbG72B23m9T8VLZGb6XWYVdEmiVi+FR4HJ6h9oSYvVDeCELS1q+P3y9LSf/2WzJ+WkTu9u3k7d2L0zODcR42HKWTvBTxVsSk5bH+lOXHcGTbICtbI1NVUSgkght5UD3cnYSoLE5ujeVaZKolA+KxFIIbvk77RzZzYOsaUvLsWTntbR57dRx+jdrSwN7yNH6JWggRDUDKRx+Tt3cvko0NXh9/hNL59kuc84x5RCRFsD1mO/vi9xGfG1/kc1uVLc28mtHUqynhHuGEuoYW/r7IWAdZEDxg7NixA7PZTHBwMMHBwQB0rGZZomMWZs4knSZ/TQxBae4AfOXzC2v1u2CTpQx0U6+mNPduTnPv5lR3rI7bq6/i0OMxUj7+mPyDB8mYv4CsFb/jPGIETgP6o7CR3Xz/5Yc9VzEJQZsabtTzlYWTzP1FkiR8ajjhU8OJlOs5HNsQzZUTqUQdTyGKxrgGhOAR+w3JeRJ/ffEZD/U8SegTz6HCRJbkTKwxHsd1f5O1fDlIEp4fzkRbt+5N46Tkp3A8+TjHko4RkRTB+fTzmIX5HzuQqOtal0aejWju3ZwW3i3QKuXsphUJWRA8QMTFxXHmzBkAOnbseHODfDPV1qsxXHMHCUzd3Wjg1pbMODiaZJnj2359O9uvbwfAw8aDZt7NaO7VnOazJuN16CxpX83FcOkSabNnk7l0Kc7PPoPjE09UqPKnmcn57Fl+CUO+idZP1cAz8P7UiSiOxCwdv0dYYjJeal+93MaVkQFw97fn4RF1SY3N4fSueC4dSSIt1Q6hfQWt+Xd0uli2r95MwpljBHUZxCWzF7GXM3Gf8S0ALi+8gP2N344MXQanUk+xL24f++P3cyXryk3jedl6FWZVDfcIx15dspoKMtZBFgQPCEIItm7dCkBYWBje/0kgYkrJJ/OXC5iS8y3piJ+uiaaOC09Rk6dqPYXRbORs2lkOJRziYMJBTiSfIDk/mfVX17P+6nrAshSo6YTGtD4RStDyvZCYSOpns0j75lsce/fGse9TaGrWLPfjzss0kBafS0JUFtciU0mJySn8PC0up1wFwZKDMRhMgsYBzjSvLq/OkLEObn72PNS/Js0eC+T4luuc2xuPnv6oFEcw5u3izIVk7NvG4ZdppvbsHxA5OSjDwzjYNYDDh2ZwNOko17KuFelTQqKGcw0aeTSiiVcTwj3C8ba7/4mKZMoOWRA8IERGRhIdHY1SqaR9+/ZFPss9mED6usvoMKCXjEg1HUm+eBnTORNGswmj2YjJbMIsBKFSdUIJxiT1JcOYQVp+Kqn5KWQasi2dXdCzD9jfow0emeCXCjZ6AVcy4dMFxNo7sszfhTT3GLzMGbQWWmrn18VelKzEqgAQAmEWCMGNl+Vvs1FgMpgxGkwYdAYMOj363DzMxhxMxmsoFG6o7R9D+lcq1lrNvMrmBJeAHJ2RXw/FAJYiRjIy1sbGQU3Lx6vTqEs1zu6N5/RODVnJLhhy1iLl6/jky8lo0zKJ89HwbsczZB96v8j+/vb+NPNqRhu/NjTzaibXCKjkyILgASAlJYWNGzcCEBoaSlRUFLGxsaSmppKWmEJ2fi78e6r/SunHUHKzKzBVC6n/CRT+Qx9GrjiDrXY914EVgMJuO0HZKoIuOlMt3g6V+f7UIjebsxAiBwkbHNy0PDE+/JblZO8HfxyLIyPfSJCbLZ1C5LzqVYGEhIQ7N7oD//XWWQOtnYrwR6oR1tGPS0eCOLJShcLkzrJ2gr67YWo/Ezl2Cuq6htDEswlNvZrSyLORLACqGLIgqOLo9Xp+/PFHzGZLcE9kZCSRkZFFG924JypRoFWoUSvUqCRQCYHSbEJlNqI0G1EWNBb/2V0CFCrLC6mwQzMCAwK9MKMXAsksaE88fxtcMGSEgyRQaJLAJo4oByNRjVLQilRqpflRL6E6vjluNx+QdKN3yfJHQW4SCZCUlshqhVKBWqsmOyWWjMTowl3Duw/n3H5XJAV0GlIHrV35ff31RjPzbyw1HNY6EKVCTqpS2Zk/f36Z9BMWFkaLFi3KpK97RalSUKelF7VbDCTlm1/Z5ludg30P8H52Ps1ynXCo0Q5T2LOglpfKVkVkQVDF2b59e6EYAFAqlfj6+lKtWjU8PT1xdXXF0c4Gu4zzaGIPoLi2D0XsESRdZtGOFCDs3BFutTC7BiM86iJcghBuNRCu1aGYpCHZOiMfbbjA8qOWIDpbtYJBraqxuWUAJ2N78/W+a5yJykChSUTlHIHa5Rg6VRqn3K5zyu06LbyaMbrhGOq71y/1cV8+epBNX88GwL1aIF1Hj2fj97GAnoad/fGqXr5BjqtPxBOXqcPTQUOfRvL66srO/PnzmTx5cpn0FR4ezsSJEyuMKADLygQPvZ7A7KYYzL7UU63GVUqALRNR7f8SY8sxmBoPAXXJpvpkKgeyIKjiCGF5nLe3t6d79+5Ur14dlVKJlBaF4vJWFGd2oojei6QrmiVMqO0w+zZG+DfD7NcUs19jsC/5fPvFxGxe/e0kl5NzAejTyJdxj9TEw8GyzMjX2YauoV5cS83l811X2HDcG31SF5S2V1B6H0Nre5iDiYc5uHkY7f3a8ULYi9RxrVOisU/v2ML2Bd8ihJmg8CZ0fWksp3Ykk5Oux8FVS6Ou1Up8HGWBySz44YZ3YHibQLRqea11RedOT/9lJQYAjh8/zrRp03jyySdv2cYqXgQJvJW5+AR0p3t0Zx4zb+c1zV/45CSi3vo+qv1zMLYcjanxMNDIqweqArIgqOJ069aNRx55BKUEUsxBlDsWobi4CUXa5SLthK075oCWmANaYw5ohfCqd2MKoPSsPRnPxNVnyTWY8HLU8ulT9Wlxi4j6QDc7Pn+8HomdazJr+2X+PKrAdKUGek1HNIE70KoPsjN2Fztjd9EloAvPhz1Pdafqtxz7+IY17F66EIDQ9p3pOOwF8rJNnNh6HYDmvYNQacr3hrzlbBJXUnJxslHRr6mcybGiM3/+fFauXHnLz48fP17mY96pz5UrV5a/F+HGtFY9O/huSEvG/GrLipwODLffx3i7NWiyolFvm4pq/1yMLV7E1GQEaMtvxY5M2SMLgqqM2YTi2l5U59agPL8WKSep8COhUFsEQHBHzEHtEN4N4B6zhOmNZj7ZdIGfD1gi6VsFu/LZU2G4O9y5cI+Xo5YPe4XyYpsgJq8/z/4LoL/4JAbbdmiCtqKRjrIpehNborfQo3oPRtUfhb9D0ZvrkTUr2b98CQCNuvemTf9nkSSJ45uuYtSb8aruSHAj93s6xtLy7xLHg5pXw0EucVzhSEhI4OpVy/8oMjKyTJ/+S8OdRMG0adOYOHFi4fugoKD7GpAo3Qi4FfkmGgU4s/z55oz8OYLvktvxh6k9S1pEUfv8dyjSr6DeMQPVgXkWj0HTkbLHoJIi/zpVNYRAij+GMnIFyrN/FhUBNi6Ya3bBVLsb5uCOoC27efT4jHxeXx7JsZgMAF5oV51XO9UodfBcdXc7Fg5uxP7Lqbz/9zmuJnmgO9sPnXMH7KptAnMka66sYf219fSv3Z/n6z+PndqOo2tXFYqB5k/0o8WT/QDISddxbp8lErzZY4HlXiHtQFQaJ2Mz0aoUPCuXOK5wJCQkMGvWrML3v/zyixWtuT0FUwv16tUDICQkhMcee+y+iQJJa3lAMGfqAcs03+LhTXlhyXFOxmbSa08Nvuz7J51Nu1Dt/RxF6iWLMDj0LcZWr8gxBpUQWRBUFbITUJ78FeXJ31CkXizcLGxcMNXpgTmkJ+bq7eE+1A2PjM3k+cXHSM014KhV8VGfenQO8bzzjrehVQ031r3Uit8jYvlkyyWyMrzJzXgGvONx8FqL0XiBJeeWsCV6C/0Uncn8bQ8ALfsOpFmvpwr7ObMnHrNJ4F3DEd/at8+9XtYIIfhqexQATzX2LZGnRKb8KBADFVkE/Jfjx4/f5Em4X6JA0hQIAgNCCCRJws1ew8/DmzDh91NsOpvEK8tP81nfDnQd1QfF6T9Q7f4ERfpVS4zBvi8xNhuFqclwsJWTcFUGZEFQmRFmFFHbUUb8hOLiJqQb9cOFyhZz7W6Y6vfFHNwBlPfvRnTkajrPLzlGjt5EXW8HvuzfgEC3snkqUCok+jX1p0d9b+btjOKn/dGYEnzIShiJFBSFi+OvxOfG8yVLCWpsx3MBzxYRA0aDmbN7Ld6BsA5+ZWJTadh3OY3D19LRKBU8/1D1ch9f5tZURjFQHAXTG/dFFGhu5AMxmBF5JqQby3Rt1EpmPR3GmytPsy4ygbHLI/nwyXr0avg0+tAnLA8m+75EkXEN9a6PUO2fg6nJCIytXgbbYpYSy1QYZEFQGclPR3lssUUIZPyTPtRcrQWmBgMx1e1VptMBt2LPpRRe/uUE+UYzzYNc+HpQ+H2ZI3ewUfFG19oMbFaNDzddYMuZJLgaTJp6PJoaO7GRNnPVN5eZLCbjghNP1XwKpULJ1ZOp6HKM2LtoCAwr3x8iIQRfbrMEbvZv5oePs1zkqaJQVcRAAfdLFBQUJlIICXOWHsW/8naolQo+6VMfjVLBquNxTPjjFAmZOka2DcTU6FlMDQeiOPsXqv1zUCSeQnXgK5THfsLY/EVMzV8ol98nmdIjC4JKhJR2BeWhb1Ge/AXJkAeA0DpjCnsaU+MhCI+QcrNl85kkxq44icEkaFfLnS/7NcD2PkfvB7jZMrd/Qw5fTePtP44SnaHGcO5hDE5h2FdbSY7xCp8c/YS1V9bybrN3uXzQCEDtFl7lmpEQYPfFVI7FZKBVKXhO9g5YnYMHDxYm5Dp37lyVEQMF/DcQsiyWKRYsWZaQMGcZ4D9aQ6mQ+ODxUJxtVfy0P5pPN18kKVvHm11ro1CoMNd7En3oEygubUK18yMUiZGod3+C6siPGJuOwtR0uOwxqGDIgqASIMVFoNo3B8X5dUg30gSaPethavYcpnpPlHvgzl8n4nlr5WlMQtA11JNPnwpDo7o/6YaLw08Xz1OnfyRSU529fg+Rm+lNzunnUfkdwc5lHadTTzNk0xAa5XShidSF2i3Kr14BFPUODGpeDS9HucSrNTl48CDTpk0rfH8/lg1WBCZPnkx4eDhgET3APYmCAkEAWARBMSgUEm8/WgcfJxs+2niBn/ZHk5FnZHrvuqiUCpAkzLW6oq/5iMVjsOtjFKkXUe/+GNXBuZgaD8fY4oVS5TiRuX/IgqACI8UcQrXnM5RR2wq3mWp0xtTiJcxB7f7J21uOLDt8nclrziKAx8N9mNE71HLhlxPJ166w9vOZmPR6Hg11YOZLD/PVtgP8fFiHMbY5mYkhaKuvQaM+wZFq64nxPkVH5Yc4UbKkRmXBtvPJnIzNxFatYFRbuYiRNSkQA1VVBPyXguP89/HerSgo6iHQ37bt8DaBuNqpeffPM6w6HkdWvoFZfcP+ScIlKTCHPo4+5DEU59ZYHnASIy1TCUd+xBQ+GGOLF8FZXoljTcrvl1ymxEjxx1H/NhDt4p4oo7YhJCWm+k+jG7kDQ79fLKsFrCAGFuy9xvs3xMDAZv7MfLxeuYqB9IQ4Vn86HX1uLr516vLomP/haKvl7R7t+fulejQPiAajE7qLA8mNHYRZ2JOgjmbIpiF8H/k9RrPxvtsohGDODe/AMy0C5JUFVuRBEwP/5ZdffuH333/n4MGDd7W/wWDxCqhQ3NJD8G+eaOTLnP4N0CgVbDmXzMjFx8jM+89+ChXm0CfQD9+Mvu9izH5NkIx5qI78gPablqj/ehkp8fRd2Stz78iCoAIhpV5Gveo5tAu7ory8FSEpMTYchP6FvRh6fYXwrGs1277ZGcVHGy8AMKptEJMeC0FRjgV6ctLTWP3xNPIy0nEPrM5jr7+NSvOPKz7I059FI55hds9L+DonYspoSO6F1zHkhGESJr479R1DNw3lfNr5+2rn5rNJnInPxk6jZITsHbAaD7oYKOBeRIFeb/EKqFHe0UNQQOe6nvzwbCMctEoOX03nmQVHScrS3dxQkjDX6oL+2XXo+/+GKagdkjChPLUC7fxOqH8bhHRtr6W+uUy5IQuCikBeGqpN76D5oR3Ks6sRSJjq90X//F6MPT5HuFS3qnlLD8Ywe6vlqfe1TjX43yM1yzXBjy43h7WzZpKVnIiTlw+9x7+H1v7mTGiSpOLRZs8zpbqK4XV/w1atIv/aYPKuD8RstuN8+nmLt+DU/fEWmM2COdsseQeGtgrA1a7scz7I3BlZDBTlbkWB0Wi5RpRCiSm1mJv6LWhR3ZUlw5vi6aDhfGI2zyw4wvX0vOIbSxLm4A4YBq5AN2wjprq9EZIC5eUtaJc+iWZRdxTn1oLZVCrbZe4OWRBYE7MJ5dEFaL9therIj0hmI6YaD6MfsQVDr7mWKoJWZv2pBKatswQovdwhmJc6BJerGDAZDKz74iOSrl7G1tGJXv97Fztnl1u2N+hMXNkfhM+JnnzZYSHda27BnNOA3ItjMWTWt3gLIr9j2KbhXMm8Uqa2bjidyPnEbBy1Koa1DizTvmVKhiwGiuduREFBlVQlEqaUfIS55E/rIT6OLBnRFH8XG66m5vHM/CNcTs657T7CJxzDE99bHoQaD0UotSjiItCsHGF5WIpYBIbcEtsgU3pkQWAlpNijaBZ2Rb3xLaT8dMyeoegHLMfQbynCq/Tlfu8H+6NSmfDHKQQwoJk/YzoGl+v4ZrOJzd/NIfbsadQ2tvSa8B4uPrcvHXz1ZCoGnQlbWz9aNfuJ55vn8HHbSYR5R5N//Rnyrg/AbLLjXPpZBm98lr+i/ioSTX23mMyCr7ZbvCjDWgfgbCt7B8obWQzcntKKgsKgQoUCTAJzRsmmDQoIdLNj6Yim1PSwIy5TxzPzj3AmLuuO+wnXYIzdPkY3+jDGNq8jtM6WtMgbJqCd2wTV9mmQeb1UtsiUDFkQlDe6bFQb30a7qDuKxEiE1hlDlw/QD99sCRasIJyOy+LlX05gMAm6hHoysUdIuXoGhBDs+WURFw/uRaFU0f3VCXgG1bjjfucPJAJQu7kXKrU9dUNm06Bmf14P+4Z3W36GuzKE3MuvY8ypid6Uz9SDUxm35z1yDLd/erkTa0/Gcyk5F2cbFUNayd6B8kYWAyWjNKKgIKhQfaNkeUFNg9Lg7WTDz8ObUs/XkdRcA0MWHuXotfSS7WzvhbH92+hGH8Xw8FTMzoFI+Wmo9n+F9uvmqFc9hxRzSI4zKENkQVCOKK7sQvtjR1RHLbXWTfWfRvfCXkt1sLssNXw/iE7N4/nFlnTEzYNc+LRP/VIXKbpXIv5ezYmNawF45PkxBNRveMd9slLzibtgKa5Uq7mlloIkKQgKep3atWZS0yWOGc3eZGT4UUh6Hl1iV4RQsPv6Rh5d3Z8jSZF3ZWuu3sRnmy8BMLJtEI42Fed/+aAQGRkpi4EScvp0yaL4C2IICgVBCVYaFIebvYafhjahaaAzWTojI3+OYO+l1JJ3oHXA1PwF9C/sR99nIabAtpYAxLOr0S7uiWbRoyhOrQBT6QWLTFFkQVAe6HNQrZ+A5te+SJnRmJ0D0A/4DUOvr8DOw9rWFSE5W8fInyNIztFT19uBeQPD/1lLXE6c27uTfct+BqDNgCHUbvVQifaLOpYCgG9tJxzdi6YK9vLqTVj9+WjUbrR2/4Mv2n9Arxo9yY9+AbPBhXxjAi9sGcULO7/GUMoApu93XyEhS0c1FxuGtpLXUctUfoQQmEyW6+AfQXD3N1xHGxU/PNOYdrXcyTOYeWHpMTafSbrzjv9GocRcpzuGQX+gG7EVY8OBN+IMjqH562W0XzdDuWcW5CTetZ0POnclCObNm0dwcDA2NjY0bdqUXbt2lWi/PXv2oFKpaNSo0d0MWymR4k+g+elRVMcWAWBsMhz9iG2Yq3ewsmU3k6Mz8vyS41xLy8PfxYbvnmlU7k+7104eY+sPcwEI7/oYjbv3LvG+MafTAAhq4F7s505OTWjY8Ffs7GqjFHH0dH+ZZX19qKeeiiEzDEkycTRuPq2XjuCnsxdKNmZaHj/usdSTeLNb7XIXTzKW2gQFmflk7szx48eJjIwkISHhlm0KpgsANE62wN17CAqw1SiZO6Ah3ep5YTAJXvvtJH8ej7urvoRXfYw9ZqN7+SiG9m8hHLyRshNQ7/oI7VeNUP8+FMWFDVAOuUeqEqUWBMuWLeP111/n3XffJSIignbt2tG9e3euXbt22/0yMjIYMmQIDz/88F0bW6kQAuXRBWh+fgxFynmEgzf6ASswdv2wQhb2MJsFb648zem4LNzs1Pz4bONyT7mbGHWRv7/8BLPJRO3WD9F24NAS76vPMxJ/2RKwFFDv1qVWbWz8adBgCa6uHTCbdaTHTWBG6yMsfmw2ToaBCLMKSX2aL4+8QMsff+LPS7d+ijELwTt/nkZvMtMq2JVH6t5byWeZ0lPVChWVF5MnT2bt2rW3FAUF0wUAmhuFue7FQ1DYl0rBZ0/Vp08jX0zC8puz5GD03Xdo54GpzVh0Lx1G32seZv9mlumEC+vR/D4E7dzGqLZPQ0opmcB/0Cm1IJg1axYjR45k1KhRhIaGMnv2bAICAvj6669vu98LL7zAoEGDaN269V0bW2kw6lCvecWygsCkx1T7UXQjtmGu3s7alt2S2VsvsflsEmqlxNyB4VR3L9/6CKnXo/nrsw8w6nUEhIXz8KiXLdHNJeT6+QyEWeDsZYuTx+0rC6qU9oTWnYOf33AAomO+RpU1lY0DX+LdJl+jMPuiUGVhsp/LxPWf0PabPSyKuI7BVDR4aX2UgYNX0rFTK5naq265Bl3KyGLgXrmdKNDpLHkHNBoNKqcCQXBvHoICVEoF03uHMqSlZXpt2rrzfLPzyr11qtRgrv8U+mfXohu1E2OLlxB27kg5iZYgxO8fQvNjJ5R7ZyOl3eNYVZhSCQK9Xs+RI0fo2rVrke1du3Zl7969t9xvwYIFXLp0iffff79E4+h0OjIzM4u8Kg0ZMWiW9EZ5ajlCUmLoPAVDnwVgV7wbuyKw+ngc3+2+CsCM3qE0DnAu1/Fz0tNYM+sD8rMy8axeg0fHjEepKt2yvYLpgmqhLiVqL0lKgquPp1bNaUiSipSU9URGDqVHsB87nv6N1t49kCSB1mMbedpZzFy3l+e35hBX61EUXrWIUlbj17OWH803utYi0K18BdSDjiwGyoZbiYICQaDValE4Wq7FshIEUFAUqTajO1iWMs/eeokvt14qkyXAwiMEY+fJ6F4+hv7J+ZhqPoJQqFAknUa9cybab1uiWdgV5YG5SOlX7nm8qkSpJoiTk5MxmUw31dz29vYmPj6+2H0uXLjAW2+9xa5du1CpSjbczJkzmTJlSmlMqxBI1w+h+WM4Uk4SwsYVw+PfYg6ueLEC/+ZYdAbvrT4LwHMPBdE7/Pbr/MsafV4eaz+fSVZyEs7ePvSeMBGNrW2p+hBmQfQZiyC43XRBcXh798HGJpCz514jO+cUJ070J7TuV3zZcQqbrj3ElIPT0dldwz74S/LjniLbuQE2Pd/lxI39h7QMoH8z/1KNKXNvyGKgbCkonfzYY48V/rbn5VkyC9rY2PxLEJRtFL8kSbzaqQb2GiWfbLrIvJ1X0JtE2WVCVWowhzyGOeQxyEtFeX4dijN/ori6G0X8cRTxx2HbVMzutTHXfMTy8m8Oqge3OuldBRX+958lhCj2H2gymRg0aBBTpkyhTp2SV5t7++23ycjIKHxFR9/DHFM5oTi9Es3SPkg5SZg966EftrHCi4G4jHzG/HoCvcnMwyEejO1cs1zHNxmNbPz6c5KuXMbG0Yme497FxqH08RUp13PIyzSg0ijwqelU6v2dnZsR3vBXbG1rotcncjJyKKlpO+kS2IVljy4lzC0MSZmPbbUlaGqsBumfJ6UOrf1KPZ7MvXH16tUSL52TKRn/Dcos8Mo6ODigcLQU6BJ6M0JX9imER7YN4p1HLfeHH/ZcZeb6C2XiKSiCrRum8GcwDFiObswJDF0/whTYBiEpUaRcQHXwazS/PIV2dh3US/ug2vUJiqjt97ZiITsB8kqxvLICUCoPgYeHB0ql8iZvQGJi4k1eA4CsrCwOHz5MREQEY8aMASzpMIUQqFQqNm7cSOfOnW/aT6vVotVWHpWmPPQd6i0TATDV6YGh51eguTnXfkUiV29i9C/HSc7RE+LtwMd96pdrsSIhBNt+nMfV40dRqjU8NvatO2YhvBUF3gG/Oi4oVXe3ktbGJoCGDZZw7tw40jP2cubMGGrWeA9/n358//D3fBP5DYvOLEKr3YtTeAwJxuEY3IMZfCaGunZaBnu70MvdCRd5lYFMFSAtzXJNubq6otAqkTQKhN6MOduAUlv23/EhrQLQqCQmrznHogPRGExmJva4TwXU7D0xNRmGqckwyM9AEbUd5aXNKC5vRcpNRnltD1zbU9hc2Hlg9gxFOFcDB2+Egw/CxhmQQLL83kiGXMjPQMpJREqLQnH+byQEQqlF9/LRCre8/FaUShBoNBqaNm3Kpk2bePLJJwu3b9q0iccff/ym9k5OTpw8ebLItnnz5rF161ZWrFhBcHD5psItc4RAuecz1Ls/AcDYdCTGR6YXfkkqKpYVBac4E5+Nm52aeQMbYq8t3+WF+5cv4dzenSiUSh4d8z98apbcg/RfYk6nAxBQv3TTBf9FpXIkNHQely5NJjFpFZcuT0GniyMw8FXGNBxDc6/mTDowidT8a3grP6KO/UvsMTflbK6OiVEJTI5KoKOrPU94OPOwqwN25Vga+kFCTkJU9pw+fZq1a9cyYsQIwDI9DBZBAKBw1GBKycecpUfpfvug3btlQLNqqJUK3vvzDL8ctgTxTulV9/4mRbNxxhz6OObQx0EIpJQLKKL3obi2Fyn+BFJalEUkXC3Z0vqbEGbQlt5raS1KfRcYN24czz77LM2aNaN169Z89913XLt2jRdffBGwuPuvX7/OokWLUCgUhIWFFdnfy8sLGxubm7ZXRpQHvioUA4Z2b2JqMxYqQaT5Vzui2HTGsqLgqwEN8Xcp3Zz9vSCE4NCq5RxduwqADsOep3qjpnfdX362gcSrN5YbljCg8HYoFGpq1ZqOVutHdMw8Yq5/h04fR62aU2np05Kl3ZYycf9EDiUc4mTU5/Sr3ovAaqP4PUXH2VwdW9Jy2JKWg0aSaO9iTwcXex5ytqe6jfqe5kWFEGQYzQ+8B2L+/PmFc94yZce/Bdbw4cO5dMmSedPf3xIfo3BU3xAEZRdYWBxPNfZDrZB4a9VpVkTEYjCZmfF4KKryENeShPCog8mjDqbGN5Y863OQUs6jSDoH2XFI2QlIWfGgz7qRMlkgCRAaO8tycn0uyosbACwJ6IasA6Xm/tteRpRaEPTv35+UlBSmTp1KXFwcYWFhrFu3jqAgS+33uLi4O+YkqAooj/2Mevt0AAydJmFq+bKVLSoZW88lMW+HpUTvlJ51aRLoUq7j71++lKNrVwLQpv+z1Gt/b3kprp9LBwFufnbYu5TNNJMkSQQGvoxW68vFS5NJSvoLvT6RuiFf4G7jzpz2c5h/Zj7fR37P+it/UTPtNN+0+RCjKpiVyZmsTs4kWmdgc1o2m9OyAfBUK2nqaEsjB1tC7LQE22jw06rR3ObpxywE1/IN7MzIYVKUJQp8ft1qdHZ1KJPjrGzIYuD+UiAKAgICCufwC1YbFAQWmu6zIADoHe6LWqlg/O+n+PNEPAaTmY/61EdtDY+bxh7h2xiTb+M7t81JRLPYkkjN7BGCfvCfYHtvXsvy5q78xKNHj2b06NHFfrZw4cLb7jt58uQqcVELrRNCocbU4sVKIwaupOTy5h+WYKxnWlSjT+PyD4hz9LQk72k7cCiNHu11z/1FFy43LPsLz9u7DxqNF2fPjSUj4wAnI5+lXujXaLW+PFf/ORp5NOK9/e9xKeMSQzYN4a2mbzGheg/GB3hwPk/PxtQsdmfkEJGVT5LBxPrUbNanZhcZw12lxEGpQK2QkAAJMAN5ZjMpBhP5/yk5a1PONSVkHjz+vczb3t4SC1UQWHg3BY7uhu5h3qiVCsYuP8m6U4kYTILP+oahucsYoXJBUlqmIJwD0PdfVunEANylIJABc+jj6N1rIzxDrW1KicjWGRnz6wmydEaaBDjzRtfaVrEjrFNXfGuF4B4QdM99mc2CmLPpQOmXG5YUV9eHaBC2iNNnXiI39wInTg6mXujX2NuH0Ny7OUu6LmHi/okcTjzM+wfe52jiUcY3GU+InQ0hdlpeqeZBvtnMiex8jmTlEZmTz8VcPVfy9eiEIMVoIsV468htjSQR7mBDNzdHGjva0MSh/KZ3ZB5MvL298fX1JSQkBHd3S/4UycHiIRA5999DUMAjoZ7MGdCQV5edZNPZJF797SRfPB1WcdOD27mjH/A7Ul4KOJbv8u2yQhYE94DwqmdtE0qEEIK3V53mYlIOXo5avujXwKpKuyzEAEDS1Wx0OUY0tkq8qt+/dNAODqE0bLCU02deJC/vEicjh1C37he4OLfCw9aDrzp8xfzT8/n+1Pf8GfUnkamRzGwzk2AnS9CsjUJBCyc7Wjj9k7xI3BADSXojuWYzerOgwBcg3djHTa3ET6NGLXsFZMoRjUZDixYtimxT2FtuFebs8q0N0LGOB/MGNuTlX0+w/Xwyr/52kjn9G1ZcT4HWAaGtvFN6FfSsypQl3+++agkiVEh82a8BnuVco+B+EXsuHQD/EBcUyvt707Sx8aNhg59xcmqGyZTN6dMvkJS8DgClQslzYc8xt+Nc3GzcLFMIG4ewNmrtLfuTJAkPtYpQexuaOtrR2tmeNjderZ3taexoS5CNRhYDMhUCxQ0PgbkcPQQFPFTLnW8Hh6NVKdhxIYX/rYjEYDKXux0PArIgqOLsj0pl9lZLxPC7PerQqJzTEt9P4i5lAOBXu3yOSaVypn6973B374YQRs6fn8D12J8KPy+YQmju3Zx8Uz6TD05myoEp5BnzysU+GZn7hcL+hiDILn9BANAq2I25AxqiVkpsOpvEm3+cwiiLgjJHFgRVmITMfP63IhKzgCfCfenftOqk2DUazCResQTo+dQqP5GjUGgJqfMpvj6DAbhy5WMuR81ECEscgIetB3Paz+GFsBdQSArWXFnD0E1DuZRxqdxslJEpawo8BCLXiDCVcRbBEvJQLXfm9G+IWiGx7lQi7/55BpPZOrZUVWRBUEUxmMyMXR5JSo6BEG8H3n8spEpV40u6loXJYMbWSY2z1/1JlHIrJElBcPDbBAX9D4C4uMWcPTcOk8niCVAqlIyqP4p5HefhbuNOVGYUwzYNY03UmnK1U0bmboiMjLxpm2T3T7iZyCvfOIJ/07GOB7OeDkMpSfx5Ip73/zqLWRYFZYYsCKoon266yNHoDBy0Sr7s1wBbTQWNzL1L4i9Ylkb51nS2itCRJIlq/iOoU+cTJElNaupmTp0aicHwT+7ypl5NWdptKS29W5JvymfKwSnyFMJdIucgKB+OHz/OypUrmT9/fpHtkkJCsrX8hphzrScIALqEevHpU/VRSLAiIpZp686Vfe2DBxRZEFRB1p9K4Kf9loJQHz1ZnyD3qleatyB+wLeWddOCenr0oH69H1CpnMjKPs6Jk4PIy7ta+LmbjRtfdviSlxq8VGQK4XLGZStaXbmQxUD5cktRYGvxEljTQ1BA9zBvPnyiHhLwy+HrfLjhPhREegCRBUEV43JSDu/8eQaA59oG8XBdTytbVPZYK37gVjg7N6NB2GK0Wn/y86M5cXIQmVnHCj9XSApG1BtRZAph6KahrLuyznpGVxISEhJuqsQnc/8prlaE4oYgMFcAQQCWjIbTe1vywPy0P5pZmy/JouAekQVBFSJPb+K1306SqzfRoroLr3WuYW2T7gvWjB+4FXZ2NWnYYAn29vUxGtM5dWoEKSmbirQpmEJo4d2CfFM+7x94n2kHp5FvzLeS1TIyJacieQgKeKqJH+8/FgLA93uuMmd7lJUtqtzIgqAKMXPDeS4k5eDpoGFW37DyKQhiBawdP3ArNBpPGoQtxNW1A2azjrPnxhIbu6hIGzcbN75s/2XhKoTVUasZtnkYVzKvWMdoGZkSoiiIIci7dWZNazCweTXeedSSeXXejii+2XnFugZVYqrmHeMB5O/IBH47EosEfNynPh4OVSP5UHFUlPiB4lAq7Qit+yU+3v0BQdSVj4osS4R/ViHM7fCvREabhrD+6nrrGS4jcwcqooeggCGtAhn/SC0AZm+9xPy9V++wh0xxyIKgChCdmsfEvyxxAy+0q07rGm5Wtuj+UdHiB4pDklTUqDGRoKBxgGVZ4rlz4zCZik4NNPNuxpKuS2jm1Yw8Yx4T909kxqEZ8hSCTIWkIgsCgFEPBfFqJ8s06ccbL/LzgWgrW1T5kAVBJUdvNDN2xUmydSaaBDgzpmOwtU26r1TE+IHisCxLHFm4LDEldTOnTo/EYEgr0q6gFsKo+qOQkFh1eRUjtozgapb8hCNTsaioUwb/ZnSHYF5sVx2AGX+fZ9nh69Y1qJIhC4JKzqebLhIZm4WzrYrPqnDcQAEF8QM+NZ0qVPzArShYlqhUOpGVdYwTJ58hPz+mSBulQskLYS8wp8Mc3LRuXEi/wJCNQ9h4baOVrJaRuRnpRi4TYai4ggDgtc41GNEmEID315zlj4hYK1tUeajad48qzuYzSSy64Rb78In6+DpX3CfmsiLu0j8BhZUFZ+dmNGzwM1qNL/n5VzhxchDZ2aduatfSpyWLuy2miWcTco25vLvvXT48/CE6k84KVsvIFEVS37hdGCp2DQFJkpjQpRbPtqwGwLt/nmHL2SQrW1U5kAVBJSUmLY93/jwNwPDWgXQK8bCyRfcfk9FM4pUsAHwqYEDh7bCzq0WDhkuxtwvBYEjhZORQUtN23tTO09aTuR3nMqLeCCQkfr/0OyM3jyQ6S54PlbEyNwSB0FdsQQAWUfDOo3Xo29gPAfxvRSQnYjKsbVaFRxYElRC90cz/VkSSmW8k3N+JcY/UtLZJ5ULytWxMBjM2DipcvG2tbU6p0Wq8CAtbhItzG8zmPM6ceZn4+N9uaqdSqHipwUt80f4LXLQunEs/x7Mbn2Vz9GYrWC0jY6HAQyAquIegAEmSmNwzhHa13Mk3mnnpl+PEpMlpw2+HLAgqIZ9vucTx65k42VjiBtRVPG6ggLiLBfEDFSv/QGlQqRwIDZ2Hl+cTgJlLl6cQdeXTIssSC2jt25olXZfQ2LMxOcYc3t77Nh8d+UieQpCxCv/EEFQOQQCgUir4/OkwQn0cSMkx8NziY6TnWqeEc2XgwbiTVCG2nUtmwb5rAHzweD2quVa+J+W7pSLnHygNCoWaWrWmExDwMgCxsQs4c2YMRmP2TW297LyY13EeQ0OHArDi4gqGbx4ur0KQKXcKPQT6ih1U+F8ctCq+GdQIXyctUSm5jFl2Ar2x8oia8kQWBJWIuIx83lplCUYb0jKAR0KrXp2CW2E2mUmMuhE/ULNyCwKwuDMDA0ZTp86nKBRa0tJ3Wgoj5V+7qa1KoWJMwzF80f4LXLWuXEi/wLMbn+XvK39bwXKZB5XKElRYHN5OWr4d3AgHrZLDV9N5e9VpuWxyMciCoJJgMJkZtyKSjDwjYX6OjO9Sy9omlSvJ0TkY9Wa0dipcfapO9UZPj+6EhS1Co/EiL+8SJ04MICPjULFt2/i2YUm3JTT1akqeMY9JByYx9eBUuZyyTPnwrxiCylhEqI63A3P6N0SlkFgbmcC3u65Y26QKhywIKglfbr1MRHQGDloln/dtgEb1YP3r4i5apgt8ajohKSpn/MCtcHQIo2HDZTg4hGE0ZnDq9CgSEv4otq2nrSdzO8wtTGT0V9RfDN00lIvpF8vZapkHDUlz4zdHAMbKJwgAWtdwY3LPugB8ue0yO84nW9miisWDdVeppOy8kMz3eyxzxjMer0eA24MTN1BAYUBhJY8fuBVajRdh9X/Cw707Qhi5eGkiV24RbFiQyGhex3l42HgQlRnFsM3D+OPiH5XyyU2mclA4ZUDlCiz8L32b+DGgmT8CGP/7Ka6m5FrbpAqDLAgqOAmZ+by50pJvYFDzanSr52Vli8ofk9FMwmWLIPCrU3kSEpUWpdKGOnU+IaDaaACuxy7g7LnXMZlyim3fzLsZS7otobVPa3QmHTOPzOSdfe+Qpc8qT7NlHhT+7Zmr5PPv7zxah8YBzmTpjIz59QQ5uopZn6G8kQVBBcZoMvO/FadIyzVQz8eRN7s+WHEDBSRdzcaot+QfqErxA8UhSRKBgS9Tp/ZHSJKG1NStHD8xgNy84uu8u9m4Mbv9bF4NfxWlpGRz9Gae2fgMx5OOl7Pl9wdvb29CQkIIDw+3tikPFOHh4YSFhRXZVmSpb+XWA2hUCr7o1wBPBw0XknJ4988zsncNWRBUaL7aHsXha+nYa5R8/nQYWrXS2iZZhdgLN5Yb1q68+QdKi6dnTxqELbwRbHiZEyf6k5Kypdi2CknBs3Wf5YeHf8DP3o/YnFie3/Y830V+h9Fc+Z98RowYwZNPPimLgnIiPDyciRMn0qJFi5s/vHH5VYWbp5ejli/6NUCtkFh/OpEf99y8wudBQxYEFZQ9l1IKo2Cn9Q4lyL1qPxnfjrgbgsCvdtWdLigOR8dwwhv+hpNTM0ymHM6ee5UrVz9HiOJv8mHuYSzptoTuQd0xCzPfn/qeF7a+QGxO5S/uUiAKZO4vtxUDAAWCvPLrAQCaBLrwbvc6gCXhW0T0g53eWBYEFZDELB0Tfj+FAPo39adHmLe1TbIaRr2psH6BXx0X6xpjBTQaT+rX+wFf32cBuH79B05GDiU/v/ibvIPagamtpjKt1TTs1facSDnBoA2DWH91fXmaLVNVKXTQVRFFAPRv5k/PBt6YhGD875Fk5Vd+r9rdIguCCobJLJjw+ylScw2EeDvw9qO1rW2SVYm/nIXZJLB31eDorrW2OVZBoVBTI/gtQurMQql0ICvrGMeOP0VS0ppbum4fDXqUJV2X0NC9ITmGHCbun8ik/ZPINtycDVFGpsQUCIKqowcsNQ8eq0s1Fxuup+fz/pqzVWJK5G6QBUEFY96OKA5cScNObYkbsHlA4wYK+Pd0wYMSP3ArPDy60Sj8dxwcGmIyZXL+wpucPvMC+fkxxbb3d/Dn287f8nz951FICv6++jeDNwzmRPKJcrZcpioghACT5UYpKavWtehgo+LTp8JQShLrIhP483i8tU2yCrIgqEDsv/z/9u48LMpy7wP4d3bWAZF9FRXZRRYVzFJcMU0tyyVT7JiGpWme6mgd3zDfY3XKsrqyslzKFLHSfEuPRse1wCUXFkFARUF2VGBYZ5i53z8mJkfWgRlm+32ua64LnrnnmfvHDTy/uZ97uYstJ5WjyROn+WOgo7Wea6R/t69WA1AOKCSAhYUnQkO+gbfXcnA4QlRX/45Ll2fg9u2voFC03bSFz+VjScgSbB239a8Bh8eW4ssrX5rEgEPSh+Tsr54BE1wYbZiXHVbEDgQAbDyShwqJ+W0iZnqtaqQqJc14db9y3MCscDdMD3PTd5X0ru5eM+4W14PDATwD++m7OgaDyxXAy2sZwocdgJ14BBSKJtwq/BDpGbMhkbT/6T/MMQy7J+1GnE8c5EyOrVlbkXA8AcV1xX1ce2Ks2H0bAt2/SJEpee4hbwS72aK2qQX/ezhX39Xpc6bZqkZGJlfg5e+zUFknhZ+TNf45xV/fVTIIRVfuAQCcB9jC0kag59oYHkvLAQgO3g6/wf8Cn2+PhoY8ZGQ+jes3/rfdnRNthDbYEL0B60euhzXfGulV6Zh3dB725e+DghnvynOkj8juu69uYrcMWvF5XPxrRiD4XA5+yanErzmV+q5Sn6KEwABs/u91/HFLud7AR3NCYSk073EDrQqz7gIAvEMc9FwTw8XhcODsPBMR4T/D2WkGAIaysiRcuvwYKqsOg7VzoX90wKPYPXk3wp3C0djSiPcuvodlx5ehSFLU9wFoiNYi0B9VD4GAa9LjeQJcbfG3Ud4AgPdS8s1qq+QeJQRbtmyBr68vLCwsEBkZidOnT3dYdv/+/Zg4cSKcnJwgFosRExODo0eP9rjCpubY1UpsS1UuiPGvGYE0buBP0ia5akEi72C6XdAVgaAf/Pw2Ijh4GywsvCGVViAv71Vcvvw4qqqOtkkMPGw88Hns53g14lVY8i1xsfIi5h2dhz25eyBXGOZ+97RAkW51tQZB6/4FHL7pJgOtlj48AI7WQty624i9f7Q/aNcUaZwQJCcnY9WqVXjjjTdw6dIlPPzww5gyZQoKC9tf5enUqVOYOHEiDh8+jAsXLiA2NhaPPfYYLl261OvKG7vb9xqx5kflPgULR3ohLth81xt4UEluNRRyBrGjBexczG8zp56yt4tG+LAf4e21HDyeLRoaryE3bzUuX34cFZU/qyUGXA4Xs/1mI2lyEqKco9Asb8aHlz/E0mNLcbP2pv6C6AQlBbrR5YJEAJhMmSia6viB+9mI+KoBhp+eLEBNY9sBu6ZI45b94IMPsHjxYjz33HMIDAzE5s2b4eXlhc8++6zd8ps3b8Zrr72G4cOHw8/PDxs3boSfnx9++umnXlfemDXL5Fj1XSZqm1oQ5iHGKxPNc5+Cjty4rNyW1DvUwaS7J3WByxXBy2sZoiJ/gZfnC+DxbNDQeA35+f9AesZsVFQchEIhVZX3sPHAlrFbsDZqLaz5ysWM5h+dj29yvjHImQgPrrFPei8oKAg+Pj6dlmF1yt8FrrV5jOeZFe4GPydr1DS24PNTN/VdnT6hUUIglUpx4cIFTJo0Se34pEmTkJqa2q1zKBQKSCQSODiY731hxhj+5+eryCqRwM6Sjw+fCoXQBKfx9JSsWY7CLOWAwoHhjnqujfHi88Xw9n4RUZEp8PZaAS7XCvX1Oci/9jrO/zEW16+/BYkkE4wpwOFw8MSgJ7A3bi+iXaMhVUjxScYnWPzfxbhec13foRADoKhTfkrm2JpHQsDncfHqnxvK7T53G5VmMA1Ro6tQVVUV5HI5XFzUu7ZdXFxQVta9hRw2bdqE+vp6zJ49u8Myzc3NqK2tVXuYkh8uleJgehl4HA42PxUKd3sLfVfJoNzKvAu5TAGxowUcvWhMRW/x+WJ4eSUgKvIX+HivglDogpaWGpSVJyMjcy5S00Jx/cYGKBQyuFq74uNHPsa64etgI7BB9t1sLPhlAbZnbzeY3gIfHx/a10DL/P392/xff1BrQsA1oxk/Dw/ujzBPMaRyBb4+Y/iDbnurRx9LH+zCZYx1q1s3KSkJiYmJSE5OhrOzc4fl3n77bdjZ2akeXl5ePammQbpcVIO3Dinnt64aPxAxA823p6QjNy4qbxcMjHCk2wVaJBD0g6fnEkRFpsDdfZHac2VleyGTKadYcTgcTB84HclxyRjtPhoyhQyfZX6GRSmLkHcvTw81V+fi4oKpU6ciMTFR31UxCYmJifjb3/7WZTmFRHmbiWsj1HWVDAaHw0HCw74AgD3nb5v8WAKNEgJHR0fweLw2vQEVFRVdZpfJyclYvHgx9u3bhwkTJnRadu3ataipqVE9iopMIzMrrWnC8r0ZkMoVGO/viMWjOr9nZ46a6mWq1QkHRdDtAm2rlVxG1pXFKCnZqTomFLpiyJD3IRK5q5V1tnLGB6M/wPqR6yEWipFbnYuFKQvxRdYXaJbrt/uUkgLt6G4yAADye8o259mZT0IAAGOH9Ie/iw0apHLsPmfaMw40SgiEQiEiIyORkpKidjwlJQWjRo3q8HVJSUlYtGgR9uzZg6lTp3b5PiKRCGKxWO1h7BqkcryYlIGqein8XWzw7yeCweXSp98HFVy+A6ZgcHC3gr2r+W75rG3NzeXIufoSMjPno7b2PDgcIdzcFiAi/BCGR/0XTo5T2n0dh8PBowMeRXJcMsZ6jIWcyfHVla8w5z9zcLqk4+nGfYGSgt7RJBkAAPmdPxMCR/O6xcnhcLB0tPLD29dnClHfbBi3znRB41sGq1evxldffYXt27cjJycHL7/8MgoLC5GQkABA+el+4cKFqvJJSUlYuHAhNm3ahOjoaJSVlaGsrAw1Neaz7zRjDK//mI3sMgkcrATYMm8orEV8fVfL4DDGkPObsvfJb0THt5SIZiqrDuNy+kzcvftfAFw4O89CZMRhDPRdA0vLAd06h6OlI/790L/x9qi34WTphOL6Yqw+vRovn3pZrwsaUVLQM5omA0ymgKL6z4Sgv3klBAAQF+wCHwdL1DS24PuL7W89bgo0TgjmzJmDzZs346233sKwYcNw6tQpHD58WDVlpbS0VG1Ngi+++AItLS148cUX4ebmpnqsXLlSe1EYuC0nC3AkuwICLgefzBkKD3uaV9+eshu1uFfaAL6QSwmBFrS01CA37xXk5b2KlpZa2FgHI3zYAfgNfgsikeZ7ZXA4HEzwmoDvpnyHhQELwefy8Vvpb5hzZA62ZGxBY0ujDqLoWle3K4m6sLAwjaduyu80AQA4FjxwrM3vwwyPy8GiGOXqhd9fLDHZ7ZF71LIvvPACXnjhhXaf27lzp9r3J06c6MlbmIwjV8rxyQnlDoZvTgtApI+9fitkwHJOK3sHBkc5QWRlfv90tKm6OhX51/4JqbQcAA9ens/D03MpuNzejxC3FlhjRdgKPOb7GDZd2oQzZWewI2cHDt08hOeCn8Njvo+Bz6X2MyUtxfUAAL6rldkO9J0W6op3juYjv7IeWSUShHoY/63sB9Hkdx3KLpVgzQHlSoTx0V54MsK9i1eYr/rqZtzMuAMACBztqufaGC/GWlBQ8C6uZC+BVFoOC4sBGBr6Lby9X9RKMnC/AeIB+PiRj/HeQ+/B3dodFY0V2PjHRjx5+Ekcvnm4T5dADgkJwbx58/rs/YxZdxYhepDstnKzLL6njS6qZBRsLfiYGOgEADhw2TRvG1BCoCOVkma8kJSOphYFHh7cH6/SSoSdunKyFEwBuA4Sw8Gd1h7oiZaWWmTnLENJ6TcAAFfXeRgW9j1sbYfq7D05HA7Geo7Fvin7sDp8NRxEDiiuL8abZ9/EvKPz8GvRr32yk+KIESMwa9YsSgq6MG/ePKxevVrj2ywtha0JgXn/bT4+THmr7efMcjTLDHPPj96gfj0daJbJsTw5A2W1zfDtb4VNs4LB51Hu1ZH6Gimy/xxMOHS8h55rY5yam0twJft5NDbeAJdriSF+76B//86n92qTiCfCvCHzMHPgTOzL34dvrn6DgtoCrE1diyH2Q7AocBFiPWN1eivh/nX4k5KSdPY+xqqnyYD8bpNyDAGXA8EAWx3VzjhE+zrATSxCaW0zTl27g4mBpjXWia5SWsYYw//8dBXpt2thZ8HHZ0+HQWxpPit79cTlX4oglyngMtAWnoH2+q6O0WlouI6MzAVobLwBodAFoSG7+jQZuJ8l3xLxgfE4OPUglgYvhTXfGnnVeXg97XU8fuhxfHv1W9RJ63T2/tRT0L6eJgMAIL2mnBHG97IB18K8P0PyuBxM+PO2wcm8O3qujfZRQqBl234vxMEM5bLEHz4VigH9aS59Z2qrmpCbVgEAiJzqbbYDlnpKIslAZtZCSKVlsLQciKGhu2FjE6jvasFGaIMlIUvw47QfsSR4CfqJ+qGsoQwfpX+EqT9NxQeXPkBxXbFO3puSAnW9SQYAQPrnQmFCPzst1sp4jR2iXDDtZH4VFArTmm1g3umelh25Uo5Nv14DALw+xQ+jBtGyxF05/9NNMAWDR4A93AbRPxxNVFenIufqS1AoGmFjE4KgwM8hEPTTd7XU2IvssTRkKeID43Hk1hHszt2NgtoCJOUlITlfudjRE4OeQJRzFHhcntbel24fKPU2GZDXSCG7odxLRhRkWL9b+jLcpx+sBDxU1kmRV1GHAFfTuY1CCYGWpF6/i1d/uAIG4OnhHnh6uKe+q2Twbmbcwc30u+BwgRHTaRlnTVRVHUVe/mtgrAV2djEICPgIfJ7hDvgS8USYMXAGpvtOx5myM9iTtwdnys7g2O1jOHb7GJwsnRDnE4fxnuMR5BCklZ4ic08KepsMAEDTBeX+FnwfW/AczG9BovYI+VwM9RTjTME9ZBbXUkJA1GUW12J5cgZkCobJQc54Y4o/dX13QdrYgrQflOszhMZ60MwCDZSWJePGjQ0AGPr3n4whfu+AyzWO9eU5HA5i3GIQ4xaDa9XX8P2175FSlILKxkrsuroLu67ugouVC2I9YjHafTTCHMNgwe/5hej+pCA7WzkFOD09vddxGKqwsDAAyqmFvU0GmEyBpj+Ut/MsaaEwNSHuyoTgSqkET+m7MlpECUEvFVQ1YOnuy2iQyhHj2w/vPREMHu1R0CnGGE7vvY6GGinEjhYIn0y9Kd1VdHsrCgs/AgC4uMzGoIH/BIejva72vjTYfjDWRK3B6vDV+K30N6QUpuD30t9R3lCOvfl7sTd/L0Q8EcIcwzDCZQRC+4cioF8ArASajctpTQpmzZoFAMjKyjLJpY4TExNVKxD6+Pj0egXHxjPlYA0t4NoJIQyg2wX3C3ZT9grklEn0XBPtooSgF4ruNmLxrku41yBDsJstPpk7FEI+jdPsypWTpbiZfgdcHgdjnvEDX2icF7S+VlK6W5UMeHo+D2+vFSbREyXkCTHOcxzGeY5DU0sTzpafxYnbJ3C2/CwqGytxrvwczpWfAwBwOVz42PrAy8YLHjYe8LD2gK3QFgKuAEKespdEKpeisaURRXVFuCW5heO3j8PZ0hkbojcgwjlCtSiPKSUFmu5N0BV5rRQNJ5SDPq3GeYDDM/7fM23y+XOw+O176st1M8bQJFPA0kj/p1FC0EO55XV4btclVNZJMaC/Fb58ZhhsaMOiLpXfqMW5/7sFABgxYwCczXxec3fdufMrCgreBgB4e62Al1eCnmukGxZ8C4zxGIMxHmPAGMNNyU2cLTuLCxUXkH03GxWNFSioLUBBbYFG561orEB1czWAvzZEAkwjKdB2MgAAdQcLADkDz9kSotD+Wj23KfC0V97GulMvQ6NUDkshDzK5Aut/zsWtuw3YtiDcKD8c0hWshw6ml6KyToohzjb4asEwOFgbxz1cfcs8XgKmYBgY7oigh2mJ4u5gTIHbxdsAMLi4zIan5/P6rlKf4HA48BX7wlfsi7lD5gIAqhqrkF+dj+L6YhTXFaOkvgQNLQ2QyqWQKWRgjEHEF0HIFaK/RX/8fPNnAMCjPo8i1jNWdW5TSQp0kQwAgKJeucWvwNsGHLoF2obYUgBbER+S5haU1DTBzc4Cq/Zl4tS1O+BygHM372H0YONLpCgh6KG/TxgMayEPz4z0gh0tPNRtsfFDkPFrMUJi3U2iu7svcDhcBAdtRUnpLnh5LjXrn5ujpSMcLR27XX5Z6DIcLTyKZ/yfafNzuz8pyM3NBaAceGjIgw7DwsIQFBQEAPD399dJMgAA4rmDoaiXgU+DfTtkJeRB0tyCuuYWrEjOwO/X78KCz8UHT4YYZTIAABxmBPs41tbWws7ODuXl5RCLTW+HKUKI/pSXl6u+vnXrFjZs2GCQSUFYWBjWrVunGgNB2z7r18Pvn0ZlnRSDHK1wvaoBlgIuti0IR4S3vb6r1kZtbS1cXFxQU1PT6TWUeggIIWbt/guri4sL1q1bhw0bNnT6Gl0kDK1TBjuybt06tWmURL9kcuVn6etVDeBzOfh4zlCDTAY0QQkBIYTcZ8SIEVi3bl2nZbTdi9D66b+rehHDIJMrUN0oU33/rxmBeNhIbxPcjxICQgh5QFcX39ZeBG0kBa3JAF3wjcfdeqnq6yfD3TEjzE2PtdEeSggIIURDrb0IWVlZvT5XSEgIJQNGRmwhgJONEP2thXhjyhB9V0draFAhIYQQoiFpiwJcDsDnGf56AzSokBBCCNERY1x4qCumFxEhhBBCNEYJASGEEEIoISCEEEIIJQSEEEIIASUEhBBCCAElBIQQQggBJQSEEEIIASUEhBBCCAElBIQQQggBJQSEEEIIASUEhBBCCAElBIQQQggBJQSEEEIIASUEhBBCCAElBIQQQggBJQSEEEIIASUEhBBCCAElBIQQQggBwNd3BbqDMQYAkEgkeq4JIYQQYlxar52t19KOGEVC0BrM4MGD9VwTQgghxDhJJBLY2dl1+DyHdZUyGACFQoGSkhLY2tqCw+Houzo6UVtbCy8vLxQVFUEsFuu7OjplLrFSnKbHXGI1lzgB84iVMQaJRAJ3d3dwuR2PFDCKHgIulwtPT099V6NPiMVik/2lfJC5xEpxmh5zidVc4gRMP9bOegZa0aBCQgghhFBCQAghhBBKCAyGSCTCm2++CZFIpO+q6Jy5xEpxmh5zidVc4gTMK9auGMWgQkIIIYToFvUQEEIIIYQSAkIIIYRQQkAIIYQQUEJACCGEEFBC0Gfu3buHBQsWwM7ODnZ2dliwYAGqq6s7fQ2Hw2n38d5776nKjB07ts3zc+fO1XE0netJrIsWLWoTR3R0tFqZ5uZmrFixAo6OjrC2tsb06dNx+/ZtHUbSOU3jlMlk+Mc//oHQ0FBYW1vD3d0dCxcuRElJiVo5Q2jTLVu2wNfXFxYWFoiMjMTp06c7LX/y5ElERkbCwsICAwcOxOeff96mzA8//ICgoCCIRCIEBQXhwIEDuqp+t2kS5/79+zFx4kQ4OTlBLBYjJiYGR48eVSuzc+fOdv9mm5qadB1KlzSJ9cSJE+3GcfXqVbVyxt6m7f3f4XA4CA4OVpUx5DbVOkb6RFxcHAsJCWGpqaksNTWVhYSEsGnTpnX6mtLSUrXH9u3bGYfDYdevX1eVGTNmDFuyZIlauerqal2H06mexBofH8/i4uLU4rhz545amYSEBObh4cFSUlLYxYsXWWxsLAsLC2MtLS26DKdDmsZZXV3NJkyYwJKTk9nVq1dZWloaGzlyJIuMjFQrp+823bt3LxMIBOzLL79k2dnZbOXKlcza2prdunWr3fI3btxgVlZWbOXKlSw7O5t9+eWXTCAQsO+//15VJjU1lfF4PLZx40aWk5PDNm7cyPh8Pjtz5kxfhdWGpnGuXLmSvfvuu+zcuXMsLy+PrV27lgkEAnbx4kVVmR07djCxWNzmb1ffNI31+PHjDADLzc1Vi+P+vzVTaNPq6mq1+IqKipiDgwN78803VWUMtU11gRKCPpCdnc0AqP2hpKWlMQDs6tWr3T7PjBkz2Lhx49SOjRkzhq1cuVJbVe21nsYaHx/PZsyY0eHz1dXVTCAQsL1796qOFRcXMy6Xy44cOaKVumtCW2167tw5BkDtH5a+23TEiBEsISFB7VhAQABbs2ZNu+Vfe+01FhAQoHbs+eefZ9HR0arvZ8+ezeLi4tTKTJ48mc2dO1dLtdacpnG2JygoiK1fv171/Y4dO5idnZ22qqg1msbamhDcu3evw3OaYpseOHCAcTgcdvPmTdUxQ21TXaBbBn0gLS0NdnZ2GDlypOpYdHQ07OzskJqa2q1zlJeX49ChQ1i8eHGb53bv3g1HR0cEBwfjlVde0es20b2J9cSJE3B2dsaQIUOwZMkSVFRUqJ67cOECZDIZJk2apDrm7u6OkJCQbv8MtUkbbQoANTU14HA4sLe3VzuurzaVSqW4cOGC2s8ZACZNmtRhXGlpaW3KT548GX/88QdkMlmnZfTRdkDP4nyQQqGARCKBg4OD2vG6ujr4+PjA09MT06ZNw6VLl7RW757oTazh4eFwc3PD+PHjcfz4cbXnTLFNt23bhgkTJsDHx0ftuKG1qa4YxeZGxq6srAzOzs5tjjs7O6OsrKxb5/j6669ha2uLJ554Qu34/Pnz4evrC1dXV2RlZWHt2rVIT09HSkqKVuquqZ7GOmXKFDz11FPw8fFBQUEB1q1bh3HjxuHChQsQiUQoKyuDUChEv3791F7n4uLS7Z+hNmmjTZuamrBmzRo8/fTTapuq6LNNq6qqIJfL4eLiona8s59zWVlZu+VbWlpQVVUFNze3Dsvoo+2AnsX5oE2bNqG+vh6zZ89WHQsICMDOnTsRGhqK2tpafPTRR3jooYeQnp4OPz8/rcbQXT2J1c3NDVu3bkVkZCSam5uxa9cujB8/HidOnMAjjzwCoON2N9Y2LS0txX/+8x/s2bNH7bghtqmuUELQC4mJiVi/fn2nZc6fPw8A7W7bzBjr9nbO27dvx/z582FhYaF2fMmSJaqvQ0JC4Ofnh6ioKFy8eBERERHdOnd36DrWOXPmqL4OCQlBVFQUfHx8cOjQoTZJkCbn1VRftalMJsPcuXOhUCiwZcsWtef6qk0782AMXcXVXvkHj2t6zr7Q0zolJSUhMTERBw8eVEsMo6Oj1QbDPvTQQ4iIiMAnn3yCjz/+WHsV7wFNYvX394e/v7/q+5iYGBQVFeH9999XJQSanrOv9LROO3fuhL29PWbOnKl23JDbVNsoIeiF5cuXdzn6e8CAAcjIyEB5eXmb5yorK9tks+05ffo0cnNzkZyc3GXZiIgICAQC5Ofna/Xi0VextnJzc4OPjw/y8/MBAK6urpBKpbh3755aL0FFRQVGjRrV7fN2pS/ilMlkmD17NgoKCnDs2LEut1zVVZu2x9HRETwer80nqoqKig7jcnV1bbc8n89H//79Oy2jye+ENvUkzlbJyclYvHgxvvvuO0yYMKHTslwuF8OHD1f9HutDb2K9X3R0NL799lvV96bUpowxbN++HQsWLIBQKOy0rCG0qc7oZ+iCeWkdgHb27FnVsTNnznR7AFp8fHybkegdyczMZADYyZMne1zf3uhtrK2qqqqYSCRiX3/9NWPsr0GFycnJqjIlJSV6H1SoaZxSqZTNnDmTBQcHs4qKim69V1+36YgRI9iyZcvUjgUGBnY6qDAwMFDtWEJCQptBhVOmTFErExcXp/cBaJrEyRhje/bsYRYWFuzAgQPdeg+FQsGioqLYs88+25uq9lpPYn3QrFmzWGxsrOp7U2lTxv4aRJmZmdnlexhKm+oCJQR9JC4ujg0dOpSlpaWxtLQ0Fhoa2maKmr+/P9u/f7/asZqaGmZlZcU+++yzNue8du0aW79+PTt//jwrKChghw4dYgEBASw8PFxvU/EY0zxWiUTC/v73v7PU1FRWUFDAjh8/zmJiYpiHhwerra1VvSYhIYF5enqyX3/9lV28eJGNGzdO79MONYlTJpOx6dOnM09PT3b58mW1KUzNzc2MMcNo09apW9u2bWPZ2dls1apVzNraWjXyes2aNWzBggWq8q3TDl9++WWWnZ3Ntm3b1mba4e+//854PB575513WE5ODnvnnXcMZopad+Pcs2cP4/P57NNPP+1wSmhiYiI7cuQIu379Ort06RJ79tlnGZ/PV0sc9UHTWD/88EN24MABlpeXx7KystiaNWsYAPbDDz+oyphCm7Z65pln2MiRI9s9p6G2qS5QQtBH7ty5w+bPn89sbW2Zra0tmz9/fpspPQDYjh071I598cUXzNLSst156IWFheyRRx5hDg4OTCgUskGDBrGXXnqpzfz9vqZprA0NDWzSpEnMycmJCQQC5u3tzeLj41lhYaHaaxobG9ny5cuZg4MDs7S0ZNOmTWtTpi9pGmdBQQED0O7j+PHjjDHDadNPP/2U+fj4MKFQyCIiItR6J+Lj49mYMWPUyp84cYKFh4czoVDIBgwY0G4C+9133zF/f38mEAhYQECA2sVFXzSJc8yYMe22XXx8vKrMqlWrmLe3NxMKhczJyYlNmjSJpaam9mFEHdMk1nfffZcNGjSIWVhYsH79+rHRo0ezQ4cOtTmnsbcpY8reR0tLS7Z169Z2z2fIbapttP0xIYQQQmjpYkIIIYRQQkAIIYQQUEJACCGEEFBCQAghhBBQQkAIIYQQUEJACCGEEFBCQAghhBBQQkAIIYQQUEJACCGEEFBCQAghhBBQQkAIIYQQUEJACCGEEAD/DzTCNz7wgJVfAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Planar paths for the Reeds-Shepp car\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys');\n", "savefig(fig,'ReedsSheppPaths_Planar.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The actual three dimensional backtracked geodesics are smooth, as illustrated in the next cell. However these paths feature a vertical tangent, aligned with the angular axis, at some points. The projections of these points appear as cusps in the two dimensional representation." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.046010Z", "iopub.status.busy": "2024-04-30T08:51:33.045894Z", "iopub.status.idle": "2024-04-30T08:51:33.211292Z", "shell.execute_reply": "2024-04-30T08:51:33.210994Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(); ax = plt.axes(projection='3d'); SetTitle3D(ax,\"Minimal paths for the Reeds-Shepp car\")\n", "for geodesic in hfmOut['geodesics']:\n", " if geodesic.shape[0]==1: continue # Eliminate the geodesic starting in an obstacle.\n", " plt.plot(*geodesic)\n", " if hfmIn.mode=='cpu':ax.scatter(*geodesic[:,-1])\n", "savefig(fig,'ReedsSheppPaths.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because the Reeds-Shepp car makes no distinction between the forward and the reverse gear, it makes sense to cut the angular domain in half. More precisely, we can identify opposite directions: $\\theta \\sim \\theta + \\pi$, for each angle $\\theta$. \n", "In that case, the computation takes place on the quotiented domain\n", "\\begin{equation*}\n", " U \\times \\mathbb P^1,\n", "\\end{equation*}\n", "where $\\mathbb P^1 = \\mathbb R/\\pi \\mathbb Z$ denotes the one-dimensional *projective* space. In other words $\\mathbb P^1= [0,\\pi[$ with periodic boundary conditions. \n", "\n", "Since the angular domain is cut in half, the number of angular directions can also be divided by two, which speeds up the computation. Note that this projective quotient makes no sense for the other models (Reeds-Shepp forward, Euler-Mumford elastica, and Dubins car) implemented in the HFM library. Indeed, they lack the reverse gear." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.212969Z", "iopub.status.busy": "2024-04-30T08:51:33.212854Z", "iopub.status.idle": "2024-04-30T08:51:33.214688Z", "shell.execute_reply": "2024-04-30T08:51:33.214445Z" } }, "outputs": [], "source": [ "hfmIn['projective']=1 # Identify opposite orientations : theta ~ theta + pi.\n", "hfmIn.nTheta=nTheta # nTheta is the number of points for discretizing [0,2*pi]" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.216101Z", "iopub.status.busy": "2024-04-30T08:51:33.216005Z", "iopub.status.idle": "2024-04-30T08:51:33.218014Z", "shell.execute_reply": "2024-04-30T08:51:33.217779Z" } }, "outputs": [ { "data": { "text/plain": [ "(200, 100, 30)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hfmIn.shape" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.219393Z", "iopub.status.busy": "2024-04-30T08:51:33.219289Z", "iopub.status.idle": "2024-04-30T08:51:33.568154Z", "shell.execute_reply": "2024-04-30T08:51:33.567850Z" }, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.31984 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geodesic backtraced from a tip $(x^*,\\theta^*)\\in U \\times \\mathbb S^1$ is sometimes identical to the one of the non-projective model, and sometimes distinct. \n", "Indeed, the projective model implicitly selects the shortest geodesic among those emanating from $(x^*,\\theta^*)$ and from $(x^*,\\theta^* +\\pi)$. Interestingly, doing so tends to reduce the number of cusps." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.569836Z", "iopub.status.busy": "2024-04-30T08:51:33.569721Z", "iopub.status.idle": "2024-04-30T08:51:33.637842Z", "shell.execute_reply": "2024-04-30T08:51:33.637576Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.639389Z", "iopub.status.busy": "2024-04-30T08:51:33.639277Z", "iopub.status.idle": "2024-04-30T08:51:33.641116Z", "shell.execute_reply": "2024-04-30T08:51:33.640857Z" } }, "outputs": [], "source": [ "# Restore the non-projective parameters.\n", "hfmIn.pop('projective',None);\n", "hfmIn.nTheta=nTheta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.2 The Reeds-Shepp forward model (without reverse gear)\n", "\n", "The Reeds-Shepp forward model cannot shift into reverse gear, and thus the planar projections of its paths feature no cusps. However, it has another distinguishing feature: in place rotations, without physical motion, of the car. In terms of curvature, these can be regarded as Dirac masses. They are admissible within the Reeds-Shepp forward model since the cost $\\mathcal C(\\kappa) := \\sqrt{1+(\\xi \\kappa)^2}$ only grows linearly with the curvature $\\kappa$." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.642530Z", "iopub.status.busy": "2024-04-30T08:51:33.642428Z", "iopub.status.idle": "2024-04-30T08:51:33.643989Z", "shell.execute_reply": "2024-04-30T08:51:33.643766Z" } }, "outputs": [], "source": [ "hfmIn['model']='ReedsSheppForward2'\n", "hfmIn['xi']=0.3" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:33.645397Z", "iopub.status.busy": "2024-04-30T08:51:33.645309Z", "iopub.status.idle": "2024-04-30T08:51:34.033973Z", "shell.execute_reply": "2024-04-30T08:51:34.033628Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.352431 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Minimal paths for the Reeds-Shepp forward model typically feature an in-place rotation at the seed and at the tip. As a result, the tangent at these endpoints does not appear to be the prescribed one." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:34.035665Z", "iopub.status.busy": "2024-04-30T08:51:34.035550Z", "iopub.status.idle": "2024-04-30T08:51:34.100550Z", "shell.execute_reply": "2024-04-30T08:51:34.100285Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Planar paths for the Reeds-Shepp *forward* car\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys');\n", "savefig(fig,'ReedsSheppForwardPaths_Planar.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the three dimensional visualization of the paths, in place rotations appear as vertical segments, parallel with the axis of the angular coordinate $\\theta$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:34.102109Z", "iopub.status.busy": "2024-04-30T08:51:34.101998Z", "iopub.status.idle": "2024-04-30T08:51:34.259905Z", "shell.execute_reply": "2024-04-30T08:51:34.259638Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(); ax = plt.axes(projection='3d'); SetTitle3D(ax,\"Minimal paths for the Reeds-Shepp *forward* car\")\n", "for geodesic in hfmOut['geodesics']:\n", " if geodesic.shape[0]==1: continue # Eliminate the geodesic starting in an obstacle.\n", " plt.plot(*geodesic)\n", " if hfmIn.mode=='cpu':ax.scatter(*geodesic[:,-1])\n", "savefig(fig,'ReedsSheppForwardPaths.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.3 Euler-Mumford elastica curves\n", "\n", "Minimal paths for this model are smooth, and have a \"natural feel\", since they are related to the equilibrium rest positions of an elastic bar. Computation time is slightly longer than for the Reeds-Shepp models, due to the larger stencils involved." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:34.261625Z", "iopub.status.busy": "2024-04-30T08:51:34.261522Z", "iopub.status.idle": "2024-04-30T08:51:34.263253Z", "shell.execute_reply": "2024-04-30T08:51:34.263005Z" } }, "outputs": [], "source": [ "hfmIn['model']='Elastica2'\n", "hfmIn['xi']=0.2" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:34.264695Z", "iopub.status.busy": "2024-04-30T08:51:34.264598Z", "iopub.status.idle": "2024-04-30T08:51:37.700686Z", "shell.execute_reply": "2024-04-30T08:51:37.700333Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 3.34521 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:37.702330Z", "iopub.status.busy": "2024-04-30T08:51:37.702233Z", "iopub.status.idle": "2024-04-30T08:51:37.772428Z", "shell.execute_reply": "2024-04-30T08:51:37.772140Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Planar paths for the Euler-Mumford elastica model\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "plt.axis('equal');\n", "savefig(fig,'EulerElasticaPaths_Planar.png')" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:37.774028Z", "iopub.status.busy": "2024-04-30T08:51:37.773923Z", "iopub.status.idle": "2024-04-30T08:51:37.930188Z", "shell.execute_reply": "2024-04-30T08:51:37.929907Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(); ax = plt.axes(projection='3d'); SetTitle3D(ax,\"Minimal paths for the Euler-Mumford elastica model\")\n", "for geodesic in hfmOut['geodesics']:\n", " if geodesic.shape[0]==1: continue # Eliminate the geodesic starting in an obstacle.\n", " plt.plot(*geodesic)\n", " if hfmIn.mode=='cpu':ax.scatter(*geodesic[:,-1])\n", "savefig(fig,'EulerElasticaPaths.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.4 The Dubins car\n", "\n", "The Dubins car model features a hard constraint: the radius of curvature of admissible paths must be bounded by the value $\\xi$ prescribed by the user. " ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:37.931850Z", "iopub.status.busy": "2024-04-30T08:51:37.931741Z", "iopub.status.idle": "2024-04-30T08:51:37.933405Z", "shell.execute_reply": "2024-04-30T08:51:37.933191Z" } }, "outputs": [], "source": [ "hfmIn['model']='Dubins2'\n", "hfmIn['xi']=0.2" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:37.934790Z", "iopub.status.busy": "2024-04-30T08:51:37.934704Z", "iopub.status.idle": "2024-04-30T08:51:39.428937Z", "shell.execute_reply": "2024-04-30T08:51:39.428508Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 1.423 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Arguments from control theory show that the minimal geodesic paths are the concatenations of straight lines, and of arcs of circles of radius $\\xi$. This qualitative property seems to be satisfied by the backtracked geodesics, although it is in no way directly encoded in the HFM software." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:39.430877Z", "iopub.status.busy": "2024-04-30T08:51:39.430728Z", "iopub.status.idle": "2024-04-30T08:51:39.504984Z", "shell.execute_reply": "2024-04-30T08:51:39.504677Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Planar paths for the Dubins car\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys');\n", "savefig(fig,'DubinsPaths_Planar.png')" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:39.506628Z", "iopub.status.busy": "2024-04-30T08:51:39.506498Z", "iopub.status.idle": "2024-04-30T08:51:39.664901Z", "shell.execute_reply": "2024-04-30T08:51:39.664606Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(); ax = plt.axes(projection='3d'); SetTitle3D(ax,\"Minimal paths for the Dubins model\")\n", "for geodesic in hfmOut['geodesics']:\n", " if geodesic.shape[0]==1: continue # Eliminate the geodesic starting in an obstacle.\n", " plt.plot(*geodesic)\n", " if hfmIn.mode=='cpu':ax.scatter(*geodesic[:,-1])\n", "savefig(fig,'DubinsPaths.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "The attentive reader will however note the presence of two geodesics, among the 24 extracted, that clearly *fail* the curvature bound constraint. These geodesics correspond to particularly difficult configurations, and two different reasons for failure can be identified. \n", "* The first incorrect path (blue) ends at a tip, located in a corner of the domain, that is mathematically *unreachable*. In other words, there is no path reaching this point from the seeds and which radius of curvature is bounded by the prescribed constant $\\xi$. A better answer, from the HFM library, would be not to backtrack anything in this case. *Note : this issue is specific to the CPU eikonal solver. The GPU eikonal solver (correctly) discards this path*\n", "* The second incorrect path (green) slightly violates the imposed curvature bound. An admissible path exists, but it is quite long and convoluted. Because the non-holonomy constraint numerically implemented by penalization, the HFM library did not detect it and selected this erroneous path instead. " ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:39.666580Z", "iopub.status.busy": "2024-04-30T08:51:39.666467Z", "iopub.status.idle": "2024-04-30T08:51:39.724656Z", "shell.execute_reply": "2024-04-30T08:51:39.724391Z" } }, "outputs": [ { "data": { "image/png": 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OROvWrXHr1i2EhYUBgMEpoJoaOnQohg0bhldeeQW5ubno168f/v77byxduhTdunXDlClTjN5mmc6dO2Pnzp1Yv349QkJCoFAo0L17d6O28fHHH2PEiBEYNmwYpk2bhhYtWiArKwtnzpzB8ePHDS6lrUxqaiqOHDkCIQTy8vL0ExNFR0fj+eefx1NPPaVft0ePHggICMDChQtRUlICZ2dnhIeH49ChQxVu29XVFc8++ywSEhLQvn177N69G59++imeffZZtG7d2qi2VqS2x9vX1xf/+te/sGLFChQUFOCxxx6Dk5MTYmNjkZGRgeXLlyMwMBD+/v549dVXIYSAi4sLfvjhB4OrkcjEyTumkUxNRSPHhRDi+eefFwDEf//7X4Pl7dq1EwDE33//Xe41p06dEg8++KBwcnISarVaBAcHi40bN9aojsquMggLCxMBAQFCo9GINm3aiJUrV4oNGzaUG8ldWFgoXn75ZdGqVSthY2Mj+vfvL06ePFmjqwwKCwvFzJkzhbu7u5AkqcJR4ps2bRIAxFdffVWj9ghROqp+5MiR4ptvvhGdOnUSarVa+Pr6ijVr1pRb98033xS+vr5Co9GIDh06iE8//VQ/MvtOJ0+eFP369RO2trYCgOjfv78Q4p9R53/99ZfB+ne3NzIyUjz88MPCx8dHaDQa4erqKvr37y++//77attT2XuloKBAvPLKK8LHx0eoVCrh5eUlnn32WXH9+vUKvx81lZWVJcaNGyeaNWumPy5C/HOVwVtvvVXuNajgapPo6Ggxfvx44eHhIVQqlWjevLkYNGiQ+Oijj6qtAYD+oVAohKOjo+jcubN4+umnRWRkZIWvOX/+vAgNDRWOjo7C3d1dzJs3T+zatavCqww6deokDhw4ILp37y40Go3w8vIS//rXv8pdFXF3uxrjeAshxOeffy569OghrK2thb29vejWrZvBz3RsbKwYOnSocHBwEM7OzuLRRx8VCQkJ5eotey+np6fXaL/UOCQh6jgslsgCjR07FkeOHMGVK1cMTpVUxdfXF0FBQfjxxx8buDoiIuPxlAFRDRUWFuL48eOIiopCeHg41qxZU+MwQERk6hgIiGooOTkZffv2haOjI5555hnMmzdP7pKIiOoNTxkQERERLzskIiIiBgIiIiICAwERERHBTAYV6nQ6JCUlwcHBgVNdEhERGUHcnkTL29sbCkXl/QBmEQiSkpIqnT+biIiIqpeYmFjlDarMIhCUzS9+8eLFWs81TlRXx44dw+rVq3Hq1CmMGzcOY8aMQUhIiNxlERFVKS8vD23btq3289MsAkHZaQIHBwc4OjrKXA1ZKjs7O1hZWUGhUECj0cDOzo7vRyIyG9WdcuegQiIiImIgICIiIgYCIiIiAgMBERERgYGAiIiIwEBAREREYCAgIiIiMBAQERERGAiIiIgIDAREREQEBgIiIiICAwERERGBgYCIiIjAQEBERERgICAiIiIwEBAREREYCIiIiAgMBERERAQGAiIiIgIDAREREYGBgIiIiMBAQERERGAgICIiIjAQEBERERgIiIiICICV3AWQeRNCICnnFi6k5eNSej4upucjNbcQ128W4frNYmh1AiqlAiqlBLVSAScbFbybWcPLyRpeThp4O1nD28karV1sobZiPiUikgsDARktLuMm9p1Lx5G464hJysX1m8XGbSCh/CKVUkKgpwOCvB3Qw9cZPX2bwc1eUz8FExFRtRgIqFpCCMQk5WHP6VTsO5eBuMybBs9bKSS0cbNDWw87tHW3g7eTNVzsVHC2VcNKIaFYq0OxVqBIq0NWfhGScwqRlHMLybcfV7MLcKNQi1NJuTiVlIutR68BANq626GfvwtGdW6OIG8HSJIkR/OJiCwCAwFVKiu/CN//nYIdJ5JwIS1fv1ylkNDD1xkD2ruia0snBHjaQ6NS1no/QggkXi/A6aQ8nLyagz/jruNs6g1cvH0KYvORRPi42ODhrt6Y1KMFHG1U9dE8IiK6AwMBGRBC4Gh8Nv73ZyL2n8tAsU4AADRWCgwOdMfQQHfc29YVDtb199aRJAmtXWzR2sUWI4I8AQDXbxYj6sp1/BKbhl/PpiM+qwBr913Cp4euYFLPlpjauxVPKRAR1SMGAgJQGgT+uJSF9w9cRvTVXP3yIG8HjO3mjZFBno36l7mzrQrDOnpgWEcP5BeW4Jcz6Qg7HI8Lafn49FA8Pj+SiCd6t8Ks+3xhp+HbmIiorviblHDqWi5W/XIBR+OzAQBqpQIPd/XCpB4tENDcQd7iANhprPBwVy+M6dIcB85n4KODV/D3tVx8eigeP/ydgldC22F4Jw+OMSAiqgMGAguWW1CMtyIuYvvxJAClQeCxHi0ws58P3B1MrzteoZAwKNAdAwPcsO9cBlbuOY+r2bfw/Dcx2HbMGUtGBqCNm53cZRIRmSUGAgt18EIm/vVdLNJvFAEAxnRpjucH+6O5k7XMlVVPkiQMDnRHP38XfPZHPD49FI8jcdfxyEdRWDS8PcaHeLO3gIjISAwEFqawWIt39l7C538mAgB8XW3xn9GB6O7jLHNlxrNWKTF3QBs8FOyFJT+cxeHLWVj641kcupiJ10d3gLMtr0YgIqopTg1nQVJybuGxsGP6MDC5Z0t8O6unWYaBO7V0tsFnj3fFK6HtoFJIiDibjkc/icK51Btyl0ZEZDYYCCzE31dz8OinfyE2OQ/Otip8NCkYix8IgHUd5g8wJQqFhCf7tsa2p3qglbMNrmbfwmOfHcW+s+lyl0ZEZBYYCCzAj6dSMGXTcaTfKEI7Dztsf6oHBrR3k7usBtHRywFfP9UDvf2ccbNYi3nbTmF3TKrcZRERmbxaBYJ169bBz88P1tbWCAkJwcGDB6tc/8svv0RwcDBsbW3h5eWFJ598EpmZmbUqmGpOpxN4b98lLNxxGoUlOgxs74atM7qjpbON3KU1KGdbFT59vCvGBDeHVggs3BGD76OT5S6LiMikGR0Itm3bhgULFuC1117DiRMncN9992HEiBFISKjgjjUADh06hCeeeAIzZszA6dOnsX37dvz111+YOXNmnYunygkh8Pruc1j3+xUAwMx+PvhgYhfYW8gkPiqlAm+M6Yix3bygE8Ar4bE8fUBEVAWjA8GaNWswY8YMzJw5Ex06dMDatWvRqlUrrF+/vsL1jxw5Al9fX8yfPx9+fn6499578cwzz+Do0aN1Lp4qJoTAG3vO46uj1yAB+M/oDlg4tC2UCsu6FE+pkLDiwQ54pKsXBIAXd8QgJim32tcREVkiowJBUVERjh07htDQUIPloaGhOHz4cIWv6du3L65evYrdu3dDCIHU1FR88803GDlyZO2rpiqt2XsJ//vzKgDgP2M6YNw93jJXJB+FQsLyBwPRz98FBcU6PLslGknZt+Qui4jI5BgVCDIyMqDVauHp6Wmw3NPTEykpKRW+pm/fvvjyyy8xYcIEqNVqNG/eHM2aNcP7779f6X4KCwuRm5tr8KCaCT+ZjE//iAcALB8ViLHdLDcMlFEpFVj7aGe097BH+o0izPkqGreKtXKXRURkUmo1qPDuWeCEEJXODBcbG4v58+djyZIlOHbsGPbs2YO4uDjMmjWr0u2vXLkSTk5O+kerVq1qU6bF+ftqDpb+cBYAMLu/HyZ0byFzRabDwdoKH08OhoutCmdSbmDVzxfkLomIyKQYFQjc3NygVCrL9QakpaWV6zUos3LlSvTr1w8vvfQSunTpgmHDhmHdunUICwtDcnLFI78XLVqEnJwc/SMxMdGYMi1Sel4h5m47hSKtDoMD3DC3v5/cJZkcLydrvDW2EwBg69FriLycJXNFRESmw6hAoFarERISgoiICIPlERER6Nu3b4WvuXnzJhQKw90olaWT4QghKnyNRqOBo6OjwYMqV6zVYf7Xp5CWVwh/N1usergTFBY2gLCm+vm74rHbPSevfXcGN26VyFwREZFpMPqUwQsvvIDPPvsMYWFhOHPmDJ5//nkkJCToTwEsWrQITzzxhH79Bx98EDt37sT69etx+fJl/PHHH5g/fz569uwJb2+e364P636Lw4nEHDhorPDhY8Gwt7aMSwtra+HQtmjRzBpJObfw9t6LcpdDRGQSjP7kmDBhAjIzM/H6668jOTkZQUFB2L17N3x8fAAAycnJBnMSTJs2DXl5efjggw/w4osvolmzZhg0aBBWrVpVf62wYMcTsvHxwSsAgBWjA+HraitvQWbATmOF/47pgGmbT+DrY9fweM+WaOthL3dZRESyqtWfkrNnz8bs2bMrfG7Tpk3lls2bNw/z5s2rza6oCjeLtFi44zR0ovT2xcM7VTyOg8rr7eeCIYHu2Hs2He/uu4z3J3aRuyQiIlnxXgZm7KPf45CUcwveTtZY/ECA3OWYnQWD2kAhARFn03GaExYRkYVjIDBTl9LzsfFw6amZ10a057iBWmjrYY8Rt3tVNkZWPPU2EZGlYCAwQ0IIvL7rHIp1AgPau2FQQNO8c2FjmN63NQDgp5g0XMsukLkaIiL5MBCYoV0xqfjzynVorBT494j2lU4KRdXr5O2I3n7O0AqBr/66Jnc5RESyYSAwM0UlOqzZewkA8Mx9vk3+VsaN4fGepTNh7jiRhBKtTuZqiIjkwUBgZnaeSEJSzi2426vxZJ/WcpfTJAxo74pmNipk3SzGsYQcucshIpIFA4EZKSzWYv3vVwAAT93rCxu1Ut6CmggrpUI/DiPiTJrM1RARyYOBwIx8fTwJqXmFaO6owYQQzvJYn4Z0cAcA7D2bXumU2kRETRkDgZkoLNbik9szEs66zxcaFXsH6lO/Ni6wVSmRkluImKQ8ucshImp0DARmYvvxJKTfKIKXowaPdGPvQH3TqJS4v50rAOAXnjYgIgvEQGAGikp0+PRQPADg6ft8obbiYWsIZacN9p1Nl7kSIqLGx08WM7Dt2DWk5hXC00GDsewdaDD3+rtCAnAp4ybS8grlLoeIqFExEJi4zBtFeG/fZQDAs/3ZO9CQmtmq0NbdDgBwJpnjCIjIsvDTxcS9s/ci8gpL0NHLAY/e00Lucpo8X7fS20fHZ3EaYyKyLAwEJuxEYg52nkwGACx+IABKBacobmi+LmWB4KbMlRARNS4GAhOl1Qms2HUOADC2mxe6tXKSuSLL4ON6OxBkMhAQkWVhIDBR249dQ2xKHhytrfDikLZyl2MxfFxK7w3BUwZEZGkYCExQ9s1i/N++0hsYzRvYBi52apkrshytb58yuJZdAJ2OMxYSkeVgIDBB7x+4jJyCErTzsMNj3TmQsDE526oAADoB5BWWyFwNEVHjYSAwMedTb+Crv64BAF4b3h5WSh6ixqS2UkBz+9LOGwwERGRB+GljQoQQeGPPeWiFwNAO7ujdxkXukiyS9vapAite1UFEFoSBwITsPZuOI3HXoVYq8EpoO7nLsUhanUDJ7UCgtuINpIjIcjAQmIjCYi1W/XwBADCjX2u0dLaRuSLLVFSi0/9frWQPARFZDgYCE7ExMhFXs2/B00GDp+71lbsci1U2kFAhQT+WgIjIEvA3nglIzrmFjw/GAQAWDm0LWzW7quWSlH0LAODpoOGATiKyKPyNZwJW/3IBBcU6dG/dDKM6e8pdjkVLyikNBN7NrGWuhIiocTEQyOzI5Sz8dDoNCgn49wPtIUk8by2nsh4CbyeO4SAiy8JAIKNirQ7/+ek8AGBi95YIbO4gc0V0Lbt0yuIW7CEgIgvDQCCjzZGJuJieD2dbFeYPbCN3OQTgckbpTY1au7CHgIgsCwOBTK5lF+DD3y4DAF4a2hbNbk+ZS/K6mH4DANDOw17mSoiIGhcDgUze+Om8fiDhw1295C6HAGTeKEJmfjEAoI2brczVEBE1LgYCGew7l45fz2XASiFh6agADiQ0EX/FXwcAtPOwg53GSuZqiIgaFwNBIyso0uK/twcSTuvTml3TJiTqSjYAoJevs7yFEBHJgIGgkX108AquZd+Cl6MGz97vK3c5dIeoK6U9BD0ZCIjIAjEQNKLL6fkI+yMeAPDaiAB2S5uQxKwCXEzPhwSgh08zucshImp0DASNRAiB13efQ7FOoH87VwwOdJO7JLrDt9HJAIC+/i5wtlPLXA0RUeOrVSBYt24d/Pz8YG1tjZCQEBw8eLDK9QsLC/Haa6/Bx8cHGo0G/v7+CAsLq1XB5urb6BQcibsOjZUC/x7BgYSmRKcT+kDwUDCv+CAiy2R0n/W2bduwYMECrFu3Dv369cPHH3+MESNGIDY2Fq1bt67wNePHj0dqaio2bNiAtm3bIi0tDSUlJXUu3lxk5RfhzZ9LBxLOHeCHVpz0xqT8eeU6rmXfgr1GiSGB7nKXQ0QkC6MDwZo1azBjxgzMnDkTALB27Vr8/PPPWL9+PVauXFlu/T179uC3337D5cuX4eLiAgDw9fWtW9Vm5q2Ii8gpKEGApz2m9ak4NJF8Pj54BQAwuktz2PBOk0RkoYw6ZVBUVIRjx44hNDTUYHloaCgOHz5c4Wu+//57dO/eHatXr0aLFi3Qvn17LFy4EAUFBZXup7CwELm5uQYPc/X31RyEnyztjl4+KhAq3lLXpPx15TqOxF2HSiFhRj8fucshIpKNUT0EGRkZ0Gq18PQ0vEWvp6cnUlJSKnzN5cuXcejQIVhbWyM8PBwZGRmYPXs2srKyKh1HsHLlSixfvtyY0kySTif0cw6MCW6Orq2cZK6I7iSEwNt7LwIAxt7jjRbNeCqHiCxXrf5cvXtAnBCi0kFyOp0OkiThyy+/RM+ePfHAAw9gzZo12LRpU6W9BIsWLUJOTo7+kZiYWJsyZff1sWuIvpYLW7USLwxuK3c5dJefY9MQfTUXNioFZvf3k7scIiJZGdVD4ObmBqVSWa43IC0trVyvQRkvLy+0aNECTk7//HXcoUMHCCFw9epVtGvXrtxrNBoNNBqNMaWZnPS8Qryz9xIAYMEgf3g6mnd7mprrN4uxYvc5AMCTfX3g4cDjQ0SWzageArVajZCQEERERBgsj4iIQN++fSt8Tb9+/ZCUlIQbN27ol50/fx4KhQItW7asRcnmYeXPF5BXWIJOXg6Y3LPpttNcvfXLBWTmF6Otux1m3ecrdzlERLIz+pTBCy+8gM8++wxhYWE4c+YMnn/+eSQkJGDWrFkASrv7n3jiCf36kyZNgqurK5588knExsbi999/x0svvYTp06fDxqZpnrM9eCETu2NSoZCA1x8MhFLBOQdMyZG4LOy8PdBzxegOUFtxoCcRkdGXHU6YMAGZmZl4/fXXkZycjKCgIOzevRs+PqUjtJOTk5GQkKBf397eHhEREZg3bx66d+8OV1dXjB8/Hv/5z3/qrxUmpKBIi+W7zgIApvRqhU7ejjJXRHdKzyvESztOAwAmhLRANw70JCICUItAAACzZ8/G7NmzK3xu06ZN5ZYFBgaWO83QVK3/PQ5Xs2+huaMG8wa2kbscukOxVofnv4lB+o0itHW3w8uhHOhJRFSGfaX16HzqDYQdLu0dWfxAAOx58yKT8s7eSzganw07tRLvTejMm0sREd2BgaCe6HQCS388ixKdwJBAdwzmFLgm5aujV7EpsjSsrXyoI9q42clcERGRaeGfSPVk+/EknEjMga1aiddGtJe7HLrDl1GJWLG7dIKop+/1QWhHD5krIiIyPQwE9SDjRiHeuT3j3XMD28DLyVrmiqjMpsgEvPnzBQDAk31a4/nB/jJXRERkmhgI6sGbP19A7q0SdOScAyZDqxP4v18v4bM/4gGU9gw8P9ift50mIqoEA0EdHbqYiR9P/TPngBVvXiS7G4UleGnHaew/nwEAmD+wDZ6935dhgIioCgwEdXCrWIvlu0qnv328ZysEcc4B2Z26lot/fRuLC+n5UCsV+O+YDniwS3O5yyIiMnkMBHXw0e9XkHi9AJ4OGswfxDkH5HSjsATv7buML6ISoROAm50aHz7WBcEtOfEQEVFNMBDU0oW0G9hw+/z0vx9ozzkHZLTvXDpW7DqH5NxCAMCozp54dVg7uNnzhkVERDXFT7Fa0OkElv14FsU6gUEBbhjCOQdkcSk9H2v3XULEmXQAQMtm1lg6KhD3tXWVuTIiIvPDQFALO04k4VhCDmxVSvx7RAAHqzWyi2k3sO73K/gpJhUCgFKS8GTf1pjT3w82aqXc5RERmSUGAiNl3ijC2xGlcw7MH9QG3s0450BjKNHqcOB8Jr46ehV/XMqCuL18SKA75g3wQ0BzB1nrIyIydwwERlr1ywXk3CpBh+b2eJxzDjQoIQT+vpaLPafTsCsmFWl5hfrnhnZwx+z7/dDBi0GAiKg+MBAY4fClLHz/dwokAK8/2IFzDtSzG7dKcOJqDk5dy0VMUi5OXctF+o0i/fMutiqMvccb4+9pgVYuNjJWSkTU9DAQ1FDpnANnAQCTe7ZE5xacc6C2rl44hfSTP6JIaY8iKztcu6XCsTQl9mY6o0CoDda1VSkxMMANwzt5oH87N6itGMKIiBoCA0ENfXzwCuKzCuDhoMGCQZwPvy4yLvyJPpfWGiybBqBErUC8oiUy7QOg9QiCg283tAzqDWsb3pmQTFNqamqdt+Hp6VkPlRDVHQNBDVxKz8dnh0rnHHhtRHvYW/PbVhe27q0QZT8YNrp8WOvyYY+bcNFlQVN0Hf4iAf55CUBeBHAJEIccoGs7HCU9noFo3lnu0on0wsLC6mU7QUFB6NmzZ71si6gu+MlWDZ1OYOkPpXMODGjvhtAOnHOgrtr3GAb0GGawTAiBW3nJUKSegpQaA0XqKSiSjkHKT4Py9HYoYndA220aSu5/FbDm7IMkr7CwMCxbtqxethUcHIzFixczFJDsGAiqEX4yGUcTsmGjUmDxA+0550BDkSTA0Rs6R2+g3TBoAUDoIF07Cqtjn0F55jtYHQ+D8uz3KB60DLpO40pfQ9QAqvvrv77CAABER0djxYoVePjhhytdh70I1BgYCKqQlV+E1REXAADzBrZBi2Yc2d6oJAVEy54obtkT2uDHYfXLIiiyLkL941xoY8NRPPojwJqDO6l+hYWFITw8vNLno6Oj632f1W0zPDycvQjU4BgIqrDqlwvIKShBoKc9nujVSu5yLJrO934UzdgPZdRHsPpjDZSXf4X0v5EoHvc/CGdfucsjM5aamor4+NIxQjExMfX6178xqgsFK1aswOLFi/Vf+/j4cEAi1SsGgkocuZyF76JL5xxY/mAg5xwwBUo1tH3mQ+c3AOodT0CReR7qzcNR9EgYROu+cldHZig1NRVr1qzRf71161YZq6la2amFjh07AgACAgIwcuRIhgKqNwwEFSgo0mLpj6VzDjzWoyVvoWtiRPMuKJz6c2koSD4J9VePovjBD6Hr8JDcpZEZKQsDphwC7hYdHV2uJ4GhgOoL/+ytwP/9ekk/58DzgznngEmy90TRpG+h7fAQJF0JVD/Og5QQKXdVZCbMMQxUZNmyZdi1a1e9zIdAxEBwlyNxWfj8z0QAwH9Hd4AD5xwwXSobFI9eD23Ag5C0RVDvmALp6l9yV0UmrqmEgTIMBVRf+Gl3hxu3SvCvb88AAMaHeOO+dq4yV0TVkhQoHvU+pJsZUCRGQv31BBQ9/gOERye5KyMTEhUVhZiYGADAuXPnmkwYKHP3QEhepki1wUBwmxACS344g6ScW2jZzBovh7aTuySqKZUNisZvgWr7ZCgTDkO180kUTf0ZsHGWuzIyAVFRUVixYoX+64a4bNAULFu2DMHBwQBKQw8AhgIyCgPBbZ8eisfu02mwUkhY9XAn2Gv4rTErKlsUP7wB0qZQKLLjYXVgBUpGrKn+ddSklYWBphoC7lbWzjvby1BANcUxBAB+O5+B//v1EgDg3yPaI8SnmbwFUe3YuKDkgXcBAFbRX0Jx6muZCyI5WVoYuNvWrVuxY8cOREVFyV0KmQmLDwSXM/Lx4o4YCAATQlpgYo+WcpdEdaDz6YeSvi8AAFQRi4C8ZJkrIjlYehgow1BAxrDoQHCjsARzv/obNwq1CGnthNdGtJe7JKoHJfe9BJ33PZCKbkC1ewEghNwlUSNiGDDEUEA1ZbGBoFirw8Idp3E54yY8HTR4d3xnqK0s9tvRtEgKFA9/B8LKGsq4A1DE7Ze7ImokDAMVYyigmrDYT8BVP1/AgfMZ0Fgp8O74znCz18hdEtUj4dER2i6PAQCUp7bJXA01BoaBqjEUUHUscij97xcy8EXUVQDAmnFB6NqKUxM3RdpO42B1fCMUl38FSgoBK4a+pophoGbunH+BVx/Q3Syuh+BK5k0s3HEaADC5Z0sMDnSXuSJqKMKrK4SDF6TCPCj/3iJ3OdSAYmJiGAZqKDY2Vu4SyERZVCAoKtHhhe0xyL1Vgm6tnPAKJx9q2hRWKOnzHADA6vDa0l4CIiKqUK0Cwbp16+Dn5wdra2uEhITg4MGDNXrdH3/8ASsrK3Tt2rU2u62zd/ZeRGxKHprZqLD2UQ4itATaLpMg7Nwh3UiB4tpRucuhBpCamqqfmY+qFx0djZiYGN77gMox+hNx27ZtWLBgAV577TWcOHEC9913H0aMGIGEhIQqX5eTk4MnnngCgwcPrnWxdfH7hQxsPlJ606I3HuoAT0eeT7YIVhroWvYCAEhX/5S5GKpvTe1GRY2FN0SiihgdCNasWYMZM2Zg5syZ6NChA9auXYtWrVph/fr1Vb7umWeewaRJk9CnT59aF1tb6XmFeCW89LzZ5J4tMSiA4wYsic5vAABAGfebrHVQ/WIYqBuGArqbUYGgqKgIx44dQ2hoqMHy0NBQHD58uNLXbdy4EZcuXcLSpUtrtJ/CwkLk5uYaPGpLCIHFP5zF9ZvFCPS0x8tD29Z6W2SedJ6dAQDS9cv1ul0fH5963R7VHMNA/WAooDsZddlhRkYGtFotPD09DZZ7enoiJSWlwtdcuHABr776Kg4ePAgrq5rtbuXKlVi+fLkxpVUq/GQyDpzPgEopYdUjnaBRKetlu2Q+hLMfAEDKTwMKbwAa+1ptp2fPnli8eDFiYmIwcuTIcj8H1DgYBupX2a2T+Z6mWo2qkyTJ4GshRLllAKDVajFp0iQsX74c7dvXfFrgRYsWIScnR/9ITEysTZlIyr6FN/acBwDMH9gGAZ61+yAgM2ftBGHjCgCQsq/UaVM9e/bE9OnT+YtTRvHx8bx0rp5xUCYBRvYQuLm5QalUlusNSEtLq/AXZF5eHo4ePYoTJ05g7ty5AACdTgchBKysrPDLL79g0KBB5V6n0Wig0dRt0J9OJ/Dad7G4UahFcEtHTO/L7l1LJlz8IF3LhHT9MoRnkNzlEBGZHKN6CNRqNUJCQhAREWGwPCIiAn379i23vqOjI06dOoWTJ0/qH7NmzUJAQABOnjyJXr161a36Kmw9ehWRcddhbaXAqoc7Qako34NBlkM0u33aIKt+xxFQ4+MkRPUvNjYWu3btkrsMkpnRUxe/8MILmDJlCrp3744+ffrgk08+QUJCAmbNmgWgtLv/2rVr+Pzzz6FQKBAUZPjXmIeHB6ytrcstr0+XM/LxdsRFAMDCoW3h62rbYPsi86BzaQMlAOl6nNylUB2EhYXpz3lT/bkzYE2fPl3GSkhORgeCCRMmIDMzE6+//jqSk5MRFBSE3bt360dcJycnVzsnQUMqKtFh4TenUVCsQx8/Z0zq0VK2WsiEOHgBAKT8dJkLodpiGGhYZaEgKCiI9zmwULW6udHs2bMxe/bsCp/btGlTla9dtmxZg/5Qr913ST8b4ZsPd4KCpwoIgCi7sZGW0xcTEVWkSc3de/hSFsIOl/ZO/HcMZyOkOyhL3wuStkjmQoiITFOTCQTX84vwSnjpXQwnhLTgXQzJUEnB7f80mbc8EVG9ahK/HYUQ+Pf3Z5B+owht3Gzx6jDexZAMKVJjAAA6jw4yV0JEZJqaRCAIP5mMX89lQKWQ8PbYINioORshGZKyS08lCdeaT5BFRGRJzD4QGMxGOKgNOno5yFwRmaSiPACAUHO2SiKiiph1INDpSk8VcDZCqo4iq3T+AeHUSuZKiExbTEyM3CWQTGp12aGp+OroNRy+nAVrKwXefIizEVIlbqRCyk2EgATh0VHuaqgWOAdB4+AERZbNbANBWl6hfjbCF4e2hZ8bZyOkiiniDwEARPMugLWTzNWQsRgGGhdDgeUy21MGHx6Iw81iLYJbOGIyZyOkKiiyLgEAdM2DZa6EjJWamso78cmA94qwTGYZCC6n5+Ob40kAgJdD23E2QqqSlFL6y004MTgSEVXGLAPBRwevQCsEBgW4IcSnmdzlkCnLT4fi8n4AgC5glMzFEBGZLrMLBFevF2DXqVQAwOz+fjJXQ6ZOEfcbJKGFzrMzhIu/3OUQEZksswsEmyIToBUCfdu4IMjbUe5yyMQprh4BAOh87pW5EiIi02ZWgeBmYQl2nkgGAMzsxzkHqHqKxNuBoFVvmSshIjJtZhUI9p3PwM1iLXxcbNCnjbPc5ZCpy0+HIvMCAEDXspfMxRARmTazCgQ/xaQBAB7u6gVJ4pUFVDVF4p8AAJ17IGDDAElEVBWzCgTHErIBACM6ecpbCJkF5cVfAAC61v1kroSIyPSZVSAo0Qn4utrCx5WzElI1hA6KSxEAAC0vNyQiqpZZBQIAuL+tq9wlkBmQUv6GVJAFobKFaNFD7nKIiEye2QUCTkRENaGM3QkA0PkPAZQqmashIjJ9ZhcIOjTn/eypGjotlLHhAABtp3EyF0NEZB7MKhDYqBVo2cxG7jLIxEkp0ZDy0yA0TtC1GSh3OUREZsGsAkF7d3veyIiqpUg4DADQte4DKNUyV0NEZB7MKxB42sldApkBRWIkAEDXqo/MlRARmQ+zCgStXXi5IVVDp4Xi6u0JiVr3lbkYIiLzYVaBwN2e3b9UNSktBlJhHoTGEcKjk9zlUB15enoiICAAwcHBcpdiUYKDgxEUFCR3GdTIrOQuwBiuDARUDUXC7dMFLXsCCqXM1VB9mD59uv7/0dHRMlZiGYKDg7F48WL07NlT7lKokZlVIHCzYyCgqv0zoJCnC5qSslDAQNCwGAYsm1mdMnC118hdApkyoftn/AAHFBIRGcWsAoGtml3AVDkp/QykW9kQajuI5l3kLoeIyKyYVSAgqoqUcR4ASgcTKszqbBgRkewYCKjJkK7HAQB0zm1kroSIyPwwEFCTobh+BQAgnP3kLYSIyAwxEFDTkZ8KABAO3jIXQkRkfhgIqMmQbmaV/sfWRd5CqMFwgiKihlOrQLBu3Tr4+fnB2toaISEhOHjwYKXr7ty5E0OHDoW7uzscHR3Rp08f/Pzzz7UumKhCQgcpO770v3aeMhdDDWH69Ol4+OGHGQoaCOcgIKMDwbZt27BgwQK89tprOHHiBO677z6MGDECCQkJFa7/+++/Y+jQodi9ezeOHTuGgQMH4sEHH8SJEyfqXDyRXlE+pMIcAIBw9Ze5GGooDAUNg2GAgFoEgjVr1mDGjBmYOXMmOnTogLVr16JVq1ZYv359heuvXbsWL7/8Mnr06IF27drhjTfeQLt27fDDDz/UuXgiveICAICABFjZyFwMNSTOsV//OnbsCB8fH7nLIJkZFQiKiopw7NgxhIaGGiwPDQ3F4cOHa7QNnU6HvLw8uLjwPC/VH6n4Zul/VDaAJMlbDBGRGTIqEGRkZECr1cLT0/AcraenJ1JSUmq0jXfeeQf5+fkYP358pesUFhYiNzfX4EFUpeL80n9VvEV2U+fj44OHH35Y7jKalICAgHK/18ny1GpQoXTXX2BCiHLLKrJ161YsW7YM27Ztg4eHR6XrrVy5Ek5OTvpHq1atalMmWZKyUwYMBE2ep6cnRo4ciWXLlsldSpOwbNkygztKkuUyKhC4ublBqVSW6w1IS0urNl1u27YNM2bMwNdff40hQ4ZUue6iRYuQk5OjfyQmJhpTJlkgg1MG1OQxFNQPhgG6k1GBQK1WIyQkBBEREQbLIyIi0Ldv5beb3bp1K6ZNm4YtW7Zg5MiR1e5Ho9HA0dHR4EFUpds9BAwEloOhoG4YBuhuRt8B5oUXXsCUKVPQvXt39OnTB5988gkSEhIwa9YsAKV/3V+7dg2ff/45gNIw8MQTT+Ddd99F79699b0LNjY2cHJyqsemkEVT25X+e4vjTSxJWSgAwGBgBIYBqojRgWDChAnIzMzE66+/juTkZAQFBWH37t36S1aSk5MN5iT4+OOPUVJSgjlz5mDOnDn65VOnTsWmTZvq3gKiOyl4i2xLw8FwxgkODualm1ShWt0jdvbs2Zg9e3aFz939IX/gwIHa7ILIKMK+OQBAyrkKaIsBpUrmioiIzAvvZUBNgnBpA6FxhFRSACnjnNzlUCMLCgrCY489JncZZoGTEFFlatVDQGRyJAV0zYOhjD8IRfJxaD3ZJWpJ7pxyd+vWrTJWYtoee+wxvPDCCzzNQhViIKAmQ3h3A+IPQko6DnR9Qu5yqJExFFSNYYCqw0BATYauRQ8AgPLK7ygROkDiGTFLw1BQMYYBqgmzCgQ3i7TgjARUGZ3v/RBqe0i51yAlHYO4HRDIsjAUGGIYoJoyqz+hNhyOl7sEMmVW1tC1Gw4AUJ75TuZiSE49e/bE2LFjLX6gIcMAGcOsAsH/jiTieEK23GWQCdMGjgYAKM98C5RNZ0wWydJDAcMAGcusThnoBPDSztPY8XRPNLPldeZUnq7NQOicWkGRkwjl0c+g7TNf7pJIRneePoiNjQUAREdHy1VOgwsODgZQemkhwwAZSxJCCLmLqE5ubi6cnJzQe9n3SC5QoH87V6x/LBgKBe97T+UpYr6B+sc5EBpHFM6KAmyc5S6JZBYVFaX/f0xMTJOc5njZsmX6GQh9fHwYBkgvNzcXnp6eyMnJqfLeQGbVQ7D64U6Y+fU5/HYhE58cuoJZ9/vJWk9RiQ5qK7M662IRdJ0egS5qHRRpp2F15AOUDFwsd0n1o/gmwNs718qdPQVlk/I0pVDAexNQfTCrT7OA5vZYMjIAAPDuvsv4LjpZtloup+dj0P/9gS+jEmEGnSyWRVKg5P5FAADlsQ3AjTSZC6o7xbld0HzSF1LySblLMXtN7S6JDANUX8wqEADA2G7eeLxnSwgAi76Nxe6Y1EavQQiBN/acR0Z+EQ5dzIIk8dSFqdH5D4HOOwRSSQFU+5bIXU6dSCmnoPpxDqS8ZChjd8pdTpPQVEIBwwDVJ7M6ZVDmX8Pbo7BEh+3Hk/DSjtOwUkgI7ejRaPvffz4Dhy5lQaWU8Oqwdo22XzKCJKE4dCXUm4dDGRsObeBo6No/IHdVxruZAfXOaZCKC6D1G4CSgeYdbkzJnbdOPneu9P4XsbGxJj3oMDg4GB07dgQABAQEMAxQvTKrQYWpqan6ARE6ncC/vjuDb6OTYaWQ8N6EzhgU4N7gtRSV6DDqwyNIuF6Ap+71wYtD2jb4Pqn2rPYtg1XUegi1HYqmH4Bo1lrukmruRhrUXz8GRVoMdM5tUDR1D2DtJHdVTU5q6j+9jPHx8VixYoVJhoLg4GAsXrxYPwaCgwappmo6qNBsAwEAaHUCr4Sfxo+nUqFSSvhgQhf0b+/WoLV8cvAK1vx6Ce72avw0rw/sNWbZyWI5tMVQbx0LxdU/oWveFUWTw81iYJ6Ufhaqb6ZAkZMAYeuGoknhEG7t5S7LIkRFRWHFihVVrtMQgaHsksHKLF682GBwJFFNWUQgAIASrQ4v7jiNn2PTYKWQ8MaYDhgd7NUgdew5nYpF38aioFiHVQ93xJgG2g/VLyk7HurNwyEVZEEbOBrFYz426fscKC5GQPX9LEhFN6Br5oPiCdsgnOW9osbS3HmZYkXquxeh7K//qjAMUG1ZTCAAgGKtDq+Gx2LX7QGGT9/rg6EdPBDgaV+nywKFECjRCdws0mL1Lxew40TpVQ33+rvgk8ldOQ+CGZESIqH+6lFIumKU9JmPkv6vyV1SeUJAGbUeVvtfhwQBXau+KHr4M8DWVe7K6C5lvQj1EQrKwgA/8KmhWFQgAErHFKz65QI2H0k0WH7nZ7aEf74ouzDA4CO97AsBaIWA7q7vjATgmft8MWeAH1RK0/0LkyqmOLUN6l2lMxcWD1gMbe+5Mld0h9wkqH55FcqLPwMASoIfR0noSkCplrkwqkxUVBRiYmLqvJ2goCCGAWpQFhcIyoSfTMbumFT8fS0HOQUl9VZDi2bWeGNMR/Ty46x35kz5xxqoDq4CAJT0mouSAa/JfvpAERsO1Z6FkIpuQChUKBm0FNqQmf+kViKiOrDYQFBGCIGs/GLobjdP6JcbrHXH+oavVyokWCkkKBQSlAoJtiolTxE0Eco/P4Rq/+sAAF2rvige+W7jX30gdJASj8Aq+ksoT39TWot3CIpHrIFwD2zcWoioSWuSUxcbQ5IkuNqzu5XK0/aaA2HnAdXPL0OReBjqsIEoGfIfaDtPbPi/ygvzYBX5LpQx2yHdSNEvLuk9FyX3/wtQKBt2/0RElWiyPQRE1ZGuX4Fq1zworpaOKNd5h0Ab/Di0gQ8CGof629HNDCgSjkCR8AeU53dBulE6+FVoHKFt/wC03aZCeN9Tf/sjIrqDxZ8yIKoRnRbKqHWwOvQ2pJJbAAChsoEuYDS0Pv0g3DtCuLUDrKyr3o62GLiZCelmBqTca5Cux0HKugTFtSgo0s8a7rKZL0oGLIau7VDAStNQLSMiAsBAQGScG2lQ/v0llKd3QJF5weApISkhXPwBW1cISVHarS8pSwNEfnppCLiVXeXmde6B0LXqC13rftD5DwZUNg3YGCKifzAQENWGEJCuHYXy7HdQpJ6GlH4G0q3rNXuppCwNDfaeEM5+EM6+0Hl2ga51H8C2YWfQJCKqjMUPKiSqFUmCaNkDJS17lH4tBHAjpbTbvygP0GkBoQV0OsBKDdi6Q9i5Qdi6ATbOsl/CSERUWwwERFWRJMDBCzoHTlNNRE0b/5whIiIiBgIiIiJiICAiIiIwEBAREREYCIiIiAgMBERERAQGAiIiIgIDAREREYGBgIiIiMBAQERERGAgICIiIpjJvQzKbsiYl5cncyVERETmpeyzs7qbG5tFIChrTNu2bWWuhIiIyDzl5eXBycmp0uclUV1kMAE6nQ5JSUlwcHCAJElyl9MgcnNz0apVKyQmJlZ5v+qmwFLaynY2PZbSVktpJ2AZbRVCIC8vD97e3lAoKh8pYBY9BAqFAi1btpS7jEbh6OjYZN+Ud7OUtrKdTY+ltNVS2gk0/bZW1TNQhoMKiYiIiIGAiIiIGAhMhkajwdKlS6HRaOQupcFZSlvZzqbHUtpqKe0ELKut1TGLQYVERETUsNhDQERERAwERERExEBAREREYCAgIiIiMBA0muvXr2PKlClwcnKCk5MTpkyZguzs7CpfI0lShY+33npLv86AAQPKPT9x4sQGbk3VatPWadOmlWtH7969DdYpLCzEvHnz4ObmBjs7O4wePRpXr15twJZUzdh2FhcX45VXXkHnzp1hZ2cHb29vPPHEE0hKSjJYzxSO6bp16+Dn5wdra2uEhITg4MGDVa7/22+/ISQkBNbW1mjTpg0++uijcuvs2LEDHTt2hEajQceOHREeHt5Q5deYMe3cuXMnhg4dCnd3dzg6OqJPnz74+eefDdbZtGlThT+zt27dauimVMuYth44cKDCdpw9e9ZgPXM/phX93pEkCZ06ddKvY8rHtN4JahTDhw8XQUFB4vDhw+Lw4cMiKChIjBo1qsrXJCcnGzzCwsKEJEni0qVL+nX69+8vnnrqKYP1srOzG7o5VapNW6dOnSqGDx9u0I7MzEyDdWbNmiVatGghIiIixPHjx8XAgQNFcHCwKCkpacjmVMrYdmZnZ4shQ4aIbdu2ibNnz4rIyEjRq1cvERISYrCe3Mf0q6++EiqVSnz66aciNjZWPPfcc8LOzk7Ex8dXuP7ly5eFra2teO6550RsbKz49NNPhUqlEt98841+ncOHDwulUineeOMNcebMGfHGG28IKysrceTIkcZqVjnGtvO5554Tq1atElFRUeL8+fNi0aJFQqVSiePHj+vX2bhxo3B0dCz3sys3Y9u6f/9+AUCcO3fOoB13/qw1hWOanZ1t0L7ExETh4uIili5dql/HVI9pQ2AgaASxsbECgMEPSmRkpAAgzp49W+PtjBkzRgwaNMhgWf/+/cVzzz1XX6XWWW3bOnXqVDFmzJhKn8/OzhYqlUp89dVX+mXXrl0TCoVC7Nmzp15qN0Z9HdOoqCgBwOAXltzHtGfPnmLWrFkGywIDA8Wrr75a4fovv/yyCAwMNFj2zDPPiN69e+u/Hj9+vBg+fLjBOsOGDRMTJ06sp6qNZ2w7K9KxY0exfPly/dcbN24UTk5O9VVivTG2rWWB4Pr165Vusyke0/DwcCFJkrhy5Yp+make04bAUwaNIDIyEk5OTujVq5d+We/eveHk5ITDhw/XaBupqanYtWsXZsyYUe65L7/8Em5ubujUqRMWLlwo622i69LWAwcOwMPDA+3bt8dTTz2FtLQ0/XPHjh1DcXExQkND9cu8vb0RFBRU4+9hfaqPYwoAOTk5kCQJzZo1M1gu1zEtKirCsWPHDL7PABAaGlppuyIjI8utP2zYMBw9ehTFxcVVriPHsQNq18676XQ65OXlwcXFxWD5jRs34OPjg5YtW2LUqFE4ceJEvdVdG3Vpa7du3eDl5YXBgwdj//79Bs81xWO6YcMGDBkyBD4+PgbLTe2YNhSzuLmRuUtJSYGHh0e55R4eHkhJSanRNjZv3gwHBwc88sgjBssnT54MPz8/NG/eHDExMVi0aBGio6MRERFRL7Ubq7ZtHTFiBB599FH4+PggLi4OixcvxqBBg3Ds2DFoNBqkpKRArVbD2dnZ4HWenp41/h7Wp/o4prdu3cKrr76KSZMmGdxURc5jmpGRAa1WC09PT4PlVX2fU1JSKly/pKQEGRkZ8PLyqnQdOY4dULt23u2dd95Bfn4+xo8fr18WGBiITZs2oXPnzsjNzcW7776Lfv36ITo6Gu3atavXNtRUbdrq5eWFTz75BCEhISgsLMT//vc/DB48GAcOHMD9998PoPLjbq7HNDk5GT/99BO2bNlisNwUj2lDYSCog2XLlmH58uVVrvPXX38BQIW3bRZC1Ph2zmFhYZg8eTKsra0Nlj/11FP6/wcFBaFdu3bo3r07jh8/jnvuuadG266Jhm7rhAkT9P8PCgpC9+7d4ePjg127dpULQcZs11iNdUyLi4sxceJE6HQ6rFu3zuC5xjqmVbm7DdW1q6L1715u7DYbQ21r2rp1K5YtW4bvvvvOIBj27t3bYDBsv379cM899+D999/He++9V3+F14IxbQ0ICEBAQID+6z59+iAxMRFvv/22PhAYu83GUtuaNm3ahGbNmuGhhx4yWG7Kx7S+MRDUwdy5c6sd/e3r64u///4bqamp5Z5LT08vl2YrcvDgQZw7dw7btm2rdt177rkHKpUKFy5cqNcPj8ZqaxkvLy/4+PjgwoULAIDmzZujqKgI169fN+glSEtLQ9++fWu83eo0RjuLi4sxfvx4xMXFYd++fdXecrWhjmlF3NzcoFQqy/1FlZaWVmm7mjdvXuH6VlZWcHV1rXIdY94T9ak27Syzbds2zJgxA9u3b8eQIUOqXFehUKBHjx7697Ec6tLWO/Xu3RtffPGF/uumdEyFEAgLC8OUKVOgVqurXNcUjmmDkWfogmUpG4D2559/6pcdOXKkxgPQpk6dWm4kemVOnTolAIjffvut1vXWRV3bWiYjI0NoNBqxefNmIcQ/gwq3bdumXycpKUn2QYXGtrOoqEg89NBDolOnTiItLa1G+2rsY9qzZ0/x7LPPGizr0KFDlYMKO3ToYLBs1qxZ5QYVjhgxwmCd4cOHyz4AzZh2CiHEli1bhLW1tQgPD6/RPnQ6nejevbt48skn61JqndWmrXcbO3asGDhwoP7rpnJMhfhnEOWpU6eq3YepHNOGwEDQSIYPHy66dOkiIiMjRWRkpOjcuXO5S9QCAgLEzp07DZbl5OQIW1tbsX79+nLbvHjxoli+fLn466+/RFxcnNi1a5cIDAwU3bp1k+1SPCGMb2teXp548cUXxeHDh0VcXJzYv3+/6NOnj2jRooXIzc3Vv2bWrFmiZcuWYu/eveL48eNi0KBBsl92aEw7i4uLxejRo0XLli3FyZMnDS5hKiwsFEKYxjEtu3Rrw4YNIjY2VixYsEDY2dnpR16/+uqrYsqUKfr1yy47fP7550VsbKzYsGFDucsO//jjD6FUKsWbb74pzpw5I958802TuUStpu3csmWLsLKyEh9++GGll4QuW7ZM7NmzR1y6dEmcOHFCPPnkk8LKysogOMrB2Lb+3//9nwgPDxfnz58XMTEx4tVXXxUAxI4dO/TrNIVjWubxxx8XvXr1qnCbpnpMGwIDQSPJzMwUkydPFg4ODsLBwUFMnjy53CU9AMTGjRsNln388cfCxsamwuvQExISxP333y9cXFyEWq0W/v7+Yv78+eWu329sxrb15s2bIjQ0VLi7uwuVSiVat24tpk6dKhISEgxeU1BQIObOnStcXFyEjY2NGDVqVLl1GpOx7YyLixMAKnzs379fCGE6x/TDDz8UPj4+Qq1Wi3vuucegd2Lq1Kmif//+BusfOHBAdOvWTajVauHr61thgN2+fbsICAgQKpVKBAYGGny4yMWYdvbv37/CYzd16lT9OgsWLBCtW7cWarVauLu7i9DQUHH48OFGbFHljGnrqlWrhL+/v7C2thbOzs7i3nvvFbt27Sq3TXM/pkKU9j7a2NiITz75pMLtmfIxrW+8/TERERFx6mIiIiJiICAiIiIwEBAREREYCIiIiAgMBERERAQGAiIiIgIDAREREYGBgIiIiMBAQERERGAgICIiIjAQEBERERgIiIiICMD/Ayiqtdu4ceX4AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[6,3]); plt.title(\"Two faulty paths for the Dubins car\"); plt.axis('equal'); \n", "geodesics = hfmOut['geodesics']\n", "for geo in [geodesics[0],geodesics[8]]: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next experiment, we cut the relaxation parameter $\\varepsilon$ in half, and we double the physical and angular grid scales, so as to better enforce the non-holonomy constraint. The blue path, leading to an unreachable tip, is eliminated as desired. The green path, formerly violating the curvature bound, is replaced with the adequate optimal admissible path.\n", "\n", "The increased grid dimensions, by a factor 2 in each of the three dimensions, however lead to an increase in time and memory complexity, by a factor $2^3=8$.\n", "Adressing the above issues with less computational overhead will be the object of future work, by enhancing the numerical scheme with e.g. anti-diffusive techniques." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:39.726623Z", "iopub.status.busy": "2024-04-30T08:51:39.726498Z", "iopub.status.idle": "2024-04-30T08:51:39.788371Z", "shell.execute_reply": "2024-04-30T08:51:39.788054Z" } }, "outputs": [], "source": [ "hfmIn2=hfmIn.copy()\n", "hfmIn2.update({\n", " 'dims':2*hfmIn['dims'],\n", " 'eps':0.05,\n", " 'gridScale':hfmIn['gridScale']/2\n", "})\n", "X2_2,Y2_2,_ = hfmIn2.Grid()\n", "X2_2,Y2_2 = X2_2[:,:,0],Y2_2[:,:,0],\n", "hfmIn2['walls']= np.logical_or((X2_2-0.3)**2 + (Y2_2-0.3)**2 <= 0.2**2,\n", " np.logical_and(X2_2==X2_2[2*70,0], Y2_2>=0.4)) " ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:39.790067Z", "iopub.status.busy": "2024-04-30T08:51:39.789972Z", "iopub.status.idle": "2024-04-30T08:51:59.826535Z", "shell.execute_reply": "2024-04-30T08:51:59.826169Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 19.6971 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n", "CPU times: user 1.61 ms, sys: 4.76 ms, total: 6.37 ms\n", "Wall time: 20 s\n" ] } ], "source": [ "%%time\n", "hfmOut = hfmIn2.Run() # Warning : takes up to a minute." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:59.828135Z", "iopub.status.busy": "2024-04-30T08:51:59.828034Z", "iopub.status.idle": "2024-04-30T08:51:59.892515Z", "shell.execute_reply": "2024-04-30T08:51:59.892209Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[6,3]); plt.title(\"Correct Dubins path\"); plt.axis('equal'); \n", "geodesics = hfmOut['geodesics']\n", "for geo in [geodesics[0],geodesics[8]]: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2_2,Y2_2,hfmIn2['walls'], cmap='Greys');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Varying the cost function\n", "\n", "The cost function $c : \\Omega = U \\times \\mathbb S^1 \\to ]0,\\infty[$ is arbitrary and chosen by the user. We considered a constant cost in the previous experiments, but a cost depending on the spatial coordinate, the angular coordinate, or both, is equally possible, as illustrated in the following experiments.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.1 Cost depending on the physical position\n", "\n", "In the next cell, the cost of motion is doubled in the lower half of the domain. Therefore, as we check numerically, minimal geodesics tend to avoid this region as much as possible." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:59.894110Z", "iopub.status.busy": "2024-04-30T08:51:59.894000Z", "iopub.status.idle": "2024-04-30T08:51:59.895961Z", "shell.execute_reply": "2024-04-30T08:51:59.895724Z" } }, "outputs": [], "source": [ "hfmIn['model']='Elastica2'\n", "hfmIn['cost'] = 1+(Y2<0.5)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:59.897347Z", "iopub.status.busy": "2024-04-30T08:51:59.897244Z", "iopub.status.idle": "2024-04-30T08:51:59.898914Z", "shell.execute_reply": "2024-04-30T08:51:59.898679Z" }, "tags": [ "TODO", "geodesic_targetTolerance_default_too_high" ] }, "outputs": [], "source": [ "if hfmIn.mode=='gpu': hfmIn['geodesic_targetTolerance']=6 # Otherwise one of the geodesics stops too early " ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:51:59.900279Z", "iopub.status.busy": "2024-04-30T08:51:59.900195Z", "iopub.status.idle": "2024-04-30T08:52:03.401877Z", "shell.execute_reply": "2024-04-30T08:52:03.401530Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 3.39174 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:03.403485Z", "iopub.status.busy": "2024-04-30T08:52:03.403392Z", "iopub.status.idle": "2024-04-30T08:52:03.475295Z", "shell.execute_reply": "2024-04-30T08:52:03.474999Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Euler-Mumford Elastica model with non-constant cost\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls']+0.1*hfmIn['cost'], cmap='Greys')\n", "savefig(fig,'Elastica_PositionDependentCost.png')" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:03.477112Z", "iopub.status.busy": "2024-04-30T08:52:03.476972Z", "iopub.status.idle": "2024-04-30T08:52:03.478610Z", "shell.execute_reply": "2024-04-30T08:52:03.478350Z" } }, "outputs": [], "source": [ "#hfmIn.pop('geodesic_targetTolerance',None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2 Orientation dependent speed\n", "\n", "We choose to model a sail-boat as a Reeds-Shepp forward car, with a speed depending on the current orientation relative to the wind." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:03.480028Z", "iopub.status.busy": "2024-04-30T08:52:03.479951Z", "iopub.status.idle": "2024-04-30T08:52:03.481875Z", "shell.execute_reply": "2024-04-30T08:52:03.481629Z" } }, "outputs": [], "source": [ "hfmIn['model']='ReedsSheppForward2'\n", "hfmIn2=hfmIn.copy()\n", "for key in ('cost','walls','seeds_Unoriented','seedValues_Unoriented'): \n", " hfmIn2.pop(key,None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More precisely, we assume that going directly against the wind is extremely slow, but that going sideways is much faster, as expressed by the following (synthetic) speed function. Wind comes from the right.\n", "\n", "Recall that *speed*, as an input field to the HFM library, is nothing else than the reciprocal of *cost*. " ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:03.483226Z", "iopub.status.busy": "2024-04-30T08:52:03.483125Z", "iopub.status.idle": "2024-04-30T08:52:03.484829Z", "shell.execute_reply": "2024-04-30T08:52:03.484576Z" } }, "outputs": [], "source": [ "hfmIn2['speed'] = 2-np.cos(2*Theta2)-0.4*np.cos(3*Theta2) #Speed function. speed = 1/cost." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:03.486165Z", "iopub.status.busy": "2024-04-30T08:52:03.486082Z", "iopub.status.idle": "2024-04-30T08:52:03.538659Z", "shell.execute_reply": "2024-04-30T08:52:03.538367Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[2,3]); plt.title(\"Orientation dependent cost\"); plt.axis('equal'); \n", "plt.scatter(0,0); # Polar plot of the speed function\n", "plt.plot(hfmIn2['speed']*np.cos(Theta2),hfmIn2['speed']*np.sin(Theta2));\n", "savefig(fig,'OrientationDependentCost.png')" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:03.540392Z", "iopub.status.busy": "2024-04-30T08:52:03.540253Z", "iopub.status.idle": "2024-04-30T08:52:03.931607Z", "shell.execute_reply": "2024-04-30T08:52:03.931279Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.361318 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn2.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We illustrate in the next cell the minimal path from the seed to the various tips. Interestingly, this path is far from straight, dispite the lack of obstacles and the fact that the cost function does not depend on the physical position.\n", "Indeed, the minimal geodesic goes in zig-zags from the seed (on the left) to the tips that are the right. In the context of sailboating, this is called *tacking*, and is what an actual sailboat would do." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:03.933426Z", "iopub.status.busy": "2024-04-30T08:52:03.933297Z", "iopub.status.idle": "2024-04-30T08:52:04.000061Z", "shell.execute_reply": "2024-04-30T08:52:03.999775Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Reeds-Shepp forward model with orientation dependent cost\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "savefig(fig,'ReedsSheppForward_OrientationDependentCost.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6. Generalized models with non-uniform curvature penalization\n", "\n", "The classical Reeds-Shepp, Reeds-Shepp forward, Euler-Mumford elastica and Dubins models penalize curvature in a uniform and fixed manner: penalization is the same for right turns and left turns, and it does not depend on the current position. This section is devoted to generalized models, which lift this restriction.\n", "\n", "For any point $(x,\\theta) \\in \\Omega$, and any tangent vector $(\\dot x, \\dot \\theta)\\in \\mathbb R^2 \\times \\mathbb R$ with physical velocity $\\dot x = (\\cos \\theta, \\sin \\theta)$, one defines\n", "\\begin{equation*}\n", " F_{(x,\\theta)} (\\dot x, \\dot \\theta) = c(x,\\theta)\\, \\mathcal C\\big( \\, \\xi(x,\\theta) (\\dot \\theta-\\kappa(x,\\theta)) \\, \\big).\n", "\\end{equation*}\n", "The fields $\\xi : \\Omega\\to ]0,\\infty[$ and $\\kappa : \\Omega \\to \\mathbb R$ are free and provided by the user. The first field, $\\xi$, locally determines the magnitude of curvature penalization. The second field, $\\kappa$, is used to break the symmetry between the right and left turns, if needed. These two fields be constant, depend on the physical position, the angular orientation, or both.\n", "\n", "As before, the metric $F$ is extended by $1$-positive homogeneity, and defined as $+\\infty$ where $\\dot x$ is not (positively) colinear with $(\\cos \\theta, \\sin \\theta)$. In addition, he colinearity constraint relaxed to $\\dot x = \\pm (\\cos \\theta, \\sin \\theta)$ in the case of the Reeds-Shepp model with reverse gear.\n", "\n", "These less common models are provided in a different executable. The memory usage of this implementation is slightly larger than for the usual models, because we cannot exploit any redundancy in the discretization stencils." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "source": [ "### 6.1 Position dependent radius of curvature\n", "\n", "In this experiment, we consider a Dubins car, subject to different bounds on the radius of curvature depending on depending on the domain region. Namely $\\xi=0.2$ on the lower part of the domain, and $\\xi=0.1$ on the upper part." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:04.001749Z", "iopub.status.busy": "2024-04-30T08:52:04.001632Z", "iopub.status.idle": "2024-04-30T08:52:04.003860Z", "shell.execute_reply": "2024-04-30T08:52:04.003609Z" } }, "outputs": [], "source": [ "# Extended models are ReedsSheppExt2, ReedsSheppForwardExt2, ElasticaExt2<5>, and DubinsExt2\n", "hfmIn.update({\n", " 'model':'DubinsExt2',\n", " 'cost':1,\n", " 'xi': 0.1*(1+(Y2<0.5)), # Now the radius of curvature xi can be a field.\n", " 'kappa':0,\n", "})" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:04.005209Z", "iopub.status.busy": "2024-04-30T08:52:04.005111Z", "iopub.status.idle": "2024-04-30T08:52:08.042715Z", "shell.execute_reply": "2024-04-30T08:52:08.042337Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 2.46649 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:08.044508Z", "iopub.status.busy": "2024-04-30T08:52:08.044378Z", "iopub.status.idle": "2024-04-30T08:52:08.114667Z", "shell.execute_reply": "2024-04-30T08:52:08.114401Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Position dependent bound on the radius of curvature\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics'][:-1]: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls']+hfmIn['xi'], cmap='Greys');\n", "savefig(fig,'Dubins_RadiusPositionDependent.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 6.2 Distinct bound on the radius of curvature for right and left turns.\n", "\n", "We consider a Dubins car subject to a distinct turning radius on the right and on the left.\n", "Let us say $\\xi_L$ on the left, and $\\xi_R$ on the right. In order to simulate this model using the HFM software, we must reformulate our constraint in terms of the parameters $\\xi$ and $\\kappa$. \n", "\\begin{equation*}\n", " \\dot \\theta \\in [\\xi_L,\\xi_R] \\quad \\Leftrightarrow \\quad \\xi |\\dot \\theta-\\kappa| \\leq 1\n", "\\end{equation*}\n", "Solving this system, we obtain\n", "\\begin{align*}\n", " \\frac 1 \\xi &= \\frac 2 {\\frac 1 {\\xi_L}+\\frac 1 {\\xi_R}} &\n", " \\kappa = \\frac 1 2 (\\frac 1 {\\xi_L}-\\frac 1 {\\xi_R})\n", "\\end{align*}" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:08.116278Z", "iopub.status.busy": "2024-04-30T08:52:08.116147Z", "iopub.status.idle": "2024-04-30T08:52:08.118346Z", "shell.execute_reply": "2024-04-30T08:52:08.118102Z" } }, "outputs": [], "source": [ "# Extended models are ReedsSheppExt2, ReedsSheppForwardExt2, ElasticaExt2<5>, and DubinsExt2\n", "xiL, xiR = 0.12,0.2\n", "hfmIn.update({\n", " 'model':'DubinsExt2',\n", " 'cost':1,\n", " 'xi':2/(1/xiL+1/xiR),\n", " 'kappa':0.5*(1/xiL-1/xiR),\n", "})" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:08.119749Z", "iopub.status.busy": "2024-04-30T08:52:08.119643Z", "iopub.status.idle": "2024-04-30T08:52:12.300591Z", "shell.execute_reply": "2024-04-30T08:52:12.300234Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 2.5934 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:12.302290Z", "iopub.status.busy": "2024-04-30T08:52:12.302176Z", "iopub.status.idle": "2024-04-30T08:52:12.371877Z", "shell.execute_reply": "2024-04-30T08:52:12.371594Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[6,3]); plt.title(\"Distinct bound, right and left, on the radius of curvature\"); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "savefig(fig,'Dubins_RadiusSideDependent.png')" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:12.373540Z", "iopub.status.busy": "2024-04-30T08:52:12.373432Z", "iopub.status.idle": "2024-04-30T08:52:12.375239Z", "shell.execute_reply": "2024-04-30T08:52:12.374987Z" } }, "outputs": [], "source": [ "hfmIn.pop('kappa',None);" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:12.376623Z", "iopub.status.busy": "2024-04-30T08:52:12.376525Z", "iopub.status.idle": "2024-04-30T08:52:12.378213Z", "shell.execute_reply": "2024-04-30T08:52:12.377974Z" } }, "outputs": [], "source": [ "if hfmIn.mode=='gpu': raise ad.DeliberateNotebookError(\n", " \"The functionality described in the rest of this notbook is absent from the GPU eikonal solver.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7. Additional functionality\n", "\n", "We briefly describe some functionalities of the HFM software that combine particularly well with the curvature penalized models, altough they are not specific to them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.1 Euclidean length of geodesics\n", "\n", "In this experiment, we simultaneously propagate the fast marching front, and compute the euclidean length of the corresponding minimal paths. This is done at runtime, and this euclidean length can be used as a stopping criterion.\n", "By (generalized) Euclidean length of the path $\\gamma : [0,1] \\to \\Omega$, we refer to the quantity defined as \n", "\\begin{equation*}\n", " L_D(\\gamma) := \\int_0^1 \\| D(\\gamma(t)) \\, \\gamma'(t) \\| \\, \\mathrm d t,\n", "\\end{equation*}\n", "where $D : \\Omega \\to \\mathbb R_+^d$ is a given field of diagonal matrices, usually chosen constant over the domain. The user provides this field by defining the *euclidean scale* of the grid for each direction of the domain.\n", "\n", "We choose for illustration the most natural case of the constant field $D_0 \\equiv \\mathrm{diag}(1,1,0)$, which ignores the angular coordinates. Hence for any orientation lifted path $\\gamma=(x,\\theta) : [0,1] \\to \\mathbb R^2 \\times \\mathbb S^1$ one has\n", "\\begin{equation*}\n", " L_{D_0}(x,\\theta) := \\int_0^1 \\|x'(t)\\| \\, \\mathrm d t.\n", "\\end{equation*}" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:12.379688Z", "iopub.status.busy": "2024-04-30T08:52:12.379595Z", "iopub.status.idle": "2024-04-30T08:52:12.381576Z", "shell.execute_reply": "2024-04-30T08:52:12.381349Z" } }, "outputs": [], "source": [ "# Define the field $D : \\Omega \\to \\mathnbb R_+^d$ \n", "gridScale = hfmIn['gridScale'] # ! Do not forget to take the discretization grid scale into account.\n", "hfmIn.update({\n", " 'euclideanScale':[gridScale,gridScale,0],\n", " 'exportEuclideanLengths':0., # Not needed here. Defaults to 1.\n", "\n", " # Optionally, set a stopping criterion.\n", " 'stopAtEuclideanLength':1.4,\n", "\n", " # Other model parameters\n", " 'model':'Elastica2',\n", " 'cost':1,\n", " 'xi':0.2,\n", "})" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:12.382916Z", "iopub.status.busy": "2024-04-30T08:52:12.382816Z", "iopub.status.idle": "2024-04-30T08:52:15.018369Z", "shell.execute_reply": "2024-04-30T08:52:15.018008Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 2.56765 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n", "Field euclideanLength_exportGeodesicFromStoppingPoint defaults to 1\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next cell, we display the point that triggered the termination criterion. This is the closest point to the seeds for which the euclidean length of the corresponding minimal path exceeds our stopping criterion. We next display that geodesic." ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:15.020034Z", "iopub.status.busy": "2024-04-30T08:52:15.019913Z", "iopub.status.idle": "2024-04-30T08:52:15.022628Z", "shell.execute_reply": "2024-04-30T08:52:15.022392Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.605 , 0.395 , 1.15191731])" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hfmOut['euclideanLength_stoppingPoint']" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:15.023920Z", "iopub.status.busy": "2024-04-30T08:52:15.023838Z", "iopub.status.idle": "2024-04-30T08:52:15.082164Z", "shell.execute_reply": "2024-04-30T08:52:15.081868Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "geo = hfmOut['geodesic_euclideanLength']\n", "plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the front propagation was aborted early, due to the chosen stopping criterion, it has not reached all the provided geodesic tips. Therefore, some of the corresponding minimal paths could not be backtraced. This is in particular the case in the left part of the domain, where the tips and seed configuration (both oriented) lead to paths that are either long or have high curvature. " ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:15.083674Z", "iopub.status.busy": "2024-04-30T08:52:15.083570Z", "iopub.status.idle": "2024-04-30T08:52:15.150846Z", "shell.execute_reply": "2024-04-30T08:52:15.150553Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We introduced the Reeds-Shepp and Reeds-Shepp forward using the concept of curvature penalization. However, they can also be regarded as standard euclidean models on the manifold $\\mathbb R^2 \\times \\mathbb S^1$, subject to non-holonomic constraints. As a result, the intrinsic and euclidean lengths of the geodesics coincide." ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:15.152536Z", "iopub.status.busy": "2024-04-30T08:52:15.152415Z", "iopub.status.idle": "2024-04-30T08:52:15.154838Z", "shell.execute_reply": "2024-04-30T08:52:15.154603Z" } }, "outputs": [], "source": [ "gridScale = hfmIn['gridScale']\n", "bundleScale = 2.*np.pi/nTheta\n", "\n", "hfmIn.update({\n", " 'model':'ReedsShepp2',\n", " 'cost':1,\n", " 'xi':0.3,\n", "\n", " 'seedValue_Unoriented':0,\n", "\n", " # Define the field $D : \\Omega \\to \\mathnbb R_+^d$ \n", " 'euclideanScale':[gridScale,gridScale, hfmIn['xi']*bundleScale ],\n", " 'exportEuclideanLengths':1,\n", " 'exportValues':1,\n", "})\n", "hfmIn.pop('stopAtEuclideanLength',None);" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:15.156184Z", "iopub.status.busy": "2024-04-30T08:52:15.156081Z", "iopub.status.idle": "2024-04-30T08:52:16.168749Z", "shell.execute_reply": "2024-04-30T08:52:16.168384Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field projective defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.941792 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The announced equality, of the intrinsic and euclidean lengths, is only approximate numerically, due to our relaxation procedure. The error difference is a reasonable 5% in the Reeds-Shepp forward case. However, an almost 13% error is observed for the standard Reeds-Shepp model, due to the difficult singularities around cusps. Future improvements to the numerical code may reduce this gap." ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:16.170496Z", "iopub.status.busy": "2024-04-30T08:52:16.170366Z", "iopub.status.idle": "2024-04-30T08:52:16.177699Z", "shell.execute_reply": "2024-04-30T08:52:16.177431Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Maximal geodesic euclidean length : 1.2543743534809964 . Difference with value function : 0.3147570145710141\n" ] } ], "source": [ "values, lengths, walls = hfmOut['values'].copy(), hfmOut['euclideanLengths'].copy(), hfmIn['walls']\n", "values[walls]=0.; lengths[walls]=0.;\n", "print(\"Maximal geodesic euclidean length : \", np.max(lengths), \n", " \". Difference with value function : \", np.max(np.abs(values-lengths)) )" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:16.179360Z", "iopub.status.busy": "2024-04-30T08:52:16.179249Z", "iopub.status.idle": "2024-04-30T08:52:16.714427Z", "shell.execute_reply": "2024-04-30T08:52:16.714093Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.457584 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n", "Maximal geodesic euclidean length : 1.6800942852822396 . Difference with value function : 0.6626059390420389\n" ] } ], "source": [ "hfmIn['model']='ReedsSheppForward2'\n", "hfmOut = hfmIn.Run()\n", "values, lengths = hfmOut['values'].copy(), hfmOut['euclideanLengths'].copy()\n", "values[walls]=0.; lengths[walls]=0.;\n", "print(\"Maximal geodesic euclidean length : \", np.max(lengths), \n", " \". Difference with value function : \", np.max(np.abs(values-lengths)) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next cells, we make a similar comparison for the Dubins model. Recall that length of a path, according to this model, is the Euclidean length if the constraint on the radius of curvature is met, and $+\\infty$ otherwise. \n", "\n", "A mismatch, between the value function $u$ and euclidean length of the corresponding minimal geodesics, is nevertheless in some locations, due to the strong singularities of this model. More precisely, this happens:\n", "* where the distance function is discontinuous, e.g. the the boundary of some circular arcs.\n", "* on the boundary of unreachable sets, e.g. at distance $\\leq \\xi$ from the left wall, for the slice $\\{\\theta=0\\}$." ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:16.716128Z", "iopub.status.busy": "2024-04-30T08:52:16.715994Z", "iopub.status.idle": "2024-04-30T08:52:17.913607Z", "shell.execute_reply": "2024-04-30T08:52:17.913189Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 1.1201 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n" ] } ], "source": [ "hfmIn['model']='Dubins2'\n", "hfmIn['euclideanScale'] = [gridScale,gridScale, 0.]\n", "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:17.915258Z", "iopub.status.busy": "2024-04-30T08:52:17.915138Z", "iopub.status.idle": "2024-04-30T08:52:17.977008Z", "shell.execute_reply": "2024-04-30T08:52:17.976751Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "values, lengths = hfmOut['values'].copy(), hfmOut['euclideanLengths'].copy()\n", "far = values>=4\n", "values[far]=0; lengths[far]=0;\n", "plt.contourf(X2,Y2,(values-lengths)[:,:,0]);" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:17.978564Z", "iopub.status.busy": "2024-04-30T08:52:17.978447Z", "iopub.status.idle": "2024-04-30T08:52:17.980313Z", "shell.execute_reply": "2024-04-30T08:52:17.980082Z" } }, "outputs": [], "source": [ "# Restore parameters\n", "hfmIn.pop('euclideanScale',None)\n", "hfmIn.pop('exportEuclideanLengths',None)\n", "hfmIn.pop('seedsUnoriented',None); #hfmInput['seedsUnoriented']=[0.3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.2 Minimal geodesic joining two seeds.\n", "\n", "In this experiment, we compute some Voronoi regions, and stop the computation as soon as two distinct regions denoted $V_0$ and $V_1$ contain *opposite* points, w.r.t. the angular coordinate. In other words as soon as a point $(x,\\theta)\\in \\Omega$ is found such that\n", "\\begin{align*}\n", " (x,\\theta) & \\in V_0 &\n", " (x,\\theta+\\pi) & \\in V_1.\n", "\\end{align*}\n", "By doing so, we can extract a minimal geodesic joining the seed points associated with these two Voronoi regions. In addition, this criterion tends to stop the fast marching algorithm rather early, when it is only propagated on a small portion of the domain, which may substantially reduce computation time." ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:17.981704Z", "iopub.status.busy": "2024-04-30T08:52:17.981607Z", "iopub.status.idle": "2024-04-30T08:52:17.983479Z", "shell.execute_reply": "2024-04-30T08:52:17.983246Z" } }, "outputs": [], "source": [ "# Voronoi diagram data\n", "hfmIn.update({\n", " 'seedFlag':0, # Use 'seedFlags' in case of several seeds\n", " 'seedFlag_Unoriented':1, # Likewise\n", " 'exportVoronoiFlags': 0, # No need to export the Voronoi diagram here\n", " \n", " # Voronoi stopping criterion : when a region contains (x,theta) and the other (x,theta+pi)\n", " 'voronoiStoppingCriterion':'OppositesMeeting',\n", "\n", " # Other model parameters\n", " 'model':'Dubins2',\n", " 'cost':1,\n", " 'xi':0.2,\n", "})" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:17.984839Z", "iopub.status.busy": "2024-04-30T08:52:17.984745Z", "iopub.status.idle": "2024-04-30T08:52:18.258788Z", "shell.execute_reply": "2024-04-30T08:52:18.258445Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.219953 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n", "Field voronoiDiagram_exportGeodesicFromMeetingPoint defaults to 1\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The meeting point is returned, as well as the minimal geodesic to each of the seeds." ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:18.260424Z", "iopub.status.busy": "2024-04-30T08:52:18.260307Z", "iopub.status.idle": "2024-04-30T08:52:18.262637Z", "shell.execute_reply": "2024-04-30T08:52:18.262418Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-0.025 0.425 0.41887902] is opposite to [-0.025 0.425 3.56047167]\n" ] } ], "source": [ "print(hfmOut['voronoiDiagram_meetingPoint0'], \" is opposite to \", hfmOut['voronoiDiagram_meetingPoint1'])" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:18.264065Z", "iopub.status.busy": "2024-04-30T08:52:18.263958Z", "iopub.status.idle": "2024-04-30T08:52:18.323038Z", "shell.execute_reply": "2024-04-30T08:52:18.322765Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for geo in hfmOut['geodesics_voronoiDiagram']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the fast marching algorithm was aborted early, only a few geodesics from the other seeds can be backtraced." ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:18.324628Z", "iopub.status.busy": "2024-04-30T08:52:18.324520Z", "iopub.status.idle": "2024-04-30T08:52:18.389062Z", "shell.execute_reply": "2024-04-30T08:52:18.388752Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for geo in hfmOut['geodesics']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the previous experiments involving Voronoi regions, in the context of Isotropic or Riemannian metrics, we considered another stopping criterion : stop as soon as a point $(x,\\theta)$ common to the two Voronoi regions is found. This criterion, while it may seem natural, is completely inadequate for curvature penalized models. The next cells illustrate numerically what happends." ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:18.390660Z", "iopub.status.busy": "2024-04-30T08:52:18.390549Z", "iopub.status.idle": "2024-04-30T08:52:18.392294Z", "shell.execute_reply": "2024-04-30T08:52:18.392068Z" } }, "outputs": [], "source": [ "hfmIn['voronoiStoppingCriterion']='RegionsMeeting'" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:18.393630Z", "iopub.status.busy": "2024-04-30T08:52:18.393547Z", "iopub.status.idle": "2024-04-30T08:52:18.849333Z", "shell.execute_reply": "2024-04-30T08:52:18.848994Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field eps defaults to 0.1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.396776 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 10.985\n", "Field voronoiDiagram_exportGeodesicFromMeetingPoint defaults to 1\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The voronoi regions first meet at the following neighbord point on the discretization grid." ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:18.851034Z", "iopub.status.busy": "2024-04-30T08:52:18.850911Z", "iopub.status.idle": "2024-04-30T08:52:18.853291Z", "shell.execute_reply": "2024-04-30T08:52:18.853028Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.025 0.235 5.02654825] is (almost) the same as [0.025 0.235 4.92182849]\n" ] } ], "source": [ "print(hfmOut['voronoiDiagram_meetingPoint0'], \" is (almost) the same as \", hfmOut['voronoiDiagram_meetingPoint1'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However the geodesics from this meeting point, backtraced to the seeds, do not form a global geodesic when concatenated. A cusp is observed instead. This is due to the asymmetry of the metrics involved in curvature penalization." ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:52:18.854929Z", "iopub.status.busy": "2024-04-30T08:52:18.854788Z", "iopub.status.idle": "2024-04-30T08:52:18.913877Z", "shell.execute_reply": "2024-04-30T08:52:18.913584Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for geo in hfmOut['geodesics_voronoiDiagram']: plt.plot(geo[0],geo[1])\n", "plt.contourf(X2,Y2,hfmIn['walls'], cmap='Greys')\n", "plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": false, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }