{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Cone\n",
    "\n",
    "This page illustrates the `Cone` shape in the Julia package\n",
    "[`ImagePhantoms`](https://github.com/JuliaImageRecon/ImagePhantoms.jl)."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Setup"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Packages needed here."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using ImagePhantoms: Object, phantom, radon, spectrum\n",
    "using ImagePhantoms: Cone, cone\n",
    "import ImagePhantoms as IP\n",
    "using ImageGeoms: ImageGeom, axesf\n",
    "using MIRTjim: jim, prompt, mid3\n",
    "using FFTW: fft, fftshift, ifftshift\n",
    "using LazyGrids: ndgrid\n",
    "using Unitful: mm, unit, °\n",
    "using Plots: plot, plot!, scatter!, default\n",
    "using Plots # gif @animate\n",
    "default(markerstrokecolor=:auto)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "The following line is helpful when running this file as a script;\n",
    "this way it will prompt user to hit a key after each figure is displayed."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "isinteractive() ? jim(:prompt, true) : prompt(:draw);"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Overview\n",
    "\n",
    "A basic shape used in constructing 3D digital image phantoms\n",
    "is the cone,\n",
    "specified by its center, base radii, height, angle(s) and value.\n",
    "All of the methods in `ImagePhantoms` support physical units,\n",
    "so we use such units throughout this example.\n",
    "(Using units is recommended but not required.)\n",
    "\n",
    "Here are 3 ways to define a `Object{Cone}`,\n",
    "using physical units."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "center = (20mm, 10mm, -15mm)\n",
    "width = (25mm, 30mm, 35mm) # x radius, y radius, height\n",
    "ϕ0s = :(π/6) # symbol version for nice plot titles\n",
    "ϕ0 = eval(ϕ0s)\n",
    "angles = (ϕ0, 0, 0)\n",
    "Object(Cone(), center, width, angles, 1.0f0) # top-level constructor\n",
    "cone( 20mm, 10mm, 5mm, 25mm, 35mm, 15mm, π/6, 0, 0, 1.0f0) # 9 arguments\n",
    "ob = cone(center, width, angles, 1.0f0) # tuples (recommended use)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Phantom image using `phantom`\n",
    "\n",
    "Make a 3D digital image of it using `phantom` and display it.\n",
    "We use `ImageGeoms` to simplify the indexing."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "deltas = (1.0mm, 1.1mm, 0.9mm)\n",
    "dims = (2^8, 2^8+2, 49) # odd\n",
    "ig = ImageGeom( ; dims, deltas, offsets=:dsp)\n",
    "oversample = 3\n",
    "img = phantom(axes(ig)..., [ob], oversample)\n",
    "p1 = jim(axes(ig), img;\n",
    "   title=\"Cone, rotation ϕ=$ϕ0s\", xlabel=\"x\", ylabel=\"y\")"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "The image integral should match the object volume:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "volume = IP.volume(ob)\n",
    "(sum(img)*prod(ig.deltas), volume)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Show middle slices"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "jim(mid3(img), \"Middle 3 planes\")"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
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