{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Field rotation\n", "\n", "Finite-difference fields (in `discretisedfield`) are always discretised in the $x$, $y$, and $z$ direction and hence aligned with the coordinate axes. Several operations, such as cutting planes or computing integrals, are only possible along the coordinate axes. In this tutorial we demonstrate how to rotate a `field` in an arbitrary direction (multiple consecutive rotations are possible as well). Rotations can be applied to scalar (`dim==1`) and vector (`dim==3`) fields only. Periodict boundary conditions are currently not supported (ignored and lost during the rotation process).\n", "\n", "The rotation of a field allows for more flexibility:\n", "\n", "- cutting planes in arbitrary directions => plots of arbitrary cut planes\n", "- computing integrals along arbitrary direction\n", "- ...\n", "\n", "This additional flexibility is predominantly needed to simulate experiments using `mag2exp` but can be used on its own. However, the limitations of this method need to be taken into account. The result of the rotation is a new `field`, and therefore discretised along (the new) $x$, $y$, and $z$ direction. This can introduce a number of numerical (maybe also systematic) errors:\n", "\n", "- Remeshing requires to choose a new cell size (done automatically by default). This can introduce errors if either cell size (volume) or the number of cells change. Care from the user is needed to ensure that either change is compatible with the respective use case.\n", "- Interpolation of the `field` values onto the new finite-differences grid introduces additional numerical errors.\n", "\n", "In general, multiple consecutive rotations of the same `field` would result in an accumultation of errors. To prevent this we use a special object to rotate the `field`. Consecutive rotations are collected and the actual rotation of a field is always computed starting from the unrotated original field.\n", "\n", "This tutorial is divided into two parts. In the first part we explain the different methods to rotate a field by looking at a few examples. The second part explains the different steps of the rotation process in more detail.\n", "\n", "## Rotating a field\n", "\n", "### Original field\n", "\n", "Let us first define a field to work with." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "import discretisedfield as df\n", "\n", "p1 = (-50, -30, -10)\n", "p2 = (50, 30, 10)\n", "n = (15, 15, 6)\n", "mesh = df.Mesh(p1=p1, p2=p2, n=n)\n", "field = df.Field(mesh, dim=3, value=(0, 1, 1))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field.plane(\"z\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `FieldRotator`\n", "\n", "Rotations of the `field` are handled by a special `FieldRotator` object." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "field_rotator = df.FieldRotator(field)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "FieldRotator\n", "" ], "text/plain": [ "FieldRotator(unrotatedField(Mesh(Region(p1=(-50, -30, -10), p2=(50, 30, 10)), n=(15, 15, 6), attributes: (unit: m, fourierspace: False, isplane: False)), dim=3, components: (x, y, z)), rotation_quaternion: [0.0, 0.0, 0.0, 1.0])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "field_rotator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `field_rotator` is initialised with an identity rotation matrix (initially no rotation is applied). The rotation matrix is not directly accessible. Instead, it can be modified using the `rotate` method explained in the following.\n", "\n", "### Rotation methods\n", "\n", "The `field_rotator` can rotate the `field` using the `rotate` method:\n", "```python\n", "field_rotator.rotate\n", "```\n", "\n", "Several different methods can be used to specify rotations. Internally, `scipy.spatial.transfom.Rotation` is used to represent and apply rotations. For details on the different methods please refer directly to the [scipy documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.transform.Rotation.html) of the relevant method. Available methods are:\n", "\n", "- `from_quat`\n", "- `from_matrix`\n", "- `from_rotvec`\n", "- `from_mrp`\n", "- `from_euler`\n", "\n", "In addition there is the method\n", "\n", "- `align_vector`\n", "\n", "which is slightly different from the scipy method `align_vectors`. See below for more details on this method.\n", "\n", "### Rotations by multiples of 90°\n", "\n", "We now show an example using Euler angles to rotate the `field` by 90° around the $x$ axis:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "field_rotator.rotate(\"from_euler\", seq=\"x\", angles=np.pi / 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The field has now been rotated internally. The rotated field can be accessed as:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "Field\n", "" ], "text/plain": [ "Field(Mesh(Region(p1=(-50.0, -10.000000000000007, -30.000000000000004), p2=(50.0, 10.000000000000007, 30.000000000000004)), n=(15, 6, 15), attributes: (unit: m, fourierspace: False, isplane: False)), dim=3, components: (x, y, z))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "field_rotator.field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see the effect of the rotation we can again plot a cross section in the xy-plane. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.field.plane(\"z\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now apply a second rotation about the $z$ axis, again by 90°. For demonstration purposes we use a different method `'from_rotvec'`. We have to pass a vector that specifies the rotation axis and whose norm gives the angle of rotation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.rotate(\"from_rotvec\", [0, 0, np.pi / 2])\n", "field_rotator.field.plane(\"z\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is possible to clear all rotations." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.clear_rotation()\n", "field_rotator.field.plane(\"z\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rotations about arbitrary angles\n", "\n", "We can rotate the field about an arbitrary angle. To keep this section simple we only show rotations about the z-axis that can be easily visualised on as single plane." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.rotate(\"from_euler\", seq=\"z\", angles=np.pi / 6)\n", "field_rotator.field.plane(\"z\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The rotated field can be seen to have jagged edges caused by the discretisation of the mesh. The number of cells has also changed compared to the original field." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(15, 15, 6)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "field.mesh.n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(19, 19, 8)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "field_rotator.field.mesh.n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the number of cells did also change along the rotation axis. The reason for this is the normalisation of the cell volume of the rotated mesh.\n", "\n", "We can see that the rotation results in a larger region. We can again combine multiple rotations. The region is maximised if we rotate about 45° in total." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.rotate(\"from_euler\", seq=\"z\", angles=np.pi / 12)\n", "field_rotator.field.plane(\"z\").mpl()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "field_rotator.clear_rotation()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The rotation is achieved by linear interpolation of the rotated object from the old mesh into the new mesh. We can change the number of discretisation cells in the new mesh by passing `n` to the rotate function." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.rotate(\"from_euler\", seq=\"z\", angles=np.pi / 6, n=(60, 60, 20))\n", "field_rotator.field.plane(\"z\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rotating a vector to point in a certain direction\n", "Sometimes it is convenient to specify a certain vector in the old and new coordinate system instead of specifying a rotation axis and an angle. This can be achieved with the method `align_vector`. Two vectors `initial` and `final` have to be specified and the rotation rotates the vector `inital` to the vector `final`. The cross product is kept fixed and hence defines the rotation axis.\n", "\n", "To give an example, we can rotate one of the corners to point in the z-direction. We start with removing all rotations." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.clear_rotation()\n", "field_rotator.field.plane(\"x\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose vector `initial=(5, 3, 1)` pointing to the point `pmax`" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(50, 30, 10)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "field.mesh.region.pmax" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want this vector to point along `final=(0, 0, 1)` direction after applying the rotation." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "field_rotator.rotate(\"align_vector\", initial=(5, 3, 1), final=(0, 0, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can visualise this \"3d\" rotation using `k3d`." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "09436ef15dde456180ff224ada5c161f", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "field_rotator.field.norm.k3d.nonzero()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using matplotlib we can plot one cut plane:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "field_rotator.field.plane(\"x\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As mentioned in the introduction, we can compute arbitrary quantities using the rotated field. As illustrative example we compute the integral along the new $x$ axis and plot the result. After computing the integral we can see the original rectangular shape of the field." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rfield = field_rotator.field\n", "(-rfield * df.dx).integral(\"x\").plane(\"x\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see the smaller integral values near the boundaries that are related to a reduced number of cells in these regions. We can also see some additional stripe-like features in the inner area that are related to numerical inaccuracies.\n", "\n", "## Details of the rotation process\n", "\n", "The rotation of a `field` can be separated into three different processes:\n", "\n", "1. rotation of the `region`\n", "2. rotation of the `mesh`\n", "3. rotation of the `field` values\n", "\n", "We discuss these processes in greater detail in the following subsections.\n", "\n", "### 1. Rotation of the region\n", "\n", "The first step of the rotation procces is rotation of the region. The rotated initial region is in general not anymore aligned with the coordinate axes. We need a new aligned region fully enclosing the rotated initial region. Therefore, this new region must be larger than the unrotated inital region in order to fully enclose the rotated initial region. The required size is obtained by rotating the three vectors pointing along the edges of the old region in $x$, $y$, and $z$ direction. Then, the $x$, $y$, and $z$ components of these rotated vectors in the new coordinate system are summed up to obtain the new edge lengths.\n", "\n", "The rotation in two dimensions is shown in the following figure. The original field is show in red, the region size for different rotations (0°, 15°, 45°, 60°) in blue.\n", "\n", "![Rotation in 2d](figures/rotation_region.svg)\n", "\n", "In this example of a quadratic field the new region grows the most for a 45° rotation. The implementation of `FieldRotator` ensures that the new region is as small as possible by accumulating and combining all rotation operations and computing the rotated field always directly from the initial unrotated field. However, the norm of the original field is not taken into account, i.e. only the size of the old region is important not the actual area containing data.\n", "\n", "As an example, to make this clearer, we show the rotation of a field where non-zero values are inside a disk. In princible, this field would not need a larger region to be rotated. However, as only the region is taken into account, the new region is larger than theoretically needed.\n", "\n", "![Rotation of a disk (non-zero part of the field) do demonstrate limitations](figures/rotation_disk.svg)\n", "\n", "### 2. Rotation of the mesh\n", "\n", "The second step of the rotation process is the rotation of the mesh. Since we already have the new region, this is basically the rotation of a cell to determine the new cell size/number of cells. This can be either done automatically or manually.\n", "\n", "If the new number of cells is either known or certain values are needed the user can specify an additional argument `n` in the `rotate` method to specify the number of cells in $x$, $y$, and $z$ direction:\n", "```\n", "field_rotator.rotate(..., n=(, , ), ...)\n", "```\n", "\n", "By default `n=None` and the new cell size is determined automatically.\n", "\n", "1. A single cell of the old mesh is rotated similarly to how the region is rotated.\n", "2. The new cell is resized to have the same volume as the old cell (the aspect ratio of the new cell is fixed).\n", "3. The number of cells in the new region is determined from the new region and cell size. Generally, we obtain non-integer cell numbers as a consequence of the cell resizing.\n", "4. The obtained cell numbers are rounded to the nearest integer value. Therefore, the cell volume is only aproximately keep constant.\n", "\n", "\n", "### 3. Rotation of the field values\n", "\n", "The last part of the rotation process is the rotation of the `field` values. This consists of two parts:\n", "\n", "1. Rotation of the field values (for vector fields only)\n", "2. Interpolation of the values on the new mesh\n", "\n", "The first step is only required for vector fields. The field values, i.e. the vector in each cell in the old mesh is rotated. This is only supported for 3d vector fields (`field.dim==3`).\n", "\n", "The second step is the mapping of the (rotated) field components onto the new rotated mesh. This is done by taking the cell positions of the new mesh, rotating them back to the old mesh, and then linearly interpolating the (rotated) field values on the old mesh to determine the field values at the new cell positions." ] } ], "metadata": { "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": "3.8.12" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "09436ef15dde456180ff224ada5c161f": { "model_module": "@jupyter-widgets/output", "model_module_version": "1.0.0", "model_name": "OutputModel", "state": { "layout": "IPY_MODEL_b9d38bc673544a1e9da17a073cdccee4", "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a7ebeb25e06643b08153a58fb832fb9a", "version_major": 2, "version_minor": 0 }, "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera_animation=[], camer…" }, "metadata": {}, "output_type": "display_data" } ] } }, "19364d057bab4a2fa4a6ea1c60240de7": { "buffers": [ { "data": "sHJMAA==", "encoding": "base64", "path": [ "color_map", "data" ] }, { "data": "6ZibQgAAAAAAAAAAAAAAAAAAAACCNbtCAAAAAAAAAAAAAAAAAAAAAKik7EIAAAAAAAAAAAAAAAAAAAAAAACAPw==", "encoding": "base64", "path": [ "model_matrix", "data" ] }, { "data": "                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ", "encoding": "base64", "path": [ "voxels", "data" ] } ], "model_module": "k3d", "model_module_version": "2.11.0", "model_name": "ObjectModel", "state": { "_view_count": null, "_view_module": null, "_view_module_version": "", "_view_name": null, "colorLegend": false, "color_map": { "dtype": "uint32", "shape": [] }, "compression_level": 0, "id": 139899911620832, "model_matrix": { "dtype": "float32", "shape": [ 4, 4 ] }, "name": "Voxels #1", "opacity": 1, "outlines": false, "outlines_color": 0, "type": "Voxels", "visible": true, "voxels": { "dtype": "uint8", "shape": [ 24, 21, 19 ] }, "wireframe": false } }, "1c27906f8e8d45e1b3f34fdc6be5f662": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.2.0", "model_name": "LayoutModel", "state": {} }, "a7ebeb25e06643b08153a58fb832fb9a": { "model_module": "k3d", "model_module_version": "2.11.0", "model_name": "PlotModel", "state": { "_backend_version": "2.11.0", "_dom_classes": [], "_view_count": null, "antialias": 3, "auto_rendering": true, "axes": [ "x\\,\\text{ (m)}", "y\\,\\text{ (m)}", "z\\,\\text{ (m)}" ], "axes_helper": 1, "background_color": 16777215, "camera": [ 137.88821726208067, -210.43329184533198, 13.767524929944317, -2.2520653792192036, -0.22286788338215402, -0.24650333418590265, 0, 0, 1 ], "camera_animation": [], "camera_auto_fit": true, "camera_damping_factor": 0, "camera_fov": 60, "camera_mode": "trackball", "camera_no_pan": false, "camera_no_rotate": false, "camera_no_zoom": false, "camera_pan_speed": 0.3, "camera_rotate_speed": 1, "camera_zoom_speed": 1.2, "clipping_planes": [], "colorbar_object_id": -1, "colorbar_scientific": false, "fps": 25, "fps_meter": false, "grid": [ -1, -1, -1, 1, 1, 1 ], "grid_auto_fit": true, "grid_color": 15132390, "grid_visible": true, "height": 512, "label_color": 4473924, "layout": "IPY_MODEL_1c27906f8e8d45e1b3f34fdc6be5f662", "lighting": 1.5, "manipulate_mode": "translate", "menu_visibility": true, "mode": "view", "name": null, "object_ids": [ 139899911620832 ], "rendering_steps": 1, "screenshot": "", "screenshot_scale": 2, "snapshot": "", "snapshot_type": "full", "time": 0, "voxel_paint_color": 0 } }, "b9d38bc673544a1e9da17a073cdccee4": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.2.0", "model_name": "LayoutModel", "state": {} } }, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 4 }