{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "38506168-7836-4153-a0f9-b5cfdd575067",
   "metadata": {},
   "source": [
    "# Define and apply an affine transform in 2D from control points\n",
    "### The same approach works for 3D points too.  \n",
    "O. Kaufmann, 2022."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e5321fe6-2872-4ec7-bedd-1502b079392b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from shapely.geometry import Point, LineString\n",
    "from shapely.affinity import affine_transform\n",
    "from geometron.geometries import transforms as ggt\n",
    "from geometron.plot import geometries as gpg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "84c2b059-d81a-4f09-866e-e4c8b3f5298d",
   "metadata": {},
   "outputs": [],
   "source": [
    "origin_coords = [np.array([0.,0.]), np.array([0.,1.]), np.array([1.,0.]), np.array([1.,1.2])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a4e8f2e9-1f7f-4f6f-b0a8-ac5d45b991a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "destination_coords = [np.array([2.5,1.5]), np.array([2.,2.]), np.array([3.,2.]), np.array([2.5,3.])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "11e11960-ed15-48df-9c81-97dd91611e23",
   "metadata": {},
   "outputs": [],
   "source": [
    "transform_matrix, residuals, rank, singular = ggt.affine_transform_matrix(origin_coords, destination_coords)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "810824f9-25ea-445d-9b14-ab0403eb98dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5450819672131152,\n",
       " -0.4508196721311477,\n",
       " 0.6803278688524602,\n",
       " 0.6967213114754098,\n",
       " 2.4754098360655745,\n",
       " 1.401639344262296]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transform_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "482bf63c-11ee-455e-9fcb-b31b25c7c499",
   "metadata": {},
   "outputs": [],
   "source": [
    "origin_gcp = [Point(p) for p in origin_coords]\n",
    "destination_gcp = [Point(p) for p in destination_coords]\n",
    "transformed_gcp = [affine_transform(p, transform_matrix) for p in origin_gcp]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "377b89e7-64de-4d06-9703-22dce00bc648",
   "metadata": {},
   "outputs": [],
   "source": [
    "ls = LineString([[1,1], [2,1], [1,4]])\n",
    "Ls = affine_transform(ls, transform_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "009cb865-4b5a-4297-b923-00e0582893ca",
   "metadata": {
    "nbsphinx-thumbnail": {
     "tooltip": "This tooltip message was defined in cell metadata"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa666ffaf10>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "for p in origin_gcp:\n",
    "    i = origin_gcp.index(p)\n",
    "    gpg.plot_shapely_obj(obj=p, ax=ax, color='g', marker='o', label='GCP - origin' if i == 0 else '_no_legend_')\n",
    "for p in destination_gcp:\n",
    "    i = destination_gcp.index(p)\n",
    "    gpg.plot_shapely_obj(obj=p, ax=ax, markeredgecolor='r', markerfacecolor='r', marker='o', label='GCP - destination' if i == 0 else '_no_legend_')\n",
    "for p in transformed_gcp:\n",
    "    i = transformed_gcp.index(p)\n",
    "    gpg.plot_shapely_obj(obj=p, ax=ax, markeredgecolor='k', markerfacecolor='w', marker='o', alpha=0.5, label='GCP - transformed' if i == 0 else '_no_legend_')\n",
    "    \n",
    "gpg.plot_shapely_obj(obj=ls, ax=ax, color='g', marker='x', label='object - origin')\n",
    "gpg.plot_shapely_obj(obj=Ls, ax=ax, color='r', marker='x', label='object - transformed')\n",
    "ax.axis('equal')\n",
    "fig.legend(bbox_to_anchor=(1.25, 1), loc='upper right', borderaxespad=0)"
   ]
  }
 ],
 "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": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}