{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6f013234",
   "metadata": {},
   "source": [
    "# Manipulating coordinate values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0aa9e4ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from ktch.datasets import load_outline_mosquito_wings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8071f111",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_outline_mosquito_wings = load_outline_mosquito_wings(as_frame=True)\n",
    "coords = data_outline_mosquito_wings.coords.to_numpy().reshape(-1,100,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bd3de90",
   "metadata": {},
   "source": [
    "## Translation\n",
    "\n",
    "You can translate the coordinate values of outline data using list comprehension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e714d214",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng()\n",
    "dx = rng.normal(0, 1, size=coords.shape[0::2])\n",
    "coords_translated = [coords[i] + dx[i] for i in range(len(coords))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c050484",
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.lineplot(x=coords[idx][:,0], y=coords[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "sns.lineplot(x=coords_translated[idx][:,0], y=coords_translated[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "ax.set_aspect('equal')\n",
    "print(\"displacement: \", dx[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49f3fe93",
   "metadata": {},
   "source": [
    "If the coordinate values are stored as `np.ndarray`, \n",
    "you can simply add the displacement vectors after `reshape(n_spesimens, 1, n_dim)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1c2a759",
   "metadata": {},
   "outputs": [],
   "source": [
    "coords_translated_array = coords + dx.reshape(dx.shape[0], 1, dx.shape[1])\n",
    "\n",
    "idx = 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.lineplot(x=coords[idx][:,0], y=coords[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "sns.lineplot(x=coords_translated_array[idx][:,0], y=coords_translated_array[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "ax.set_aspect('equal')\n",
    "print(\"displacement: \", dx[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93ea6ae7",
   "metadata": {},
   "source": [
    "## Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5fd4e7c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = rng.uniform(0.5,1.5, size=coords.shape[0])\n",
    "coords_scaled = [s[i]*coords[i] for i in range(len(coords))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba30cfc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.lineplot(x=coords[idx][:,0], y=coords[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "sns.lineplot(x=coords_scaled[idx][:,0], y=coords_scaled[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "ax.set_aspect('equal')\n",
    "print(\"scale: \", s[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f202dfe",
   "metadata": {},
   "source": [
    "If the coordinate values are stored as `np.ndarray`, \n",
    "you can simply add the displacement vectors after `reshape(n_spesimens, 1, 1)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d72afba",
   "metadata": {},
   "outputs": [],
   "source": [
    "coords_scaled_arr = s.reshape(s.shape[0], 1, 1)*coords\n",
    "\n",
    "idx = 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.lineplot(x=coords[idx][:,0], y=coords[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "sns.lineplot(x=coords_scaled_arr[idx][:,0], y=coords_scaled_arr[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "ax.set_aspect('equal')\n",
    "print(\"scale: \", s[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "869c26ee",
   "metadata": {},
   "source": [
    "## Rotation\n",
    "We provide `rotation_matrix_2d` helper function to generate the rotation matrix.\n",
    "\n",
    "Alternatively, you can use `scipy.spatial.transform.Rotation` or define by yourself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bc8edaa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ktch.outline import rotation_matrix_2d\n",
    "from scipy.spatial.transform import Rotation as R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a05a232",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.pi/4\n",
    "print(rotation_matrix_2d(theta))\n",
    "print(R.from_rotvec(theta*np.array([0,0,1])).as_matrix()[0:2,0:2])\n",
    "print(np.array([[np.cos(theta),-np.sin(theta)],[np.sin(theta), np.cos(theta)]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e61b3d21",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = rng.uniform(0, 2*np.pi, size=coords.shape[0])\n",
    "coords_rotated = [(rotation_matrix_2d(theta[i]) @ coords[i].T).T for i in range(len(coords))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78c3db02",
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.lineplot(x=coords[idx][:,0], y=coords[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "sns.lineplot(x=coords_rotated[idx][:,0], y=coords_rotated[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "ax.set_aspect('equal')\n",
    "print(\"theta: \", theta[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b6004cb",
   "metadata": {},
   "source": [
    "When the coordinate values are stored as `np.ndarray`, \n",
    "the rotated array is calculated by applying the `matmul (@)` operator on the array of rotation matrixes transposed to `n_samples x n_dim x n_dim` and the array of the coordinate values transposed to `n_samples x n_dim x n_coordinates`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fc1daaf7",
   "metadata": {},
   "outputs": [],
   "source": [
    "coords_rotated_arr = (rotation_matrix_2d(theta).transpose(2, 0, 1) @ coords.transpose(0, 2, 1)).transpose(0, 2, 1)\n",
    "\n",
    "idx = 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "sns.lineplot(x=coords[idx][:,0], y=coords[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "sns.lineplot(x=coords_rotated_arr[idx][:,0], y=coords_rotated_arr[idx][:,1], sort= False,estimator=None,ax=ax)\n",
    "ax.set_aspect('equal')\n",
    "print(\"scale: \", s[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30e8e2b0",
   "metadata": {},
   "source": [
    "## Changing the starting point\n",
    "The starting point (arclength parameter $t = 0$) is often adjusted for aligning the outlines.\n",
    "\n",
    "You can use the `numpy.roll` function for the purpose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bbd1a58d",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_staring_points = np.array([rng.integers(0,len(coord)) for coord in coords], dtype=int)\n",
    "coords_changed_start = [np.roll(coords[i], -new_staring_points[i], axis=0) for i in range(len(coords))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f2b86c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = 0\n",
    "\n",
    "fig, ax = plt.subplots(1,2, figsize=(12,7))\n",
    "sns.lineplot(x=coords[idx][:,0], y=coords[idx][:,1], sort= False,estimator=None,ax=ax[0])\n",
    "sns.lineplot(x=coords_changed_start[idx][:,0], y=coords_changed_start[idx][:,1], \n",
    "             sort= False,color=\"C1\",estimator=None,ax=ax[1])\n",
    "ax[0].set_aspect('equal')\n",
    "ax[1].set_aspect('equal')\n",
    "print(\"starting point: \", new_staring_points[idx])"
   ]
  }
 ],
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