{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi-Object Queries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from geo3d.query import distance_between_points, minimize_points_to_points_distance, distances_plane_to_points\n",
    "from geo3d import Point, Plane, Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Point-to-Point Distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distance between points can be queried as "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pointA = Point([1,2,3])\n",
    "pointB = Point([1,2,6])\n",
    "distance_between_points(pointA, pointB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plane-to-Points Distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distance from a plane to an array of points, positive along the plane normal vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3., -6.])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plane = Plane(\n",
    "    normal=Vector([0,0,-1]), \n",
    "    point=Point([1,2,0])\n",
    ")\n",
    "points = [[1,2,3], [1,2,6]]\n",
    "distances_plane_to_points(plane, points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transformation minimizing group-to-group distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For two point groups, find the transformation -- applied to the first group -- that minimizes the RMS distance between the corresponding points in the two groups:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we extract a rotation of 90 degrees between the point groups, that is, `groupA` needs to be rotated by 90 degrees to coincide with `groupB`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <table>\n",
       "                <tr>\n",
       "                    <th>rotation matrix</th>\n",
       "                    <th>Fixed angles<br>(xyz, extr., deg.)</th>\n",
       "                    <th>Euler angles<br>(xyz, intr., deg.)</th>\n",
       "                    <th>translation<br></th>\n",
       "                </tr>\n",
       "                <tr><td><table><tr><td>-0.00000000</td><td>-1.00000000</td><td>0.00000000</td></tr><tr><td>1.00000000</td><td>-0.00000000</td><td>-0.00000000</td></tr><tr><td>0.00000000</td><td>0.00000000</td><td>1.00000000</td></tr></table></td><td><table><tr><td>θx</td><td>0.00000</td></tr><tr><td>θy</td><td>-0.00000</td></tr><tr><td>θz</td><td>90.00000</td></tr></table></td><td><table><tr><td>θx</td><td>0.00000</td></tr><tr><td>θy</td><td>0.00000</td></tr><tr><td>θz</td><td>90.00000</td></tr></table></td><td><table><tr><td>x</td><td>0.00000</td></tr><tr><td>y</td><td>0.00000</td></tr><tr><td>z</td><td>0.00000</td></tr></table></td></tr></table>"
      ],
      "text/plain": [
       "<geo3d.geometry.Frame at 0x27a1d940>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groupA = [[1,0,0], [0,1,0], [-1,0,0], [0,-1,0], [0,0,1], [0,0,-1]]\n",
    "groupB = [[0,1,0], [-1,0,0], [0,-1,0], [1,0,0], [0,0,1], [0,0,-1]]\n",
    "minimize_points_to_points_distance(groupA, groupB)"
   ]
  }
 ],
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