{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from geo3d.fit import fit_plane\n",
    "from geo3d import Point, Plane, Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plane Fit to Points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit a plane to an array of points. The fitted plane is defined by a `Plane.point` attribute giving the centroid of the fitted points, and a normal vector attribute `Plane.normal`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plane(normal=<Vector at 2697000856352> [0. 0. 1.], point=<Point at 2697005808896> [0.         0.33333333 0.        ])"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "points = [[1,0,0], [0,1,0], [-1,0,0]]\n",
    "plane = fit_plane(points)\n",
    "plane"
   ]
  },
  {
   "source": [
    "Express the plane as coefficients `a`, `b`, `c`, `d` in $a x + b y + c z + d = 0$:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(0.0, 0.0, 1.0, -0.0)"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "(a,b,c,d) = plane.as_abcd()\n",
    "(a,b,c,d)"
   ]
  }
 ],
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