Ray tracing review.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import review as rv\n",
    "import graphicsFunctions as gf\n",
    "import importlib\n",
    "import numpy as np\n",
    "from ggplot import *\n",
    "import visualizations as vs\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'graphicsFunctions' from '/Users/rivka/Desktop/graphics/github/review/graphicsFunctions.py'>"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(gf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'review' from '/Users/rivka/Desktop/graphics/github/review/review.py'>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(rv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'visualizations' from '/Users/rivka/Desktop/graphics/github/review/visualizations.py'>"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "importlib.reload(vs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Ray casting question (from generated reviews (1)) (orthographic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "i, j = 1, 3\n",
    "nx, ny = 724, 344\n",
    "l, r, b, t = -5, -4, 0, 4\n",
    "e = np.array((-2, 3, -1))\n",
    "u = np.array((0.82, 0.41, -0.41))\n",
    "v = np.array((0, -0.71, -0.71))\n",
    "w = np.array((0.56, -0.74, 0.37))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4.99792817679558, 0.040697674418604654)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uc = l + (r-l)*(i+0.5)/nx\n",
    "uc = -5 + (-4--5)*(1.5)/724\n",
    "vc = b + (t-b)*(j+0.5)/ny\n",
    "uc, vc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-6.0983011  0.9219541  1.0202552]\n",
      "[-0.56  0.74 -0.37]\n"
     ]
    }
   ],
   "source": [
    "origin = e + uc*u + vc*v\n",
    "direction = -w\n",
    "print(origin)\n",
    "print(direction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# End ray casting question"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Polygon intersection question (from generated reviews (2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'f) Is the intersection point in front of the viewpoint e?'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"Ray R has starting point e=􏰀−5.58 4.41 0.42􏰁 and direction d=􏰀0.8 P has vertices 􏰀−1.38 −0.06 −1.59􏰁􏰀−4.5 5.87 2.0􏰁􏰀−1.38 3.22 b) What is the normal to P?\"\n",
    "\"c) What is the t intersection point of R and P?\"\n",
    "\"d) What is the (x, y, z) intersection point on R at t? e) Is the intersection point inside the polygon?\"\n",
    "\"f) Is the intersection point in front of the viewpoint e?\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "e = np.array((-5.58, 4.41, 0.42))\n",
    "d = np.array((0.8, 0.27, 0.53))\n",
    "p = np.array(((-1.38, -0.06, -1.59), \n",
    "              (-4.5, 5.87, 2.0), \n",
    "              (-1.38, 3.22, 1.69),\n",
    "             (1.12, 5.56, 5.9),\n",
    "             (1.75, 1.19, 2.0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.46852129,  0.62469505, -0.62469505])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is the normal to p?\n",
    "n = gf.normalize(np.cross(p[1]-p[0], p[2]-p[1]))\n",
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0294117647058822"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is the t intersection point of R and P?\n",
    "t = (p[0]-e).dot(n)/d.dot(n)\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-3.96, 4.96, 1.50'"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is the (x, y, z) intersection point on R at t?\n",
    "x, y, z = e + t*d\n",
    "\"%.2f, %.2f, %.2f\" % (x, y, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Is the intersection point inside the polygon?\n",
    "# Is the intersection point in front of the viewpoint e?\n",
    "t > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "Previous vertex above py: False\n",
      "Current vertex above py: False\n",
      "1\n",
      "Previous vertex above py: False\n",
      "Current vertex above py: True\n",
      "checking x intersection\n",
      "2\n",
      "Previous vertex above py: True\n",
      "Current vertex above py: False\n",
      "checking x intersection\n",
      "x intersection is on right of px: flipping inside to True\n",
      "3\n",
      "Previous vertex above py: False\n",
      "Current vertex above py: True\n",
      "both on right: flipping inside to False\n",
      "4\n",
      "Previous vertex above py: True\n",
      "Current vertex above py: False\n",
      "both on right: flipping inside to True\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gf.pointInPolygon((x, y, z), p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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aWgq1Wg3n/FvIVDR/pfepKS87M03788ykRIozk/K8AM6suqQ4L4Azq64/zmvfvn2Ii4uD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\nBwAAADyMEQ4AAAB4GCMcAAAA8LD/B1R5c0mlA28cAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11697d9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (-9223372036562639623)>"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vs.plotPolygon(p) + vs.plotPoint((x,y,z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.0212141652613829"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# If endpoints of edge are above and bel\n",
    "# Ax + By + C = 0\n",
    "# (y0-y1)x + (x1-x0)y + x0y1 - x1y0 = 0 (Given)\n",
    "# equation of edge 01\n",
    "A = p[0][1]-p[1][1]\n",
    "B = p[1][0]-p[0][0]\n",
    "C = p[0][0]*p[1][1] - p[1][0]*p[0][1]\n",
    "xc = (-B * 4.96 - C)/A\n",
    "xc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xc > x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.4261798002219757"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xc = gf.xIntersect(p[1], p[2], y)\n",
    "xc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xc > x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# End polygon intersection question"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Barycentric coordinates question (3)\n",
    "t = np.array(((-0.47, 5.71, -6.23),\n",
    "            (-2.33, 3.11, -5.49),\n",
    "            (-3.63, 1.63, -4.74)))\n",
    "e = np.array((-4.52, 2.35, 1.31))\n",
    "d = np.array((-0.51, 0.85, -0.17))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t: 2.99\n"
     ]
    }
   ],
   "source": [
    "# What are the beta and gamma barycentric coordinates and the t distance along the ray of the intersection between R and the plane defined by T?\n",
    "n = gf.normalize(np.cross(t[1]-t[0], t[2]-t[1]))\n",
    "tp = (t[0]-e).dot(n)/d.dot(n)\n",
    "print(\"t: %.2f\" % tp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-6.04449016,  4.89081694,  0.80183661])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "px = e + tp*d\n",
    "px"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-32.135365717059571, 20.67919949221513)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (y0-y1)x + (x1-x0)y + x0y1 - x1y0 -- Given \n",
    "c, f01 = gf.lineEq(t[0], t[1])\n",
    "gamma = f01(px)/f01(t[2])\n",
    "c, f02 = gf.lineEq(t[0], t[2])\n",
    "beta = f02(px)/f02(t[1])\n",
    "(beta, gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Is the intersection point inside the triangle?\n",
    "beta > 0 and gamma > 0 and 1-beta-gamma > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Is the intersection point in front of the viewpoint e?\n",
    "tp > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# End barycentric question"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Ray casting question (perspective) (12)\n",
    "i, j = 4, 4\n",
    "nx, ny = 386, 706\n",
    "l, r, b, t = 1, 3, -1, 0\n",
    "e = np.array((3, 1, -2))\n",
    "ux = np.array((-0.44, -0.22, 0.87))\n",
    "vx = np.array((-0.58, -0.58, 0.58))\n",
    "wx = np.array((-0.85, -0.17, -0.51))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0233160621761659, -0.9936260623229461)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = l + (r-l) * (i+0.5)/nx\n",
    "v = b + (t-b) * (j+0.5)/ny\n",
    "u, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  1, -2])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "origin = e\n",
    "origin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ip = 3       # error: not given in question"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.67604405,  0.86117358,  1.84398186])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = ip*-wx + u*ux + v*vx \n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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