03_adding_a_sphere_base.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 03 Adding a sphere\n",
    "\n",
    "* 구(sphere)를 정의하고 ray가 구를 통과하는지를 확인하는 예제 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as LA\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(vec: np.array, eps: float = 1e-6):\n",
    "  return vec / (LA.norm(vec) + eps) \n",
    "\n",
    "def blend(color1: np.array, color2: np.array, t: float):\n",
    "  return (1.0-t)*color1 + t*color2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Ray:\n",
    "  def __init__(self, origin: np.array, direction: np.array) -> None:\n",
    "    self.origin: np.array = origin    \n",
    "    self.direction: np.array = normalize(direction)\n",
    "\n",
    "  def at(self, t: float) -> np.array:\n",
    "    return self.origin + t*self.direction"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 원의 방정식\n",
    "* 중심이 원점에 있고 반지름이 R인 구의 방정식은 $x^2 + y^2 + z^2 = R^2$으로 나타냅니다.\n",
    "  * 한 점 $[x, y, z]^\\intercal$가 구의 표면에 위치하는 경우에만 $x^2 + y^2 + z^2 = R^2$가 성립합니다.\n",
    "  * 한 점 $[x, y, z]^\\intercal$가 구의 위부에 위치한다면 $x^2 + y^2 + z^2 > R^2$가 되고 반대로 구의 내부에 위치한다면 $x^2 + y^2 + z^2 < R^2$가 됩니다.\n",
    "* 구의 중심이 $[C_x, C_y, C_z]^\\intercal$에 있다면 구의 방정식은 다음과 같이 나타낼수 있습니다.\n",
    "$$(x-c_x)^2 + (y-c_y)^2 + (z-c_z)^2 = r^2$$\n",
    "* $\\mathbf{C} = (C_x, C_y, c_z)$에서 $\\mathbf{P} = (x, y, z)$로 향하는 벡터가 있을때 다음과 같이 나타낼 수 있습니다.\n",
    "$$(\\mathbf{P}-\\mathbf{C}) \\cdot (\\mathbf{P}-\\mathbf{C}) = (x - C_x)^2 + (y - C_y)^2 + (z - C_z)^2$$\n",
    "* 위의 식을 벡터 형식으로 정리하면 $(\\mathbf{P}-\\mathbf{C}) \\cdot (\\mathbf{P}-\\mathbf{C}) = r^2$가 됩니다.\n",
    "  * 위의 식을 만족하는 모든 점 $\\mathbf{P}$는 구의 표면에 위치 합니다."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 구와 ray\n",
    "* 여기서는 Ray가 구와 만나는지 알아보려 합니다.\n",
    "  * Ray를 $\\mathbf{A} + t\\mathbf{b} = \\mathbf{P}(t)$와 같이 $t$에 대한 함수로 나타낼 수 있습니다.\n",
    "    * $\\mathbf{A}$는 ray의 시작점, $\\mathbf{b}$는 ray의 방향을 나타냅니다.\n",
    "  * 특정 $t$에 대해서 $\\mathbf{P}(t)$가 구의 방정식을 만족한다면 ray과 구와 만난다고 할 수 있습니다.\n",
    "* 다음의 수식 $(\\mathbf{P}(t)-\\mathbf{C}) \\cdot (\\mathbf{P}(t)-\\mathbf{C}) = r^2$을 만족하는 $t$를 찾습니다.\n",
    "  * 위의 수식에서 $\\mathbf{P}(t)$를 전개하면 다음과 같습니다.\n",
    "$$(\\mathbf{A} + t\\mathbf{b}-\\mathbf{C}) \\cdot (\\mathbf{A} + t\\mathbf{b}-\\mathbf{C}) = r^2$$\n",
    "  * 위의 수식을 정리하고 대수를 모두 좌측으로 옮기면 다음과 같습니다.\n",
    "$$ t^2 \\mathbf{b} \\cdot \\mathbf{b} + 2t\\mathbf{b} \\cdot (\\mathbf{A} - \\mathbf{C}) + (\\mathbf{A} - \\mathbf{C}) \\cdot (\\mathbf{A} - \\mathbf{C}) - r^2 = 0$$\n",
    "\n",
    "<center>\n",
    "<img src=\"./images/ray_and_sphere.png\" width=\"500px\" height=\"350px\" title=\"broadcasting\"/>\n",
    "</center>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 근의 공식\n",
    "$$ax^2 + bx + c = 0$$\n",
    "* $a = \\mathbf{b} \\cdot \\mathbf{b}$\n",
    "* $b = 2 \\mathbf{b} \\cdot (\\mathbf{A} - \\mathbf{C})$\n",
    "* $c = (\\mathbf{A} - \\mathbf{C}) \\cdot (\\mathbf{A} - \\mathbf{C}) - r^2$\n",
    "$$x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$\n",
    "* 판별식: $b^2 - 4ac$\n",
    "  * $b^2 - 4ac < 0$: 근 없음\n",
    "  * $b^2 - 4ac = 0$: 근 하나\n",
    "  * $b^2 - 4ac > 0$: 근 두 개 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_hit_sphere(center: np.array, radius: float, ray: Ray):\n",
    "  dir_center_to_origin = ray.origin - center\n",
    "   \n",
    "  a = np.dot(ray.direction, ray.direction)\n",
    "  b = 2.0*np.dot(dir_center_to_origin, ray.direction)   \n",
    "  c = np.dot(dir_center_to_origin, dir_center_to_origin) - radius**2.0\n",
    "\n",
    "  discriminant = b**2 - 4*a*c\n",
    "  return discriminant >= 0"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 근의 공식 간단화\n",
    "$$\\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$\n",
    "$$ = \\frac{-2h \\pm \\sqrt{(2h)^2 - 4ac}}{2a}$$\n",
    "$$ = \\frac{-2h \\pm 2\\sqrt{h^2 - ac}}{2a}$$\n",
    "$$ = \\frac{-h \\pm \\sqrt{h^2 - ac}}{a}$$\n",
    "\n",
    "* 판별식: $h^2 - ac$\n",
    "  * $h^2 - ac < 0$: 근 없음\n",
    "  * $h^2 - ac = 0$: 근 하나\n",
    "  * $h^2 - ac > 0$: 근 두 개 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_hit_sphere(center: np.array, radius: float, ray: Ray):\n",
    "  dir_center_to_origin = ray.origin - center\n",
    "   \n",
    "  a = np.dot(ray.direction, ray.direction)\n",
    "  half_b = np.dot(dir_center_to_origin, ray.direction)   \n",
    "  c = np.dot(dir_center_to_origin, dir_center_to_origin) - radius**2.0\n",
    "  \n",
    "  discriminant = half_b**2 - a*c\n",
    "  return discriminant >= 0"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* ray_color 함수\n",
    "  * ray가 구와 만나면 구의 색을 반환\n",
    "  * ray가 구와 만나지 않으면 배경의 색을 반환"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ray_color(ray: Ray) -> np.array:\n",
    "  sphere_center = np.array([0, 0, -1])\n",
    "  if (is_hit_sphere(center=sphere_center, radius=0.5, ray=ray)):\n",
    "     return np.array([1.0, 0.0, 0.0])\n",
    "\n",
    "  t = 0.5*(ray.direction[1] + 1.0)\n",
    "  color1 = np.array([1.0, 1.0, 1.0])\n",
    "  color2 = np.array([0.5, 0.7, 1.0])\n",
    "  return blend(color1=color1, color2=color2, t=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# image\n",
    "aspect_ratio = 16.0 / 9.0\n",
    "image_height = 200\n",
    "image_width = int(aspect_ratio * image_height)\n",
    "\n",
    "image = np.zeros([image_height, image_width, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# camera\n",
    "viewport_height = 2.0\n",
    "viewport_width = aspect_ratio * viewport_height\n",
    "focal_length = 1.0\n",
    "\n",
    "camera_origin = np.array([0.0, 0.0, 0.0])\n",
    "horizontal_vec = np.array([viewport_width, 0.0, 0.0])\n",
    "vertical_vec = np.array([0.0, viewport_height, 0.0])\n",
    "frontal_vec = np.array([0.0, 0.0, focal_length])\n",
    "lower_left_corner = camera_origin - horizontal_vec/2.0 - vertical_vec/2.0 - frontal_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.71 s, sys: 13.4 ms, total: 1.72 s\n",
      "Wall time: 1.72 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "for row in range(image_height):\n",
    "  for col in range(image_width):\n",
    "    u = float(col) / (image_width - 1)\n",
    "    v = float(row) / (image_height - 1)\n",
    "\n",
    "    ray = Ray(origin=camera_origin,\n",
    "              direction=(lower_left_corner + u*horizontal_vec + v*vertical_vec) - camera_origin)\n",
    "        \n",
    "    image[row, col] = ray_color(ray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(image, origin='lower')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.10.8"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}