{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# perspective projection\n",
    "\n",
    "```\n",
    "x' = x / z\n",
    "y' = y / z\n",
    "```\n",
    "\n",
    "divide by distance. that's it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# a cube: 8 vertices, 12 edges\n",
    "\n",
    "vertices = [\n",
    "    (-1, -1, -1),\n",
    "    ( 1, -1, -1),\n",
    "    ( 1,  1, -1),\n",
    "    (-1,  1, -1),\n",
    "    (-1, -1,  1),\n",
    "    ( 1, -1,  1),\n",
    "    ( 1,  1,  1),\n",
    "    (-1,  1,  1),\n",
    "]\n",
    "\n",
    "edges = [\n",
    "    (0, 1), (1, 2), (2, 3), (3, 0),  # front\n",
    "    (4, 5), (5, 6), (6, 7), (7, 4),  # back\n",
    "    (0, 4), (1, 5), (2, 6), (3, 7),  # connecting\n",
    "]\n",
    "\n",
    "print(f\"{len(vertices)} vertices, {len(edges)} edges\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the formula\n",
    "\n",
    "def project(x, y, z):\n",
    "    return (x / z, y / z)\n",
    "\n",
    "# example: a point at (2, 1, 4)\n",
    "x, y, z = 2, 1, 4\n",
    "x_proj, y_proj = project(x, y, z)\n",
    "\n",
    "print(f\"3d point: ({x}, {y}, {z})\")\n",
    "print(f\"2d projection: ({x_proj}, {y_proj})\")\n",
    "print(f\"\\nfarther away = smaller on screen\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# static cube\n",
    "\n",
    "from IPython.display import HTML\n",
    "\n",
    "HTML(\"\"\"\n",
    "<canvas id=\"static\" width=\"300\" height=\"300\" style=\"background:#111\"></canvas>\n",
    "<script>\n",
    "(function() {\n",
    "    const canvas = document.getElementById('static');\n",
    "    const ctx = canvas.getContext('2d');\n",
    "    const w = canvas.width, h = canvas.height;\n",
    "    \n",
    "    const vertices = [\n",
    "        [-1,-1,-1], [1,-1,-1], [1,1,-1], [-1,1,-1],\n",
    "        [-1,-1, 1], [1,-1, 1], [1,1, 1], [-1,1, 1]\n",
    "    ];\n",
    "    const edges = [\n",
    "        [0,1],[1,2],[2,3],[3,0],\n",
    "        [4,5],[5,6],[6,7],[7,4],\n",
    "        [0,4],[1,5],[2,6],[3,7]\n",
    "    ];\n",
    "    \n",
    "    function project(x, y, z) {\n",
    "        z += 4;  // push back so z > 0\n",
    "        return [x/z * 100 + w/2, y/z * 100 + h/2];\n",
    "    }\n",
    "    \n",
    "    ctx.strokeStyle = '#0f0';\n",
    "    ctx.lineWidth = 2;\n",
    "    \n",
    "    for (const [i, j] of edges) {\n",
    "        const [x1, y1] = project(...vertices[i]);\n",
    "        const [x2, y2] = project(...vertices[j]);\n",
    "        ctx.beginPath();\n",
    "        ctx.moveTo(x1, y1);\n",
    "        ctx.lineTo(x2, y2);\n",
    "        ctx.stroke();\n",
    "    }\n",
    "})();\n",
    "</script>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# spinning cube\n",
    "\n",
    "from IPython.display import HTML\n",
    "\n",
    "HTML(\"\"\"\n",
    "<canvas id=\"spin\" width=\"300\" height=\"300\" style=\"background:#111\"></canvas>\n",
    "<script>\n",
    "(function() {\n",
    "    const canvas = document.getElementById('spin');\n",
    "    const ctx = canvas.getContext('2d');\n",
    "    const w = canvas.width, h = canvas.height;\n",
    "    \n",
    "    const vertices = [\n",
    "        [-1,-1,-1], [1,-1,-1], [1,1,-1], [-1,1,-1],\n",
    "        [-1,-1, 1], [1,-1, 1], [1,1, 1], [-1,1, 1]\n",
    "    ];\n",
    "    const edges = [\n",
    "        [0,1],[1,2],[2,3],[3,0],\n",
    "        [4,5],[5,6],[6,7],[7,4],\n",
    "        [0,4],[1,5],[2,6],[3,7]\n",
    "    ];\n",
    "    \n",
    "    function rotateY(x, y, z, a) {\n",
    "        const c = Math.cos(a), s = Math.sin(a);\n",
    "        return [x*c - z*s, y, x*s + z*c];\n",
    "    }\n",
    "    \n",
    "    function project(x, y, z) {\n",
    "        z += 4;\n",
    "        return [x/z * 100 + w/2, y/z * 100 + h/2];\n",
    "    }\n",
    "    \n",
    "    let angle = 0;\n",
    "    function draw() {\n",
    "        ctx.fillStyle = '#111';\n",
    "        ctx.fillRect(0, 0, w, h);\n",
    "        ctx.strokeStyle = '#0f0';\n",
    "        ctx.lineWidth = 2;\n",
    "        \n",
    "        for (const [i, j] of edges) {\n",
    "            const a = rotateY(...vertices[i], angle);\n",
    "            const b = rotateY(...vertices[j], angle);\n",
    "            const [x1, y1] = project(...a);\n",
    "            const [x2, y2] = project(...b);\n",
    "            ctx.beginPath();\n",
    "            ctx.moveTo(x1, y1);\n",
    "            ctx.lineTo(x2, y2);\n",
    "            ctx.stroke();\n",
    "        }\n",
    "        \n",
    "        angle += 0.02;\n",
    "        requestAnimationFrame(draw);\n",
    "    }\n",
    "    draw();\n",
    "})();\n",
    "</script>\n",
    "\"\"\")"
   ]
  }
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