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  1. <!DOCTYPE html>
  2. <html lang="zh-CN">
  3. <head>
  4. <meta charset="UTF-8">
  5. <title>3D Mandelbrot WebGL Renderer</title>
  6. <style>
  7. body { margin: 0; overflow: hidden; background: #000; }
  8. canvas { display: block; width: 100vw; height: 100vh; }
  9. #instruction {
  10. position: absolute;
  11. top: 10px; left: 10px;
  12. color: rgba(255,255,255,0.8);
  13. background: rgba(0,0,0,0.6);
  14. padding: 15px;
  15. border-radius: 8px;
  16. font-family: sans-serif;
  17. pointer-events: none;
  18. user-select: none;
  19. }
  20. </style>
  21. </head>
  22. <body>
  23. <div id="instruction">
  24. <h3>复数分形探索器 (WebGL)</h3>
  25. <p>• 滚轮:无极缩放 (Zoom)</p>
  26. <p>• 拖拽:移动视野 (Pan)</p>
  27. <p>• 算法:Distance Estimation (DEM) + Phong Lighting</p>
  28. <p style="font-size:12px; color:#aaa;">对应你上传的图2风格</p>
  29. </div>
  30. <canvas id="glcanvas"></canvas>
  31. <script id="vs" type="x-shader/x-vertex">
  32. attribute vec2 position;
  33. void main() {
  34. gl_Position = vec4(position, 0.0, 1.0);
  35. }
  36. </script>
  37. <script id="fs" type="x-shader/x-fragment">
  38. precision highp float;
  39. uniform vec2 u_resolution;
  40. uniform vec2 u_center;
  41. uniform float u_zoom;
  42. uniform float u_time;
  43. // 复数乘法
  44. vec2 complexMul(vec2 a, vec2 b) {
  45. return vec2(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
  46. }
  47. // HSV转RGB辅助函数
  48. vec3 hsv2rgb(vec3 c) {
  49. vec4 K = vec4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);
  50. vec3 p = abs(fract(c.xxx + K.xyz) * 6.0 - K.www);
  51. return c.z * mix(K.xxx, clamp(p - K.xxx, 0.0, 1.0), c.y);
  52. }
  53. void main() {
  54. // 1. 坐标归一化
  55. vec2 uv = (gl_FragCoord.xy - 0.5 * u_resolution.xy) / u_resolution.y;
  56. // 2. 应用缩放和位移 (映射到复数平面 C)
  57. vec2 c = u_center + uv * (4.0 / u_zoom);
  58. // Z用于迭代,DZ用于距离估算(导数)
  59. vec2 z = vec2(0.0);
  60. vec2 dz = vec2(0.0);
  61. float iter = 0.0;
  62. const float max_iter = 500.0; // 最大迭代次数
  63. float escapeRadius = 1024.0; // 逃逸半径
  64. // 3. 核心迭代循环 Z = Z^2 + C
  65. // 同时计算导数 dZ = 2*Z*dZ + 1 (用于计算距离)
  66. float trap = 1e20; // 轨道陷阱变量(用于图1那种球体效果,这里简化做纹理)
  67. for (float i = 0.0; i < max_iter; i++) {
  68. // 导数迭代: dz = 2*z*dz + 1
  69. dz = 2.0 * complexMul(z, dz) + vec2(1.0, 0.0);
  70. // 主函数迭代: z = z^2 + c
  71. z = complexMul(z, z) + c;
  72. // 记录最小距离作为纹理(类似Orbit Trap)
  73. trap = min(trap, abs(z.x * z.y));
  74. // 检查逃逸
  75. if (dot(z, z) > escapeRadius) {
  76. iter = i;
  77. break;
  78. }
  79. iter = i;
  80. }
  81. // 4. 距离估算 (Distance Estimation)
  82. // d = 0.5 * |z| * log(|z|) / |dz|
  83. float r = length(z);
  84. float dist = 0.5 * r * log(r) / length(dz);
  85. // 5. 渲染逻辑
  86. vec3 color = vec3(0.0);
  87. if (iter < max_iter) {
  88. // --- 外部着色 (External) ---
  89. // 平滑迭代数 (消除颜色断层)
  90. float smoothIter = iter - log2(log2(dot(z,z))) + 4.0;
  91. // 模拟3D光照 (基于距离场的法线计算)
  92. // 我们不通过差分计算法线,而是直接用距离函数衰减来模拟光晕
  93. float edge = clamp(pow(dist, 0.2) * 1.5, 0.0, 1.0);
  94. // 基础色调:蓝色 -> 奶油色 -> 深紫 (模仿图2)
  95. float t = smoothIter * 0.05 - u_time * 0.02;
  96. vec3 col1 = vec3(0.1, 0.2, 0.5); // 深蓝
  97. vec3 col2 = vec3(0.95, 0.8, 0.6); // 奶油/金
  98. vec3 col3 = vec3(0.4, 0.0, 0.4); // 紫
  99. vec3 baseColor = 0.5 + 0.5 * cos(6.28318 * (vec3(1.0) * t + vec3(0.0, 0.33, 0.67)));
  100. // 混合颜色
  101. color = baseColor * edge;
  102. // 添加类似图2的"山脊"高光
  103. // 如果距离非常小(靠近集合边界),则调亮
  104. float ridge = 1.0 / (1.0 + 100.0 * dist);
  105. color += vec3(1.0, 0.9, 0.8) * ridge;
  106. } else {
  107. // --- 内部着色 (Internal / Mandelbrot Set) ---
  108. color = vec3(0.0); // 黑色核心
  109. }
  110. gl_FragColor = vec4(color, 1.0);
  111. }
  112. </script>
  113. <script>
  114. // WebGL 初始化样板代码
  115. const canvas = document.getElementById('glcanvas');
  116. const gl = canvas.getContext('webgl');
  117. if (!gl) { alert("您的浏览器不支持WebGL"); }
  118. // 编译着色器
  119. function createShader(gl, type, source) {
  120. const shader = gl.createShader(type);
  121. gl.shaderSource(shader, source);
  122. gl.compileShader(shader);
  123. if (!gl.getShaderParameter(shader, gl.COMPILE_STATUS)) {
  124. console.error(gl.getShaderInfoLog(shader));
  125. gl.deleteShader(shader);
  126. return null;
  127. }
  128. return shader;
  129. }
  130. const vsSource = document.getElementById('vs').text;
  131. const fsSource = document.getElementById('fs').text;
  132. const vertexShader = createShader(gl, gl.VERTEX_SHADER, vsSource);
  133. const fragmentShader = createShader(gl, gl.FRAGMENT_SHADER, fsSource);
  134. const program = gl.createProgram();
  135. gl.attachShader(program, vertexShader);
  136. gl.attachShader(program, fragmentShader);
  137. gl.linkProgram(program);
  138. gl.useProgram(program);
  139. // 设置矩形顶点 (覆盖全屏)
  140. const positionBuffer = gl.createBuffer();
  141. gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);
  142. gl.bufferData(gl.ARRAY_BUFFER, new Float32Array([
  143. -1, -1, 1, -1, -1, 1,
  144. -1, 1, 1, -1, 1, 1,
  145. ]), gl.STATIC_DRAW);
  146. const positionLocation = gl.getAttribLocation(program, "position");
  147. gl.enableVertexAttribArray(positionLocation);
  148. gl.vertexAttribPointer(positionLocation, 2, gl.FLOAT, false, 0, 0);
  149. // Uniforms 变量位置
  150. const uResolution = gl.getUniformLocation(program, "u_resolution");
  151. const uCenter = gl.getUniformLocation(program, "u_center");
  152. const uZoom = gl.getUniformLocation(program, "u_zoom");
  153. const uTime = gl.getUniformLocation(program, "u_time");
  154. // 交互状态
  155. let state = {
  156. x: -0.745, // 经典的“海马谷”位置
  157. y: 0.1,
  158. zoom: 1.0,
  159. targetZoom: 1.0,
  160. dragging: false,
  161. lastX: 0,
  162. lastY: 0
  163. };
  164. function resize() {
  165. canvas.width = window.innerWidth;
  166. canvas.height = window.innerHeight;
  167. gl.viewport(0, 0, canvas.width, canvas.height);
  168. }
  169. window.addEventListener('resize', resize);
  170. resize();
  171. // 交互逻辑
  172. canvas.addEventListener('mousedown', e => {
  173. state.dragging = true;
  174. state.lastX = e.clientX;
  175. state.lastY = e.clientY;
  176. });
  177. window.addEventListener('mouseup', () => state.dragging = false);
  178. window.addEventListener('mousemove', e => {
  179. if (state.dragging) {
  180. const dx = e.clientX - state.lastX;
  181. const dy = e.clientY - state.lastY;
  182. state.lastX = e.clientX;
  183. state.lastY = e.clientY;
  184. // 移动速度随缩放层级调整
  185. const moveSpeed = 4.0 / (state.zoom * canvas.height);
  186. state.x -= dx * moveSpeed;
  187. state.y += dy * moveSpeed; // WebGL Y轴通常相反,但在复数平面视情况而定
  188. }
  189. });
  190. canvas.addEventListener('wheel', e => {
  191. e.preventDefault();
  192. const zoomSpeed = 1.05;
  193. if (e.deltaY < 0) state.targetZoom *= zoomSpeed;
  194. else state.targetZoom /= zoomSpeed;
  195. }, { passive: false });
  196. // 渲染循环
  197. function render(time) {
  198. time *= 0.001;
  199. // 简单的平滑缩放
  200. state.zoom += (state.targetZoom - state.zoom) * 0.1;
  201. gl.uniform2f(uResolution, canvas.width, canvas.height);
  202. gl.uniform2f(uCenter, state.x, state.y);
  203. gl.uniform1f(uZoom, state.zoom);
  204. gl.uniform1f(uTime, time);
  205. gl.drawArrays(gl.TRIANGLES, 0, 6);
  206. requestAnimationFrame(render);
  207. }
  208. requestAnimationFrame(render);
  209. </script>
  210. </body>
  211. </html>