当前位置：首页 > article >正文

WebGL笔记：矩阵缩放的数学原理和实现

article 2025/2/22 16:28:02

矩阵缩放的数学原理

和平移一样，以同样的原理，也可以理解缩放矩阵
让向量OA基于原点进行缩放
- x方向上缩放：sx
- y方向上缩放：sy
- z方向上缩放：sz
最终得到向量OB

矩阵缩放的应用

比如我要让顶点在x轴向缩放2，y轴向缩放3，轴向缩放4

1 ）顶点着色器的核心代码

<script id="vertexShader" type="x-shader/x-vertex">
    attribute vec4 a_Position;
    // 列主序
    mat4 m4 = mat4(
      2.0, 0.0, 0.0, 0.0,
      0.0, 3.0, 0.0, 0.0,
      0.0, 0.0, 4.0, 0.0,
      0.0, 0.0, 0.0, 1.0
    );
    void main() {
      gl_Position = m4 * a_Position;
    }
</script>

2 ）完整代码

<canvas id="canvas"></canvas>
<script id="vertexShader" type="x-shader/x-vertex">
  attribute vec4 a_Position;
  float sx = 2.0;
  float sy = 3.0;
  float sz = 4.0;
  // 列主序
  mat4 m4 = mat4(
    sx,  0.0, 0.0, 0.0,
    0.0, sy,  0.0, 0.0,
    0.0, 0.0, sz,  0.0,
    0.0, 0.0, 0.0, 1.0
  );
  void main() {
    gl_Position = m4 * a_Position;
  }
</script>
<script id="fragmentShader" type="x-shader/x-fragment">
  void main() {
    gl_FragColor = vec4(1.0, 1.0, 0.0, 1.0);
  }
</script>
<script type="module">
  import { initShaders } from './utils.js';

  const canvas = document.getElementById('canvas');
  canvas.width = window.innerWidth;
  canvas.height = window.innerHeight;
  const gl = canvas.getContext('webgl');

  const vsSource = document.getElementById('vertexShader').innerText;
  const fsSource = document.getElementById('fragmentShader').innerText;
  initShaders(gl, vsSource, fsSource);

  const vertices = new Float32Array([
    0.0, 0.1,
    -0.1, -0.1,
    0.1, -0.1
  ])

  const vertexBuffer = gl.createBuffer();
  gl.bindBuffer(gl.ARRAY_BUFFER, vertexBuffer);
  gl.bufferData(gl.ARRAY_BUFFER, vertices, gl.STATIC_DRAW);
  const a_Position = gl.getAttribLocation(gl.program, 'a_Position');
  gl.vertexAttribPointer(a_Position, 2, gl.FLOAT, false, 0, 0);
  gl.enableVertexAttribArray(a_Position);

  gl.clearColor(0.0, 0.0, 0.0, 1.0);
  gl.clear(gl.COLOR_BUFFER_BIT);
  gl.drawArrays(gl.TRIANGLES, 0, 3);
</script>