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WebGL笔记：矩阵缩放的数学原理和实现

news 2025/8/5 5:37:35

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>