【WebGL之巅】10-仿射变换之旋转三角形

对应《WebGL编程指南》代码：11-RotatedTriangle

要点：旋转变换、gl.uniform4f()、gl.getUniformLocation()、矢量的加法

步骤

目的：将三角形逆时针旋转90度

计算90度的正余弦值 → 传给顶点着色器uniform变量

知识点

一、正旋转

①描述旋转操作：绕Z轴，逆时针旋转β角度。

②关于“逆时针”的约定：如果β是正值，观察者在Z轴正半轴某处，视线沿着Z轴负方向观察，看到的物体是逆时针旋转的，称为为正旋转。同时满足右手法则旋转（右手握拳，大拇指指向旋转轴的正方向，其余手指的方向就是旋转的方向。）

二、角度计算

$x’ = xcosβ - ysinβ$

$y’ = xsinβ + ycosβ$

$z’ = z$

代码实现：

'uniform float u_CosB, u_SinB;\n' +
'void main() {\n' +
    'gl_Position.x = a_Position.x * u_CosB - a_Position.y * u_SinB;\n' +
    'gl_Position.y = a_Position.x * u_SinB + a_Position.y * u_CosB;\n' +
    'gl_Position.z = a_Position.z;\n' +
    'gl_Position.w = 1.0;\n' +
'}\n';

角度转弧度制（三角函数的计算一般是用弧度计算）：弧度 = π*角度/180°，单位：rad

var radian = Math.PI * ANGLE / 180.0;   // 转为弧度制（πβ/180°）= π/2
var cosB = Math.cos(radian); // 0
var sinB = Math.sin(radian); // 1
console.log(cosB, sinB) // 6.123233995736766e-17 1

三、a_Position的分量访问

vec4 a_Position = (x, y, z, w)

可用 a_Position.x、a_Position.y来访问

实例

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>rotate triangle</title>
</head>
<body onload="main()">
<canvas id="webgl" width="400" height="400">
    Please use the browser supporting "canvas".
</canvas>

<script src="../lib/webgl-utils.js"></script>
<script src="../lib/webgl-debug.js"></script>
<script src="../lib/cuon-utils.js"></script>
<script src="RotatedTriangle.js"></script>
</body>
</html>

/**
 * Created by hushhw on 17/12/14.
 */
//RotatedTriangle.js
var VSHADER_SOURCE =
    //x' = x cos b - y sin b
    //y' = x sin b + y cosb
    //z' = z
    'attribute vec4 a_Position;\n' +
    'uniform float u_CosB, u_SinB;\n' +
    'void main() {\n' +
        'gl_Position.x = a_Position.x * u_CosB - a_Position.y * u_SinB;\n' +
        'gl_Position.y = a_Position.x * u_SinB + a_Position.y * u_CosB;\n' +
        'gl_Position.z = a_Position.z;\n' +
        'gl_Position.w = 1.0;\n' +
    '}\n';

var FSHADER_SOURCE=
    'void main(){'+
        'gl_FragColor = vec4(1.0, 0.0, 0.0, 1.0);'+
    '}';

// 旋转角度 
var ANGLE = 90.0;

function main(){

    var canvas = document.getElementById("webgl");
    if(!canvas){
        console.log("Failed to retrieve the <canvas> element");
        return;
    }

    var gl = getWebGLContext(canvas);
    if(!gl){
        console.log("Failed to get the rendering context for WebGL");
        return;
    }

    if(!initShaders(gl,VSHADER_SOURCE,FSHADER_SOURCE)){
        console.log("Failed to initialize shaders.");
        return;
    }

    //设置顶点位置
    var n = initVertexBuffers(gl);
    if (n < 0) {
        console.log('Failed to set the positions of the vertices');
        return;
    }

    // 角度计算
    var radian = Math.PI * ANGLE / 180.0;   // 转为弧度制（πβ/180°）
    var cosB = Math.cos(radian);
    var sinB = Math.sin(radian);

    var u_CosB = gl.getUniformLocation(gl.program, 'u_CosB');
    if(u_CosB < 0){
        console.log("Failed to get the storage location of u_CosB");
        return;
    }

    var u_SinB = gl.getUniformLocation(gl.program, 'u_SinB');
    if(u_SinB < 0){
        console.log("Failed to get the storage location of u_SinB");
        return;
    }
    // 赋值给uniform变量
    gl.uniform1f(u_CosB, cosB);
    gl.uniform1f(u_SinB, sinB);

    gl.clearColor(0.0, 0.0, 0.0, 1.0);

    gl.clear(gl.COLOR_BUFFER_BIT);

    gl.drawArrays(gl.TRIANGLES, 0, n);
}

function initVertexBuffers(gl) {
    var vertices = new Float32Array(
        [0.0, 0.5, -0.5, -0.5, 0.5, -0.5]
    );
    var n=3; //点的个数

    //创建缓冲区对象
    var vertexBuffer = gl.createBuffer();
    if(!vertexBuffer){
        console.log("Failed to create thie buffer object");
        return -1;
    }

    //将缓冲区对象保存到目标上
    gl.bindBuffer(gl.ARRAY_BUFFER, vertexBuffer);

    //向缓存对象写入数据
    gl.bufferData(gl.ARRAY_BUFFER, vertices, gl.STATIC_DRAW);

    var a_Position = gl.getAttribLocation(gl.program, 'a_Position');
    if(a_Position < 0){
        console.log("Failed to get the storage location of a_Position");
        return -1;
    }

    //将缓冲区对象分配给a_Postion变量
    gl.vertexAttribPointer(a_Position, 2, gl.FLOAT, false, 0, 0);

    //连接a_Postion变量与分配给它的缓冲区对象
    gl.enableVertexAttribArray(a_Position);

    return n;
}

效果

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步骤

知识点

一、正旋转

二、角度计算

三、a_Position的分量访问

实例

效果

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