WebGL或OpenGL关于模型视图投影变换的设置技巧

c/c++

浏览数:19

2019-9-15


1. 具体实例

看了不少的关于WebGL/OpenGL的资料,笔者发现这些资料在讲解图形变换的时候都讲了很多的原理,然后举出一个特别简单的实例(坐标是1.0,0.5的那种)来讲解。确实一看就懂,但用到实际的场景之中就一脸懵逼了(比如地形的三维坐标都是很大的数字)。所以笔者这里结合一个具体的实例,总结下WebGL/OpenGL中,关于模型变换、视图变换、投影变换的设置技巧。

绘制任何复杂的场景之前,都可以先绘制出其包围盒,能应用于包围盒的图形变换,基本上就能用于该场景了,因此,笔者这里绘制一幅地形的包围盒。它的最大最小范围为:

//包围盒范围
var minX = 399589.072;
var maxX = 400469.072;
var minY = 3995118.062;
var maxY = 3997558.062;
var minZ = 732;
var maxZ = 1268;

2. 解决方案

WebGL是OpenGL的子集,因此我这里直接用WebGL的例子,但是各种接口函数跟OpenGL是非常类似的,尤其是图形变换的函数。

1) Cube.html

<!DOCTYPE html>
<html lang="zh">
  <head>
    <meta charset="utf-8" />
    <title>Hello cube</title>
  </head>

  <body onload="main()">
    <canvas id="webgl" width="600" height="600">
    Please use a browser that supports "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="lib/cuon-matrix.js"></script>
    <script src="Cube.js"></script>
  </body>
</html>

2) Cube.js

// Vertex shader program
var VSHADER_SOURCE =
    'attribute vec4 a_Position;\n' +
    'attribute vec4 a_Color;\n' +
    'uniform mat4 u_MvpMatrix;\n' +
    'varying vec4 v_Color;\n' +
    'void main() {\n' +
    '  gl_Position = u_MvpMatrix * a_Position;\n' +
    '  v_Color = a_Color;\n' +
    '}\n';

// Fragment shader program
var FSHADER_SOURCE =
    '#ifdef GL_ES\n' +
    'precision mediump float;\n' +
    '#endif\n' +
    'varying vec4 v_Color;\n' +
    'void main() {\n' +
    '  gl_FragColor = v_Color;\n' +
    '}\n';

//包围盒范围
var minX = 399589.072;
var maxX = 400469.072;
var minY = 3995118.062;
var maxY = 3997558.062;
var minZ = 732;
var maxZ = 1268;

//包围盒中心
var cx = (minX + maxX) / 2.0;
var cy = (minY + maxY) / 2.0;
var cz = (minZ + maxZ) / 2.0;

//当前lookAt()函数初始视点的高度
var eyeHight = 2000.0;

//根据视点高度算出setPerspective()函数的合理角度
var fovy = (maxY - minY) / 2.0 / eyeHight;
fovy = 180.0 / Math.PI * Math.atan(fovy) * 2;

//setPerspective()远截面
var far = 3000;

//
function main() {
    // Retrieve <canvas> element
    var canvas = document.getElementById('webgl');

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

    // Initialize shaders
    if (!initShaders(gl, VSHADER_SOURCE, FSHADER_SOURCE)) {
        console.log('Failed to intialize shaders.');
        return;
    }

    // Set the vertex coordinates and color
    var n = initVertexBuffers(gl);
    if (n < 0) {
        console.log('Failed to set the vertex information');
        return;
    }

    // Get the storage location of u_MvpMatrix
    var u_MvpMatrix = gl.getUniformLocation(gl.program, 'u_MvpMatrix');
    if (!u_MvpMatrix) {
        console.log('Failed to get the storage location of u_MvpMatrix');
        return;
    }

    // Register the event handler
    var currentAngle = [0.0, 0.0]; // Current rotation angle ([x-axis, y-axis] degrees)
    initEventHandlers(canvas, currentAngle);

    // Set clear color and enable hidden surface removal
    gl.clearColor(0.0, 0.0, 0.0, 1.0);
    gl.enable(gl.DEPTH_TEST);

    // Start drawing
    var tick = function () {

        //setPerspective()宽高比
        var aspect = canvas.width / canvas.height;

        //
        draw(gl, n, aspect, u_MvpMatrix, currentAngle);
        requestAnimationFrame(tick, canvas);
    };
    tick();
}

function initEventHandlers(canvas, currentAngle) {
    var dragging = false;         // Dragging or not
    var lastX = -1, lastY = -1;   // Last position of the mouse

    // Mouse is pressed
    canvas.onmousedown = function (ev) {
        var x = ev.clientX;
        var y = ev.clientY;
        // Start dragging if a moue is in <canvas>
        var rect = ev.target.getBoundingClientRect();
        if (rect.left <= x && x < rect.right && rect.top <= y && y < rect.bottom) {
            lastX = x;
            lastY = y;
            dragging = true;
        }
    };

    //鼠标离开时
    canvas.onmouseleave = function (ev) {
        dragging = false;
    };

    // Mouse is released
    canvas.onmouseup = function (ev) {
        dragging = false;
    };

    // Mouse is moved
    canvas.onmousemove = function (ev) {
        var x = ev.clientX;
        var y = ev.clientY;
        if (dragging) {
            var factor = 100 / canvas.height; // The rotation ratio
            var dx = factor * (x - lastX);
            var dy = factor * (y - lastY);
            // Limit x-axis rotation angle to -90 to 90 degrees
            //currentAngle[0] = Math.max(Math.min(currentAngle[0] + dy, 90.0), -90.0);
            currentAngle[0] = currentAngle[0] + dy;
            currentAngle[1] = currentAngle[1] + dx;
        }
        lastX = x, lastY = y;
    };

    //鼠标缩放
    canvas.onmousewheel = function (event) {
        var lastHeight = eyeHight;
        if (event.wheelDelta > 0) {
            eyeHight = Math.max(1, eyeHight - 80);
        } else {
            eyeHight = eyeHight + 80;
        }

        far = far + eyeHight - lastHeight;
    };
}

function draw(gl, n, aspect, u_MvpMatrix, currentAngle) {
    //模型矩阵
    var modelMatrix = new Matrix4();
    modelMatrix.rotate(currentAngle[0], 1.0, 0.0, 0.0); // Rotation around x-axis 
    modelMatrix.rotate(currentAngle[1], 0.0, 1.0, 0.0); // Rotation around y-axis    
    modelMatrix.translate(-cx, -cy, -cz);

    //视图矩阵
    var viewMatrix = new Matrix4();
    viewMatrix.lookAt(0, 0, eyeHight, 0, 0, 0, 0, 1, 0);

    //投影矩阵
    var projMatrix = new Matrix4();
    projMatrix.setPerspective(fovy, aspect, 10, far);

    //模型视图投影矩阵
    var mvpMatrix = new Matrix4();
    mvpMatrix.set(projMatrix).multiply(viewMatrix).multiply(modelMatrix);

    // Pass the model view projection matrix to u_MvpMatrix
    gl.uniformMatrix4fv(u_MvpMatrix, false, mvpMatrix.elements);

    // Clear color and depth buffer
    gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);

    // Draw the cube
    gl.drawElements(gl.TRIANGLES, n, gl.UNSIGNED_BYTE, 0);
}

function initVertexBuffers(gl) {
    // Create a cube
    //    v6----- v5
    //   /|      /|
    //  v1------v0|
    //  | |     | |
    //  | |v7---|-|v4
    //  |/      |/
    //  v2------v3

    var verticesColors = new Float32Array([
        // Vertex coordinates and color
        maxX, maxY, maxZ, 1.0, 1.0, 1.0,  // v0 White
        minX, maxY, maxZ, 1.0, 0.0, 1.0,  // v1 Magenta
        minX, minY, maxZ, 1.0, 0.0, 0.0,  // v2 Red
        maxX, minY, maxZ, 1.0, 1.0, 0.0,  // v3 Yellow
        maxX, minY, minZ, 0.0, 1.0, 0.0,  // v4 Green
        maxX, maxY, minZ, 0.0, 1.0, 1.0,  // v5 Cyan
        minX, maxY, minZ, 0.0, 0.0, 1.0,  // v6 Blue
        minX, minY, minZ, 1.0, 0.0, 1.0   // v7 Black
    ]);

    // Indices of the vertices
    var indices = new Uint8Array([
        0, 1, 2, 0, 2, 3,    // front
        0, 3, 4, 0, 4, 5,    // right
        0, 5, 6, 0, 6, 1,    // up
        1, 6, 7, 1, 7, 2,    // left
        7, 4, 3, 7, 3, 2,    // down
        4, 7, 6, 4, 6, 5     // back
    ]);

    // Create a buffer object
    var vertexColorBuffer = gl.createBuffer();
    var indexBuffer = gl.createBuffer();
    if (!vertexColorBuffer || !indexBuffer) {
        return -1;
    }

    // Write the vertex coordinates and color to the buffer object
    gl.bindBuffer(gl.ARRAY_BUFFER, vertexColorBuffer);
    gl.bufferData(gl.ARRAY_BUFFER, verticesColors, gl.STATIC_DRAW);

    var FSIZE = verticesColors.BYTES_PER_ELEMENT;
    // Assign the buffer object to a_Position and enable the assignment
    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;
    }
    gl.vertexAttribPointer(a_Position, 3, gl.FLOAT, false, FSIZE * 6, 0);
    gl.enableVertexAttribArray(a_Position);
    // Assign the buffer object to a_Color and enable the assignment
    var a_Color = gl.getAttribLocation(gl.program, 'a_Color');
    if (a_Color < 0) {
        console.log('Failed to get the storage location of a_Color');
        return -1;
    }
    gl.vertexAttribPointer(a_Color, 3, gl.FLOAT, false, FSIZE * 6, FSIZE * 3);
    gl.enableVertexAttribArray(a_Color);

    // Write the indices to the buffer object
    gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, indexBuffer);
    gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, indices, gl.STATIC_DRAW);

    return indices.length;
}

3) 运行结果

这份代码改进《WebGL编程指南》一书里面绘制一个简单立方体的例子,引用的几个JS-lib也是该书提供。本例全部源代码地址链接为:https://share.weiyun.com/52XmsFv ,密码:h1lbay。
用chrome打开Cube.html,会出现一个长方体的包围盒,还可以用鼠标左键旋转,鼠标滚轮缩放:

3. 详细讲解

本例的思路是通过JS的requestAnimationFrame()函数不停的调用绘制函数draw(),同时将一些变量关联到鼠标操作事件和draw(),达到页面图形变换的效果。这里笔者就不讲原理,重点讲一讲设置三个图形变换的具体过程,网上已经有非常多的原理介绍了。

1) 模型变换

在draw()函数中设置模型矩阵:

//模型矩阵
var modelMatrix = new Matrix4();
modelMatrix.rotate(currentAngle[0], 1.0, 0.0, 0.0); // Rotation around x-axis 
modelMatrix.rotate(currentAngle[1], 0.0, 1.0, 0.0); // Rotation around y-axis    
modelMatrix.translate(-cx, -cy, -cz);

由于这个包围盒(长方体)的坐标值都非常大,所以第一步需要对其做平移变换translate(-cx, -cy, -cz),cx,cy,cz就是包围盒的中心:

//包围盒中心
var cx = (minX + maxX) / 2.0;
var cy = (minY + maxY) / 2.0;
var cz = (minZ + maxZ) / 2.0;

接下来是旋转变换,数组currentAngle记录了绕X轴和Y轴旋转的角度,初始值为0。配合onmousedown,onmouseup,onmousemove三个鼠标事件,将页面鼠标X、Y方向的移动,转换成绕X轴,Y轴的角度值,累计到currentAngle中,从而实现了三维模型随鼠标旋转。

// Mouse is moved
canvas.onmousemove = function (ev) {
    var x = ev.clientX;
    var y = ev.clientY;
    if (dragging) {
        var factor = 100 / canvas.height; // The rotation ratio
        var dx = factor * (x - lastX);
        var dy = factor * (y - lastY);
        // Limit x-axis rotation angle to -90 to 90 degrees
        //currentAngle[0] = Math.max(Math.min(currentAngle[0] + dy, 90.0), -90.0);
        currentAngle[0] = currentAngle[0] + dy;
        currentAngle[1] = currentAngle[1] + dx;
    }
    lastX = x, lastY = y;
};

注意模型矩阵的平移变换要放后面,需要把坐标轴换到包围盒中心,才能绕三维模型自转。

2) 视图变换

通过lookAt()函数设置视图矩阵:

//当前lookAt()函数初始视点的高度
var eyeHight = 2000.0;

// …

//视图矩阵
var viewMatrix = new Matrix4();
viewMatrix.lookAt(0, 0, eyeHight, 0, 0, 0, 0, 1, 0);

视图变换调整的是观察者的状态,lookAt()函数分别设置了视点、目标观察点以及上方向。虽然可以在任何位置去观察三维场景的点,从而得到渲染结果。但在实际的应用当中,这个函数设置的结果很难以想象,所以笔者设置成,观察者站在包围盒中心上方的位置,对准坐标系原点(注意这个时候经过模型变换,包围盒的中心点已经是坐标系原点了),常见的Y轴作为上方向。这样,视图内无论如何都是可见的。
这里将视点的高度设置成变量eyeHight,初始值为2000,是一个大于0的经验值。同时通过鼠标的滚轮事件onmousewheel()调整该值,从而实现三维模型的缩放的:

 //鼠标缩放
 canvas.onmousewheel = function (event) {
     var lastHeight = eyeHight;
     if (event.wheelDelta > 0) {
         eyeHight = Math.max(1, eyeHight - 80);
     } else {
         eyeHight = eyeHight + 80;
     } 
 };

3) 投影变换

通过setPerspective()来设置投影变换:

//根据视点高度算出setPerspective()函数的合理角度
var fovy = (maxY - minY) / 2.0 / eyeHight;
fovy = 180.0 / Math.PI * Math.atan(fovy) * 2;

//setPerspective()远截面
var far = 3000;

//setPerspective()宽高比
var aspect = canvas.width / canvas.height;

//...

//投影矩阵
var projMatrix = new Matrix4();
projMatrix.setPerspective(fovy, aspect, 10, far);

前面的视图变换已经论述了,这个模型是在中心点上方去观察中心点,相当于视线垂直到前界面near的表面,那么setPerspective()就可以确定其角度fovy了,示意图如下:

很明显的看出,当光线射到包围盒的中心,包围盒Y方向长度的一半,除以视点高,就是fovy一般的正切值。

宽高比aspect即是页面canvas元素的宽高比。

近界面near一般设置成较近的值,但是不能太近(比如小于1),否则会影响深度判断的精度造成页面闪烁。《OpenGL绘制纹理,缩放相机导致纹理闪烁的解决方法gluPerspective ()》论述了这个问题。

而远界面far也是需要跟着鼠标滚轮一起变换的,否则当eyeHight变大,三维物体会逐渐离开透视变换的视锥体:

//鼠标缩放
canvas.onmousewheel = function (event) {
    var lastHeight = eyeHight;
    if (event.wheelDelta > 0) {
        eyeHight = Math.max(1, eyeHight - 80);
    } else {
        eyeHight = eyeHight + 80;
    }

    far = far + eyeHight - lastHeight;
};

4) 模型视图投影矩阵

将三个矩阵都应用起来,就得到最终的模型视图投影矩阵。注意计算式是:投影矩阵 * 视图矩阵 * 模型矩阵:

//模型视图投影矩阵
var mvpMatrix = new Matrix4();
mvpMatrix.set(projMatrix).multiply(viewMatrix).multiply(modelMatrix);

4. 存在问题

本例中的三维物体随着鼠标旋转,是把鼠标X、Y方向的移动距离转换成绕X轴,Y轴方向的角度来实现的。但是如何用鼠标实现绕Z轴(第三轴)旋转呢?例如像OSG这样的渲染引擎,是可以用鼠标绕第三个轴旋转的(当然操作有点费力)。这里希望大家能批评指正下。

作者:charlee44