WebGL简易教程(十二)：包围球与投影
1. 概述
在之前的教程中，都是通过物体的包围盒来设置模型视图投影矩阵（MVP矩阵），来确定物体合适的位置的。但是在很多情况下，使用包围盒并不方便计算，可以利用包围盒再生成一个包围球，利用包围球来设置MVP矩阵。
在《WebGL简易教程(十)：光照》中，给地形赋予了固定方向的平行光。这篇教程的例子就是想模拟在平行光的视角下地形的情况。对于点光源光，可以用透视投影来实现渲染的效果；而平行光就需要通过正射投影来模拟。并且，这种正射并不是垂直到达地面，而是附带一定角度[1]：
在这种情况下使用包围盒来计算合适的位置有点难度，使用包围球来设置MVP矩阵更加方便。
2. 实现详解
包围球是利用包围盒生成的，所以首先需要定义一个球体对象:
//定义一个球体
function Sphere(cuboid) {
this.centerX = cuboid.CenterX();
this.centerY = cuboid.CenterY();
this.centerZ = cuboid.CenterZ();
this.radius = Math.max(Math.max(cuboid.LengthX(), cuboid.LengthY()), cuboid.LengthZ()) / 2.0;
}
Sphere.prototype = {
constructor: Sphere
}
这个球体对象的构造函数传入了一个包围盒对象，以包围盒的中心为球体的中心，包围盒长、宽、高的最大值作为包围球的直径。在构造出包围盒之后，利用包围盒参数构造出包围球，将其保存在自定义的Terrain对象中：
var terrain = new Terrain();
//....
terrain.cuboid = new Cuboid(minX, maxX, minY, maxY, minZ, maxZ);
terrain.sphere = new Sphere(terrain.cuboid);
接下来就是改进设置MVP矩阵的函数setMVPMatrix()了。如果仍然想像之前那样进行透视投影，几乎可以不用做改动：
//设置MVP矩阵
function setMVPMatrix(gl, canvas, sphere, lightDirection) {
//...
//投影矩阵
var fovy = 60;
var projMatrix = new Matrix4();
projMatrix.setPerspective(fovy, canvas.width / canvas.height, 1, 10000);
//计算lookAt()函数初始视点的高度
var angle = fovy / 2 * Math.PI / 180.0;
var eyeHight = (sphere.radius * 2 * 1.1) / 2.0 / angle;
//视图矩阵
var viewMatrix = new Matrix4(); // View matrix
viewMatrix.lookAt(0, 0, eyeHight, 0, 0, 0, 0, 1, 0);
//...
}
之前是通过透视变换的张角和包围盒的Y方向长度来计算合适的视野高度，现在只不过将包围盒的Y方向长度换成包围球的直径。这样的写法兼容性更高，因为包围球的直径是包围盒XYZ三个方向的最大长度。这个时候的初始渲染状态为：
最后实现下特定角度平行光视角下的地形渲染情况。前面说到过这种情况下是需要设置正射投影的，具体设置过程如下：
//设置MVP矩阵
function setMVPMatrix(gl, canvas, sphere, lightDirection) {
//...
//模型矩阵
var modelMatrix = new Matrix4();
modelMatrix.scale(curScale, curScale, curScale);
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(-sphere.centerX, -sphere.centerY, -sphere.centerZ);
//视图矩阵
var viewMatrix = new Matrix4();
var r = sphere.radius + 10;
viewMatrix.lookAt(lightDirection.elements[0] * r, lightDirection.elements[1] * r, lightDirection.elements[2] * r, 0, 0, 0, 0, 1, 0);
//投影矩阵
var projMatrix = new Matrix4();
var diameter = sphere.radius * 2.1;
var ratioWH = canvas.width / canvas.height;
var nearHeight = diameter;
var nearWidth = nearHeight * ratioWH;
projMatrix.setOrtho(-nearWidth / 2, nearWidth / 2, -nearHeight / 2, nearHeight / 2, 1, 10000);
//...
}
- 通过模型变换，将世界坐标系的中心平移到包围球的中心。
- 设置视图矩阵的时候将观察点放到这个(0,0,0)，也就是这个包围球中心；由于视野的方向也就是光线的方向知道，那么可以通过这个方向将视点位置设在与(0,0,0)相距比包围球半径远一点点的位置，就可以保证这个地形都能够被看见。
- 通过包围球的直径，来计算正射投影的盒装可视空间的最小范围。
这个时候的初始渲染状态为：
3. 具体代码
具体实现代码如下：
// 顶点着色器程序
var VSHADER_SOURCE =
'attribute vec4 a_Position;\n' + //位置
'attribute vec4 a_Color;\n' + //颜色
'attribute vec4 a_Normal;\n' + //法向量
'uniform mat4 u_MvpMatrix;\n' +
'varying vec4 v_Color;\n' +
'varying vec4 v_Normal;\n' +
'void main() {\n' +
' gl_Position = u_MvpMatrix * a_Position;\n' + //设置顶点的坐标
' v_Color = a_Color;\n' +
' v_Normal = a_Normal;\n' +
'}\n';
// 片元着色器程序
var FSHADER_SOURCE =
'precision mediump float;\n' +
'uniform vec3 u_DiffuseLight;\n' + // 漫反射光颜色
'uniform vec3 u_LightDirection;\n' + // 漫反射光的方向
'uniform vec3 u_AmbientLight;\n' + // 环境光颜色
'varying vec4 v_Color;\n' +
'varying vec4 v_Normal;\n' +
'void main() {\n' +
//对法向量归一化
' vec3 normal = normalize(v_Normal.xyz);\n' +
//计算光线向量与法向量的点积
' float nDotL = max(dot(u_LightDirection, normal), 0.0);\n' +
//计算漫发射光的颜色
' vec3 diffuse = u_DiffuseLight * v_Color.rgb * nDotL;\n' +
//计算环境光的颜色
' vec3 ambient = u_AmbientLight * v_Color.rgb;\n' +
' gl_FragColor = vec4(diffuse+ambient, v_Color.a);\n' +
'}\n';
//定义一个矩形体：混合构造函数原型模式
function Cuboid(minX, maxX, minY, maxY, minZ, maxZ) {
this.minX = minX;
this.maxX = maxX;
this.minY = minY;
this.maxY = maxY;
this.minZ = minZ;
this.maxZ = maxZ;
}
Cuboid.prototype = {
constructor: Cuboid,
CenterX: function () {
return (this.minX + this.maxX) / 2.0;
},
CenterY: function () {
return (this.minY + this.maxY) / 2.0;
},
CenterZ: function () {
return (this.minZ + this.maxZ) / 2.0;
},
LengthX: function () {
return (this.maxX - this.minX);
},
LengthY: function () {
return (this.maxY - this.minY);
},
LengthZ: function () {
return (this.maxZ - this.minZ);
}
}
//定义一个球体
function Sphere(cuboid) {
this.centerX = cuboid.CenterX();
this.centerY = cuboid.CenterY();
this.centerZ = cuboid.CenterZ();
this.radius = Math.max(Math.max(cuboid.LengthX(), cuboid.LengthY()), cuboid.LengthZ()) / 2.0;
}
Sphere.prototype = {
constructor: Sphere
}
//定义DEM
function Terrain() { }
Terrain.prototype = {
constructor: Terrain,
setWH: function (col, row) {
this.col = col;
this.row = row;
}
}
var currentAngle = [0.0, 0.0]; // 绕X轴Y轴的旋转角度 ([x-axis, y-axis])
var curScale = 1.0; //当前的缩放比例
function main() {
var demFile = document.getElementById('demFile');
if (!demFile) {
console.log("Failed to get demFile element!");
return;
}
demFile.addEventListener("change", function (event) {
//判断浏览器是否支持FileReader接口
if (typeof FileReader == 'undefined') {
console.log("你的浏览器不支持FileReader接口！");
return;
}
var input = event.target;
var reader = new FileReader();
reader.onload = function () {
if (reader.result) {
//读取
var terrain = new Terrain();
if (!readDEMFile(reader.result, terrain)) {
console.log("文件格式有误，不能读取该文件！");
}
//绘制
onDraw(gl, canvas, terrain);
}
}
reader.readAsText(input.files[0]);
});
// 获取 <canvas> 元素
var canvas = document.getElementById('webgl');
// 获取WebGL渲染上下文
var gl = getWebGLContext(canvas);
if (!gl) {
console.log('Failed to get the rendering context for WebGL');
return;
}
// 初始化着色器
if (!initShaders(gl, VSHADER_SOURCE, FSHADER_SOURCE)) {
console.log('Failed to intialize shaders.');
return;
}
// 指定清空<canvas>的颜色
gl.clearColor(0.0, 0.0, 0.0, 1.0);
// 开启深度测试
gl.enable(gl.DEPTH_TEST);
//清空颜色和深度缓冲区
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
}
//绘制函数
function onDraw(gl, canvas, terrain) {
// 设置顶点位置
var n = initVertexBuffers(gl, terrain);
if (n < 0) {
console.log('Failed to set the positions of the vertices');
return;
}
//注册鼠标事件
initEventHandlers(canvas);
//设置灯光
var lightDirection = setLight(gl);
//绘制函数
var tick = function () {
//设置MVP矩阵
setMVPMatrix(gl, canvas, terrain.sphere, lightDirection);
//清空颜色和深度缓冲区
gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
//绘制矩形体
gl.drawElements(gl.TRIANGLES, n, gl.UNSIGNED_SHORT, 0);
//请求浏览器调用tick
requestAnimationFrame(tick);
};
//开始绘制
tick();
}
//设置灯光
function setLight(gl) {
var u_AmbientLight = gl.getUniformLocation(gl.program, 'u_AmbientLight');
var u_DiffuseLight = gl.getUniformLocation(gl.program, 'u_DiffuseLight');
var u_LightDirection = gl.getUniformLocation(gl.program, 'u_LightDirection');
if (!u_DiffuseLight || !u_LightDirection || !u_AmbientLight) {
console.log('Failed to get the storage location');
return;
}
//设置漫反射光
gl.uniform3f(u_DiffuseLight, 1.0, 1.0, 1.0);
// 设置光线方向(世界坐标系下的)
var solarAltitude = 45.0;
var solarAzimuth = 315.0;
var fAltitude = solarAltitude * Math.PI / 180; //光源高度角
var fAzimuth = solarAzimuth * Math.PI / 180; //光源方位角
var arrayvectorX = Math.cos(fAltitude) * Math.cos(fAzimuth);
var arrayvectorY = Math.cos(fAltitude) * Math.sin(fAzimuth);
var arrayvectorZ = Math.sin(fAltitude);
var lightDirection = new Vector3([arrayvectorX, arrayvectorY, arrayvectorZ]);
lightDirection.normalize(); // Normalize
gl.uniform3fv(u_LightDirection, lightDirection.elements);
//设置环境光
gl.uniform3f(u_AmbientLight, 0.2, 0.2, 0.2);
return lightDirection;
}
//读取DEM函数
function readDEMFile(result, terrain) {
var stringlines = result.split("\n");
if (!stringlines || stringlines.length <= 0) {
return false;
}
//读取头信息
var subline = stringlines[0].split("\t");
if (subline.length != 6) {
return false;
}
var col = parseInt(subline[4]); //DEM宽
var row = parseInt(subline[5]); //DEM高
var verticeNum = col * row;
if (verticeNum + 1 > stringlines.length) {
return false;
}
terrain.setWH(col, row);
//读取点信息
var ci = 0;
var pSize = 9;
terrain.verticesColors = new Float32Array(verticeNum * pSize);
for (var i = 1; i < stringlines.length; i++) {
if (!stringlines[i]) {
continue;
}
var subline = stringlines[i].split(',');
if (subline.length != pSize) {
continue;
}
for (var j = 0; j < pSize; j++) {
terrain.verticesColors[ci] = parseFloat(subline[j]);
ci++;
}
}
if (ci !== verticeNum * pSize) {
return false;
}
//包围盒
var minX = terrain.verticesColors[0];
var maxX = terrain.verticesColors[0];
var minY = terrain.verticesColors[1];
var maxY = terrain.verticesColors[1];
var minZ = terrain.verticesColors[2];
var maxZ = terrain.verticesColors[2];
for (var i = 0; i < verticeNum; i++) {
minX = Math.min(minX, terrain.verticesColors[i * pSize]);
maxX = Math.max(maxX, terrain.verticesColors[i * pSize]);
minY = Math.min(minY, terrain.verticesColors[i * pSize + 1]);
maxY = Math.max(maxY, terrain.verticesColors[i * pSize + 1]);
minZ = Math.min(minZ, terrain.verticesColors[i * pSize + 2]);
maxZ = Math.max(maxZ, terrain.verticesColors[i * pSize + 2]);
}
terrain.cuboid = new Cuboid(minX, maxX, minY, maxY, minZ, maxZ);
terrain.sphere = new Sphere(terrain.cuboid);
return true;
}
//注册鼠标事件
function initEventHandlers(canvas) {
var dragging = false; // Dragging or not
var lastX = -1,
lastY = -1; // Last position of the mouse
//鼠标按下
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;
};
//鼠标释放
canvas.onmouseup = function (ev) {
dragging = false;
};
//鼠标移动
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);
currentAngle[0] = currentAngle[0] + dy;
currentAngle[1] = currentAngle[1] + dx;
}
lastX = x, lastY = y;
};
//鼠标缩放
canvas.onmousewheel = function (event) {
if (event.wheelDelta > 0) {
curScale = curScale * 1.1;
} else {
curScale = curScale * 0.9;
}
};
}
//设置MVP矩阵
function setMVPMatrix(gl, canvas, sphere, lightDirection) {
// 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;
}
//模型矩阵
var modelMatrix = new Matrix4();
modelMatrix.scale(curScale, curScale, curScale);
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(-sphere.centerX, -sphere.centerY, -sphere.centerZ);
/*
//----------------------透视---------------------
//投影矩阵
var fovy = 60;
var projMatrix = new Matrix4();
projMatrix.setPerspective(fovy, canvas.width / canvas.height, 1, 10000);
//计算lookAt()函数初始视点的高度
var angle = fovy / 2 * Math.PI / 180.0;
var eyeHight = (sphere.radius * 2 * 1.1) / 2.0 / angle;
//视图矩阵
var viewMatrix = new Matrix4(); // View matrix
viewMatrix.lookAt(0, 0, eyeHight, 0, 0, 0, 0, 1, 0);
//----------------------透视---------------------
*/
//----------------------正射---------------------
//视图矩阵
var viewMatrix = new Matrix4();
var r = sphere.radius + 10;
viewMatrix.lookAt(lightDirection.elements[0] * r, lightDirection.elements[1] * r, lightDirection.elements[2] * r, 0, 0, 0, 0, 1, 0);
//投影矩阵
var projMatrix = new Matrix4();
var diameter = sphere.radius * 2.1;
var ratioWH = canvas.width / canvas.height;
var nearHeight = diameter;
var nearWidth = nearHeight * ratioWH;
projMatrix.setOrtho(-nearWidth / 2, nearWidth / 2, -nearHeight / 2, nearHeight / 2, 1, 10000);
//----------------------正射---------------------
//MVP矩阵
var mvpMatrix = new Matrix4();
mvpMatrix.set(projMatrix).multiply(viewMatrix).multiply(modelMatrix);
//将MVP矩阵传输到着色器的uniform变量u_MvpMatrix
gl.uniformMatrix4fv(u_MvpMatrix, false, mvpMatrix.elements);
}
//
function initVertexBuffers(gl, terrain) {
//DEM的一个网格是由两个三角形组成的
// 0------1 1
// | |
// | |
// col col------col+1
var col = terrain.col;
var row = terrain.row;
var indices = new Uint16Array((row - 1) * (col - 1) * 6);
var ci = 0;
for (var yi = 0; yi < row - 1; yi++) {
//for (var yi = 0; yi < 10; yi++) {
for (var xi = 0; xi < col - 1; xi++) {
indices[ci * 6] = yi * col + xi;
indices[ci * 6 + 1] = (yi + 1) * col + xi;
indices[ci * 6 + 2] = yi * col + xi + 1;
indices[ci * 6 + 3] = (yi + 1) * col + xi;
indices[ci * 6 + 4] = (yi + 1) * col + xi + 1;
indices[ci * 6 + 5] = yi * col + xi + 1;
ci++;
}
}
//
var verticesColors = terrain.verticesColors;
var FSIZE = verticesColors.BYTES_PER_ELEMENT; //数组中每个元素的字节数
// 创建缓冲区对象
var vertexColorBuffer = gl.createBuffer();
var indexBuffer = gl.createBuffer();
if (!vertexColorBuffer || !indexBuffer) {
console.log('Failed to create the buffer object');
return -1;
}
// 将缓冲区对象绑定到目标
gl.bindBuffer(gl.ARRAY_BUFFER, vertexColorBuffer);
// 向缓冲区对象写入数据
gl.bufferData(gl.ARRAY_BUFFER, verticesColors, gl.STATIC_DRAW);
//获取着色器中attribute变量a_Position的地址
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_Position变量
gl.vertexAttribPointer(a_Position, 3, gl.FLOAT, false, FSIZE * 9, 0);
// 连接a_Position变量与分配给它的缓冲区对象
gl.enableVertexAttribArray(a_Position);
//获取着色器中attribute变量a_Color的地址
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;
}
// 将缓冲区对象分配给a_Color变量
gl.vertexAttribPointer(a_Color, 3, gl.FLOAT, false, FSIZE * 9, FSIZE * 3);
// 连接a_Color变量与分配给它的缓冲区对象
gl.enableVertexAttribArray(a_Color);
// 向缓冲区对象分配a_Normal变量,传入的这个变量要在着色器使用才行
var a_Normal = gl.getAttribLocation(gl.program, 'a_Normal');
if (a_Normal < 0) {
console.log('Failed to get the storage location of a_Normal');
return -1;
}
gl.vertexAttribPointer(a_Normal, 3, gl.FLOAT, false, FSIZE * 9, FSIZE * 6);
//开启a_Normal变量
gl.enableVertexAttribArray(a_Normal);
// 将顶点索引写入到缓冲区对象
gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, indexBuffer);
gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, indices, gl.STATIC_DRAW);
return indices.length;
}
4. 参考
本来部分代码和插图来自《WebGL编程指南》，源代码链接：地址 。会在此共享目录中持续更新后续的内容。
