版权声明:本文为博主原创文章,未经博主允许不得转载。 https://blog.csdn.net/xufeng0991/article/details/76039883
要将三维物体在二维的平面上显示,必须经过投影,投影分为两种:
- 正射投影 长方体的可视空间 物体大小不随位置变化
- 透视投影 四棱锥的可是空间 近大远小
下面的例子绘制了三个三角形,可以通过wasd修改远近界面。
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>WebGL</title>
<style>
body { background-color: gray; }
canvas { border: 2px solid; }
</style>
</head>
<body onload="main()">
<canvas id="container" width="1280px" height="720px"></canvas>
<p id="nearFar"></p>
</body>
</html>
<script type="text/javascript" src="js/oproj.js"></script>
/**
* 正射投影矩阵
* [email protected]
* */
var g_vs = `
attribute vec4 a_Position;
attribute vec4 a_Color;
uniform mat4 u_ProjMat;
varying vec4 v_Color;
void main() {
gl_Position = u_ProjMat * a_Position;
v_Color = a_Color;
}`;
var g_fs = `
precision mediump float;
varying vec4 v_Color;
void main(){
gl_FragColor = v_Color;
}`;
var g_near = 0.0;
var g_far = 0.5;
var g_nf;
function main() {
g_nf = document.getElementById("nearFar");
var gl = getGL();
var shaderProgram = initShader(gl);
var n = initVertexBuffers(gl, shaderProgram);
draw(gl, shaderProgram, n);
document.onkeydown = function (event) {
if(event.key === 'a') {
g_near += 0.01;
draw(gl, shaderProgram, n);
} else if(event.key === 'd') {
g_near -= 0.01;
draw(gl, shaderProgram, n);
} else if(event.key === 'w') {
g_far += 0.01;
draw(gl, shaderProgram, n);
} else if(event.key === 's') {
g_far -= 0.01;
draw(gl, shaderProgram, n);
} else {
}
}
}
function getGL() {
var canvas = document.getElementById("container");
return canvas.getContext("webgl") || canvas.getContext("experimental-webgl");
}
function initShader(gl) {
var vs = gl.createShader(gl.VERTEX_SHADER);
gl.shaderSource( vs, g_vs);
gl.compileShader(vs);
var fs = gl.createShader(gl.FRAGMENT_SHADER);
gl.shaderSource( fs, g_fs);
gl.compileShader(fs);
var shaderProgram = gl.createProgram();
gl.attachShader(shaderProgram, vs);
gl.attachShader(shaderProgram, fs);
gl.linkProgram(shaderProgram);
gl.useProgram(shaderProgram);
return shaderProgram;
}
function initVertexBuffers(gl, shaderProgram) {
var verticesColors = new Float32Array([
// 顶点坐标 颜色
0.0, 0.6,-0.4, 0.4, 1.0, 0.4,
-0.5, -0.4, -0.4, 0.4, 1.0, 0.4,
0.5, -0.4, -0.4, 1.0, 0.4, 0.4,
0.5, 0.4, -0.2, 1.0, 0.4, 0.4,
-0.5, 0.4, -0.2, 1.0, 1.0, 0.4,
0.0, -0.6, -0.2, 1.0, 1.0, 0.4,
0.0, 0.5, 0.0, 0.4, 0.4, 1.0,
-0.5, -0.5, 0.0, 0.4, 0.4, 1.0,
0.5, -0.5, 0.0, 1.0, 0.4, 0.4,
]);
var FSIZE = verticesColors.BYTES_PER_ELEMENT;
var vertexColorBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, vertexColorBuffer);
gl.bufferData(gl.ARRAY_BUFFER, verticesColors, gl.STATIC_DRAW);
var a_Position = gl.getAttribLocation(shaderProgram, "a_Position");
gl.vertexAttribPointer(a_Position, 3, gl.FLOAT, false, FSIZE * 6, 0);
gl.enableVertexAttribArray(a_Position);
var a_Color = gl.getAttribLocation(shaderProgram, "a_Color");
gl.vertexAttribPointer(a_Color, 3, gl.FLOAT, false, FSIZE * 6, FSIZE * 3);
gl.enableVertexAttribArray(a_Color);
return verticesColors.length / 6;
}
function draw(gl, shaderProgram, n) {
g_nf.innerHTML = "near:" + g_near + ",far:" + g_far;
var u_ProjMat = gl.getUniformLocation(shaderProgram, "u_ProjMat");
var viewMat = getOrthoProjection(-1, 1, -1, 1, g_near, g_far);
gl.uniformMatrix4fv(u_ProjMat, false, viewMat);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT);
gl.drawArrays(gl.TRIANGLES, 0, n);
}
function getOrthoProjection(left, right, bottom, top, near, far) {
var rw = 1 / (right - left);
var rh = 1 / (top - bottom);
var rd = 1 / (far - near);
return new Float32Array([
2 * rw, 0, 0, 0,
0, 2 * rw, 0, 0,
0, 0, -2 * rd, 0.0,
-(right + left) * rw, -(top + bottom) * rh, -(far + near) * rd, 1
]);
}
如图:
下面的例子是先将图像变换到相机空间中,然后在进行投影变换。
/**
* 正射投影矩阵
* [email protected]
* */
var g_vs = `
attribute vec4 a_Position;
attribute vec4 a_Color;
uniform mat4 u_ViewMat;
uniform mat4 u_ProjMat;
varying vec4 v_Color;
void main() {
gl_Position = u_ProjMat * u_ViewMat * a_Position;
v_Color = a_Color;
}`;
var g_fs = `
precision mediump float;
varying vec4 v_Color;
void main(){
gl_FragColor = v_Color;
}`;
var g_near = 0.0;
var g_far = 0.5;
var g_nf;
function main() {
g_nf = document.getElementById("nearFar");
var gl = getGL();
var shaderProgram = initShader(gl);
var n = initVertexBuffers(gl, shaderProgram);
draw(gl, shaderProgram, n);
document.onkeydown = function (event) {
if(event.key === 'a') {
g_near += 0.01;
draw(gl, shaderProgram, n);
} else if(event.key === 'd') {
g_near -= 0.01;
draw(gl, shaderProgram, n);
} else if(event.key === 'w') {
g_far += 0.01;
draw(gl, shaderProgram, n);
} else if(event.key === 's') {
g_far -= 0.01;
draw(gl, shaderProgram, n);
} else {
}
}
}
function getGL() {
var canvas = document.getElementById("container");
return canvas.getContext("webgl") || canvas.getContext("experimental-webgl");
}
function initShader(gl) {
var vs = gl.createShader(gl.VERTEX_SHADER);
gl.shaderSource( vs, g_vs);
gl.compileShader(vs);
var fs = gl.createShader(gl.FRAGMENT_SHADER);
gl.shaderSource( fs, g_fs);
gl.compileShader(fs);
var shaderProgram = gl.createProgram();
gl.attachShader(shaderProgram, vs);
gl.attachShader(shaderProgram, fs);
gl.linkProgram(shaderProgram);
gl.useProgram(shaderProgram);
return shaderProgram;
}
function initVertexBuffers(gl, shaderProgram) {
var verticesColors = new Float32Array([
// 顶点坐标 颜色
0.0, 0.6,-0.4, 0.4, 1.0, 0.4,
-0.5, -0.4, -0.4, 0.4, 1.0, 0.4,
0.5, -0.4, -0.4, 1.0, 0.4, 0.4,
0.5, 0.4, -0.2, 1.0, 0.4, 0.4,
-0.5, 0.4, -0.2, 1.0, 1.0, 0.4,
0.0, -0.6, -0.2, 1.0, 1.0, 0.4,
0.0, 0.5, 0.0, 0.4, 0.4, 1.0,
-0.5, -0.5, 0.0, 0.4, 0.4, 1.0,
0.5, -0.5, 0.0, 1.0, 0.4, 0.4,
]);
var FSIZE = verticesColors.BYTES_PER_ELEMENT;
var vertexColorBuffer = gl.createBuffer();
gl.bindBuffer(gl.ARRAY_BUFFER, vertexColorBuffer);
gl.bufferData(gl.ARRAY_BUFFER, verticesColors, gl.STATIC_DRAW);
var a_Position = gl.getAttribLocation(shaderProgram, "a_Position");
gl.vertexAttribPointer(a_Position, 3, gl.FLOAT, false, FSIZE * 6, 0);
gl.enableVertexAttribArray(a_Position);
var a_Color = gl.getAttribLocation(shaderProgram, "a_Color");
gl.vertexAttribPointer(a_Color, 3, gl.FLOAT, false, FSIZE * 6, FSIZE * 3);
gl.enableVertexAttribArray(a_Color);
return verticesColors.length / 6;
}
function draw(gl, shaderProgram, n) {
g_nf.innerHTML = "near:" + g_near + ",far:" + g_far;
var u_ProjMat = gl.getUniformLocation(shaderProgram, "u_ProjMat");
var projMat = getOrthoProjection(-1, 1, -1, 1, g_near, g_far);
gl.uniformMatrix4fv(u_ProjMat, false, projMat);
var u_ViewMat = gl.getUniformLocation(shaderProgram, "u_ViewMat");
var viewMat = lookAt(0, 0, 0, 0, 0, -1, 0, 1, 0);
gl.uniformMatrix4fv(u_ViewMat, false, viewMat);
gl.clearColor(0.0, 0.0, 0.0, 1.0);
gl.clear(gl.COLOR_BUFFER_BIT);
gl.drawArrays(gl.TRIANGLES, 0, n);
}
function getOrthoProjection(left, right, bottom, top, near, far) {
var rw = 1 / (right - left);
var rh = 1 / (top - bottom);
var rd = 1 / (far - near);
return new Float32Array([
2 * rw, 0, 0, 0,
0, 2 * rw, 0, 0,
0, 0, -2 * rd, 0.0,
-(right + left) * rw, -(top + bottom) * rh, -(far + near) * rd, 1
]);
}
/**
* 以下代码为lookAt的实现
* */
/**
* 由平移向量获取平移矩阵
* */
function getTranslationMatrix(x, y, z) {
return new Float32Array([
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
x, y, z, 1.0,
]);
}
/**
* 由旋转弧度和旋转轴获取旋转矩阵
* */
function getRotationMatrix(rad, x, y, z) {
if (x > 0) {
// 绕x轴的旋转矩阵
return new Float32Array([
1.0, 0.0, 0.0, 0.0,
0.0, Math.cos(rad), -Math.sin(rad), 0.0,
0.0, Math.sin(rad), Math.cos(rad), 0.0,
0.0, 0.0, 0.0, 1.0,
]);
} else if (y > 0) {
// 绕y轴的旋转矩阵
return new Float32Array([
Math.cos(rad), 0.0, -Math.sin(rad), 0.0,
0.0, 1.0, 0.0, 0.0,
Math.sin(rad), 0.0, Math.cos(rad), 0.0,
0.0, 0.0, 0.0, 1.0,
]);
} else if(z > 0) {
// 绕z轴的旋转矩阵
return new Float32Array([
Math.cos(rad), Math.sin(rad), 0.0, 0.0,
-Math.sin(rad), Math.cos(rad), 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0,
]);
} else {
// 没有指定旋转轴,报个错,返回一个单位矩阵
console.error("error: no axis");
return new Float32Array([
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0,
]);
}
}
/**
* 视图矩阵
* */
function lookAt(eyeX, eyeY, eyeZ, centerX, centerY, centerZ, upX, upY, upZ) {
var zAxis = subVector([centerX, centerY, centerZ], [eyeX, eyeY, eyeZ]);
var N = normalizeVector(zAxis);
var xAxis = crossMultiVector(N, [upX, upY, upZ]);
var U = normalizeVector(xAxis);
var V = crossMultiVector(U, N);
// 旋转的逆矩阵
var r = new Float32Array([
U[0], V[0], -N[0], 0,
U[1], V[1], -N[1], 0,
U[2], V[2], -N[2], 0,
0, 0, 0, 1
]);
// 平移的逆矩阵
var t = getTranslationMatrix(-eyeX, -eyeY, -eyeZ);
return multiMatrix44(r, t);
}
/**
* 由缩放因子获取缩放矩阵
* */
function getScaleMatrix(xScale, yScale, zScale) {
return new Float32Array([
xScale, 0.0, 0.0, 0.0,
0.0, yScale, 0.0, 0.0,
0.0, 0.0, zScale, 0.0,
0.0, 0.0, 0.0, 1.0,
]);
}
/**
* 向量点乘
* */
function dotMultiVector(v1, v2) {
var res = 0;
for (var i = 0; i < v1.length; i++) {
res += v1[i] * v2[i];
}
return res;
}
/**
* 向量叉乘
* */
function crossMultiVector(v1, v2) {
return [
v1[1] * v2[2] - v1[2] * v2[1],
v1[2] * v2[0] - v1[0] * v2[2],
v1[0] * v2[1] - v1[1] * v2[0]
];
}
/**
* 向量减法
* */
function subVector(v1, v2){
return [v1[0] - v2[0], v1[1] - v2[1], v1[2] - v2[2]];
}
/**
* 向量加法
* */
function addVector(v1, v2){
return [v1[0] + v2[0], v1[1] + v2[1], v1[2] + v2[2]];
}
/**
* 向量归一化
* */
function normalizeVector(v) {
var len = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
return (len > 0.00001) ? [v[0]/len, v[1]/len, v[2]/len] : [0, 0, 0];
}
/**
* 4 x 4 矩阵的转置
* */
function transposeMatrix(mat) {
var res = new Float32Array(16);
for (var i = 0; i < 4; i++) {
for (var j = 0; j < 4; j++) {
res[i * 4 + j] = mat[j * 4 + i];
}
}
return res;
}
/**
* 4 x 4 矩阵乘法
* */
function multiMatrix44(m1, m2) {
var mat1 = transposeMatrix(m1);
var mat2 = transposeMatrix(m2);
var res = new Float32Array(16);
for (var i = 0; i < 4; i++) {
var row = [mat1[i * 4], mat1[i * 4 + 1], mat1[i * 4 + 2], mat1[i * 4 + 3]];
for (var j = 0; j < 4; j++) {
var col = [mat2[j], mat2[j + 4], mat2[j + 8], mat2[j + 12]];
res[i * 4 + j] = dotMultiVector(row, col);
}
}
return transposeMatrix(res);
}
如图,也可以修改远近界面。