47 Three.js使用THREE.ParametricGeometry生成平面图形、波浪图形、和克莱因瓶

简介

使用THREE.ParametricGeometry可以根据传入的公式，计算出相应的几何体。这是一个很具有扩展性的几何体。

简单实现

var geometry = new THREE.ParametricGeometry(function, slices, stacks);

通过上面的方法，就可以创建出一个THREE.ParametricGeometry的几何体。相关的参数为：

属性	是否必需	描述
function	是	该属性为一个函数，该函数以u、v值作为参数定义每个顶点的位置。需要返回`THREE.Vector3`的值
slices	是	该属性定义`u`值应该分成多少份
stacks	是	该属性定义`v`值应该分成多少份

方法讲解

在我们设置好相关的属性值之后，THREE.ParametricGeometry会根据我们定义的slices和stacks将u和v生成的值传给function循环调用。u和v的范围是0-1。
举个列子：如果我们要生成一个width为10，depth为10的平面图形，将slices设置为5，stacks设置为4。function的表达式为

    //创建平面模型的方法var plane = function (u, v) {var x = u*10;var y = 0;var z = v*10;return new THREE.Vector3(x, y, z);};

那么，在运算的时候，会生成的点就是：

u:0/5; v:0/4; return: THREE.Vector3(0, 0, 0);
u:1/5; v:0/4; return: THREE.Vector3(2, 0, 0);
u:2/5; v:0/4; return: THREE.Vector3(4, 0, 0);
u:3/5; v:0/4; return: THREE.Vector3(6, 0, 0);
u:4/5; v:0/4; return: THREE.Vector3(8, 0, 0);
u:5/5; v:0/4; return: THREE.Vector3(10, 0, 0);
u:0/5; v:1/4; return: THREE.Vector3(0, 0, 2.5);
u:1/5; v:1/4; return: THREE.Vector3(2, 0, 2.5);
u:2/5; v:1/4; return: THREE.Vector3(4, 0, 2.5);
...
u:3/5; v:4/4; return: THREE.Vector3(6, 0, 10);
u:4/5; v:4/4; return: THREE.Vector3(8, 0, 10);
u:5/5; v:4/4; return: THREE.Vector3(10, 0, 10);

然后，程序通过生成的这些一组一组的点，生成相应的面，再绘制出来。

案例代码

设置slices和stacks为120时，分的层次很多，所以生成的图形很平滑。

如果设置slices和stacks为12，分的层次少，则能够看出来点的关系。

通过上面我们可以看出来程序通过我们生成的点，绘制出来了，相应的图形。

案例查看地址：http://www.wjceo.com/blog/threejs/2018-02-12/49.html

以下是相关案例代码：

<!DOCTYPE html>
<html lang="en">
<head><meta charset="UTF-8"><title>Title</title><style type="text/css">html, body {margin: 0;height: 100%;}canvas {display: block;}</style>
</head>
<body onload="draw();">
</body>
<script src="https://johnson2heng.github.io/three.js-demo/lib/three.js"></script>
<script src="https://johnson2heng.github.io/three.js-demo/lib/js/controls/OrbitControls.js"></script>
<script src="https://johnson2heng.github.io/three.js-demo/lib/js/libs/stats.min.js"></script>
<script src="https://johnson2heng.github.io/three.js-demo/lib/js/libs/dat.gui.min.js"></script>
<script>var renderer;function initRender() {renderer = new THREE.WebGLRenderer({antialias:true});//renderer.setClearColor(new THREE.Color(0xEEEEEE, 1.0)); //设置背景颜色renderer.setSize(window.innerWidth, window.innerHeight);document.body.appendChild(renderer.domElement);}var camera;function initCamera() {camera = new THREE.PerspectiveCamera(45, window.innerWidth/window.innerHeight, 1, 10000);camera.position.set(0, 0, 150);}var scene;function initScene() {scene = new THREE.Scene();}var light;function initLight() {scene.add(new THREE.AmbientLight(0x404040));light = new THREE.DirectionalLight(0xffffff);light.position.set(1,1,1);scene.add(light);}//创建平面模型的方法var plane = function (u, v) {var x = u*50;var y = 0;var z = v*50;return new THREE.Vector3(x, y, z);};//创建波浪图形的方法var radialWave = function (u, v) {var r = 50;var x = Math.sin(u) * r;var z = Math.sin(v / 2) * 2 * r;var y = (Math.sin(u * 4 * Math.PI) + Math.cos(v * 2 * Math.PI)) * 2.8;return new THREE.Vector3(x, y, z);};var klein = function (u, v) {u *= Math.PI;v *= 2 * Math.PI;u = u * 2;var x, y, z;if (u < Math.PI) {x = 3 * Math.cos(u) * (1 + Math.sin(u)) + (2 * (1 - Math.cos(u) / 2)) * Math.cos(u) * Math.cos(v);z = -8 * Math.sin(u) - 2 * (1 - Math.cos(u) / 2) * Math.sin(u) * Math.cos(v);} else {x = 3 * Math.cos(u) * (1 + Math.sin(u)) + (2 * (1 - Math.cos(u) / 2)) * Math.cos(v + Math.PI);z = -8 * Math.sin(u);}y = -2 * (1 - Math.cos(u) / 2) * Math.sin(v);return new THREE.Vector3(x, y, z);};function initModel() {//轴辅助 （每一个轴的长度）object = new THREE.AxisHelper( 50 );scene.add( object );var mesh = createMesh(new THREE.ParametricGeometry(klein, 12, 12));scene.add(mesh);}//生成模型function createMesh(geom) {//设置当前的模型矩阵沿xy轴偏移，让图片处于显示中心geom.applyMatrix(new THREE.Matrix4().makeTranslation(0, 0, 0));// 创建法向量纹理var meshMaterial = new THREE.MeshNormalMaterial({flatShading: THREE.FlatShading,transparent: true,opacity: 0.9});//  创建一个线框纹理var wireFrameMat = new THREE.MeshBasicMaterial();wireFrameMat.wireframe = true;// 创建模型var mesh = THREE.SceneUtils.createMultiMaterialObject(geom, [meshMaterial,wireFrameMat]);return mesh;}//初始化性能插件var stats;function initStats() {stats = new Stats();document.body.appendChild(stats.dom);}//用户交互插件 鼠标左键按住旋转，右键按住平移，滚轮缩放var controls;function initControls() {controls = new THREE.OrbitControls( camera, renderer.domElement );// 如果使用animate方法时，将此函数删除//controls.addEventListener( 'change', render );// 使动画循环使用时阻尼或自转 意思是否有惯性controls.enableDamping = true;//动态阻尼系数 就是鼠标拖拽旋转灵敏度//controls.dampingFactor = 0.25;//是否可以缩放controls.enableZoom = true;//是否自动旋转controls.autoRotate = false;//设置相机距离原点的最远距离controls.minDistance  = 20;//设置相机距离原点的最远距离controls.maxDistance  = 10000;//是否开启右键拖拽controls.enablePan = true;}//生成gui设置配置项var gui;function initGui() {//声明一个保存需求修改的相关数据的对象gui = {};var datGui = new dat.GUI();//将设置属性添加到gui当中，gui.add(对象，属性，最小值，最大值）//调用生成一次图形gui.asGeom();}function render() {renderer.render( scene, camera );}//窗口变动触发的函数function onWindowResize() {camera.aspect = window.innerWidth / window.innerHeight;camera.updateProjectionMatrix();render();renderer.setSize( window.innerWidth, window.innerHeight );}function animate() {//更新控制器controls.update();render();//更新性能插件stats.update();requestAnimationFrame(animate);}function draw() {initRender();initScene();initCamera();initLight();initModel();initControls();initStats();//initGui();animate();window.onresize = onWindowResize;}
</script>
</html>