<!DOCTYPE html>
<html>
<head>
<title>Example 02.04 - Geometries</title>
<script src="https://cdn.bootcss.com/three.js/r67/three.js"></script>
<script type="text/javascript" src="../libs/ParametricGeometries.js"></script>
<script type="text/javascript" src="../libs/ConvexGeometry.js"></script>
<script src="https://cdn.bootcss.com/stats.js/r10/Stats.min.js"></script>
<script type="text/javascript" src="https://cdn.bootcss.com/dat-gui/0.7.3/dat.gui.js"></script>
<style>
body {
/* set margin to 0 and overflow to hidden, to go fullscreen */
margin: 0;
overflow: hidden;
}
</style>
</head>
<body>
<div id="Stats-output">
</div>
<div id="WebGL-output">
</div>
<script type="text/javascript">
// 初始化
function init() {
var stats = initStats();
// 创建一个场景
var scene = new THREE.Scene();
// 创建一个相机
var camera = new THREE.PerspectiveCamera(45, window.innerWidth / window.innerHeight, 0.1, 1000);
// 创建渲染器
var renderer = new THREE.WebGLRenderer();
renderer.setClearColor(new THREE.Color(0xEEEEEE, 1.0));
renderer.setSize(window.innerWidth, window.innerHeight);
renderer.shadowMapEnabled = true;
// 创建地面
var planeGeometry = new THREE.PlaneGeometry(60, 40, 1, 1);
var planeMaterial = new THREE.MeshLambertMaterial({color: 0xffffff});
var plane = new THREE.Mesh(planeGeometry, planeMaterial);
plane.receiveShadow = true;
// 旋转地面
plane.rotation.x = -0.5 * Math.PI;
plane.position.x = 0;
plane.position.y = 0;
plane.position.z = 0;
// 把地面添加到场景中去
scene.add(plane);
// 相机对准场景
camera.position.x = -50;
camera.position.y = 30;
camera.position.z = 20;
camera.lookAt(new THREE.Vector3(-10, 0, 0));
// 添加自然光
var ambientLight = new THREE.AmbientLight(0x090909);
scene.add(ambientLight);
// 添加聚光灯
var spotLight = new THREE.SpotLight(0xffffff);
spotLight.position.set(-40, 40, 50);
spotLight.castShadow = true;
scene.add(spotLight);
// 添加形状
addGeometries(scene);
// 生成的渲染到DOM元素中去
document.getElementById("WebGL-output").appendChild(renderer.domElement);
var step = 0;
render();
function addGeometries(scene) {
var geoms = [];
geoms.push(new THREE.CylinderGeometry(1, 4, 4));
// 基本立体型
geoms.push(new THREE.BoxGeometry(2, 2, 2));
// 圆形
geoms.push(new THREE.SphereGeometry(2));
//用于生成二十面体几何的类
geoms.push(new THREE.IcosahedronGeometry(4));
//几何/凸面
var points = [
new THREE.Vector3(2, 2, 2),
new THREE.Vector3(2, 2, -2),
new THREE.Vector3(-2, 2, -2),
new THREE.Vector3(-2, 2, 2),
new THREE.Vector3(2, -2, 2),
new THREE.Vector3(2, -2, -2),
new THREE.Vector3(-2, -2, -2),
new THREE.Vector3(-2, -2, 2)
];
geoms.push(new THREE.ConvexGeometry(points));
// create a lathgeometry
//http://en.wikipedia.org/wiki/Lathe_(graphics)
var pts = [];//points array - the path profile points will be stored here
var detail = .1;//half-circle detail - how many angle increments will be used to generate points
var radius = 3;//radius for half_sphere
for (var angle = 0.0; angle < Math.PI; angle += detail)//loop from 0.0 radians to PI (0 - 180 degrees)
pts.push(new THREE.Vector3(Math.cos(angle) * radius, 0, Math.sin(angle) * radius));//angle/radius to x,z
geoms.push(new THREE.LatheGeometry(pts, 12));
//面包圈
geoms.push(new THREE.OctahedronGeometry(3));
// create a geometry based on a function
geoms.push(new THREE.ParametricGeometry(THREE.ParametricGeometries.mobius3d, 20, 10));
//
geoms.push(new THREE.TetrahedronGeometry(3));
geoms.push(new THREE.TorusGeometry(3, 1, 10, 10));
geoms.push(new THREE.TorusKnotGeometry(3, 0.5, 50, 20));
var j = 0;
for (var i = 0; i < geoms.length; i++) {
var cubeMaterial = new THREE.MeshLambertMaterial({wireframe: true, color: Math.random() * 0xffffff});
var materials = [
new THREE.MeshLambertMaterial({color: Math.random() * 0xffffff, shading: THREE.FlatShading}),
new THREE.MeshBasicMaterial({color: 0x000000, wireframe: true})
];
var mesh = THREE.SceneUtils.createMultiMaterialObject(geoms[i], materials);
mesh.traverse(function (e) {
e.castShadow = true
});
mesh.position.x = -24 + ((i % 4) * 12);
mesh.position.y = 4;
mesh.position.z = -8 + (j * 12);
if ((i + 1) % 4 == 0) j++;
scene.add(mesh);
}
}
function render() {
stats.update();
requestAnimationFrame(render);
renderer.render(scene, camera);
}
function initStats() {
var stats = new Stats();
stats.setMode(0); // 0: fps, 1: ms
stats.domElement.style.position = 'absolute';
stats.domElement.style.left = '0px';
stats.domElement.style.top = '0px';
document.getElementById("Stats-output").appendChild(stats.domElement);
return stats;
}
}
window.onload = init
</script>
</body>
</html>
ParametricGeometries.js
/*
* @author zz85
*
* Experimenting of primitive geometry creation using Surface Parametric equations
*
*/
THREE.ParametricGeometries = {
klein: function (v, u) {
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);
},
plane: function (width, height) {
return function(u, v) {
var x = u * width;
var y = 0;
var z = v * height;
return new THREE.Vector3(x, y, z);
};
},
mobius: function(u, t) {
// flat mobius strip
// http://www.wolframalpha.com/input/?i=M%C3%B6bius+strip+parametric+equations&lk=1&a=ClashPrefs_*Surface.MoebiusStrip.SurfaceProperty.ParametricEquations-
u = u - 0.5;
var v = 2 * Math.PI * t;
var x, y, z;
var a = 2;
x = Math.cos(v) * (a + u * Math.cos(v/2));
y = Math.sin(v) * (a + u * Math.cos(v/2));
z = u * Math.sin(v/2);
return new THREE.Vector3(x, y, z);
},
mobius3d: function(u, t) {
// volumetric mobius strip
u *= Math.PI;
t *= 2 * Math.PI;
u = u * 2;
var phi = u / 2;
var major = 2.25, a = 0.125, b = 0.65;
var x, y, z;
x = a * Math.cos(t) * Math.cos(phi) - b * Math.sin(t) * Math.sin(phi);
z = a * Math.cos(t) * Math.sin(phi) + b * Math.sin(t) * Math.cos(phi);
y = (major + x) * Math.sin(u);
x = (major + x) * Math.cos(u);
return new THREE.Vector3(x, y, z);
}
};
/*********************************************
*
* Parametric Replacement for TubeGeometry
*
*********************************************/
THREE.ParametricGeometries.TubeGeometry = function(path, segments, radius, segmentsRadius, closed, debug) {
this.path = path;
this.segments = segments || 64;
this.radius = radius || 1;
this.segmentsRadius = segmentsRadius || 8;
this.closed = closed || false;
if (debug) this.debug = new THREE.Object3D();
var scope = this,
tangent, normal, binormal,
numpoints = this.segments + 1,
x, y, z, tx, ty, tz, u, v,
cx, cy, pos, pos2 = new THREE.Vector3(),
i, j, ip, jp, a, b, c, d, uva, uvb, uvc, uvd;
var frames = new THREE.TubeGeometry.FrenetFrames(path, segments, closed),
tangents = frames.tangents,
normals = frames.normals,
binormals = frames.binormals;
// proxy internals
this.tangents = tangents;
this.normals = normals;
this.binormals = binormals;
var ParametricTube = function(u, v) {
v *= 2 * Math.PI;
i = u * (numpoints - 1);
i = Math.floor(i);
pos = path.getPointAt(u);
tangent = tangents[i];
normal = normals[i];
binormal = binormals[i];
if (scope.debug) {
scope.debug.add(new THREE.ArrowHelper(tangent, pos, radius, 0x0000ff));
scope.debug.add(new THREE.ArrowHelper(normal, pos, radius, 0xff0000));
scope.debug.add(new THREE.ArrowHelper(binormal, pos, radius, 0x00ff00));
}
cx = -scope.radius * Math.cos(v); // TODO: Hack: Negating it so it faces outside.
cy = scope.radius * Math.sin(v);
pos2.copy(pos);
pos2.x += cx * normal.x + cy * binormal.x;
pos2.y += cx * normal.y + cy * binormal.y;
pos2.z += cx * normal.z + cy * binormal.z;
return pos2.clone();
};
THREE.ParametricGeometry.call(this, ParametricTube, segments, segmentsRadius);
};
THREE.ParametricGeometries.TubeGeometry.prototype = Object.create( THREE.Geometry.prototype );
/*********************************************
*
* Parametric Replacement for TorusKnotGeometry
*
*********************************************/
THREE.ParametricGeometries.TorusKnotGeometry = function ( radius, tube, segmentsR, segmentsT, p, q, heightScale ) {
var scope = this;
this.radius = radius || 200;
this.tube = tube || 40;
this.segmentsR = segmentsR || 64;
this.segmentsT = segmentsT || 8;
this.p = p || 2;
this.q = q || 3;
this.heightScale = heightScale || 1;
var TorusKnotCurve = THREE.Curve.create(
function() {
},
function(t) {
t *= Math.PI * 2;
var r = 0.5;
var tx = (1 + r * Math.cos(q * t)) * Math.cos(p * t),
ty = (1 + r * Math.cos(q * t)) * Math.sin(p * t),
tz = r * Math.sin(q * t);
return new THREE.Vector3(tx, ty * heightScale, tz).multiplyScalar(radius);
}
);
var segments = segmentsR;
var radiusSegments = segmentsT;
var extrudePath = new TorusKnotCurve();
THREE.ParametricGeometries.TubeGeometry.call( this, extrudePath, segments, tube, radiusSegments, true, false );
};
THREE.ParametricGeometries.TorusKnotGeometry.prototype = Object.create( THREE.Geometry.prototype );
/*********************************************
*
* Parametric Replacement for SphereGeometry
*
*********************************************/
THREE.ParametricGeometries.SphereGeometry = function(size, u, v) {
function sphere(u, v) {
u *= Math.PI;
v *= 2 * Math.PI;
var x = size * Math.sin(u) * Math.cos(v);
var y = size * Math.sin(u) * Math.sin(v);
var z = size * Math.cos(u);
return new THREE.Vector3(x, y, z);
}
THREE.ParametricGeometry.call(this, sphere, u, v, !true);
};
THREE.ParametricGeometries.SphereGeometry.prototype = Object.create( THREE.Geometry.prototype );
/*********************************************
*
* Parametric Replacement for PlaneGeometry
*
*********************************************/
THREE.ParametricGeometries.PlaneGeometry = function(width, depth, segmentsWidth, segmentsDepth) {
function plane(u, v) {
var x = u * width;
var y = 0;
var z = v * depth;
return new THREE.Vector3(x, y, z);
}
THREE.ParametricGeometry.call(this, plane, segmentsWidth, segmentsDepth);
};
THREE.ParametricGeometries.PlaneGeometry.prototype = Object.create( THREE.Geometry.prototype );
ConvexGeometry.js
/**
* @author qiao / https://github.com/qiao
* @fileoverview This is a convex hull generator using the incremental method.
* The complexity is O(n^2) where n is the number of vertices.
* O(nlogn) algorithms do exist, but they are much more complicated.
*
* Benchmark:
*
* Platform: CPU: P7350 @2.00GHz Engine: V8
*
* Num Vertices Time(ms)
*
* 10 1
* 20 3
* 30 19
* 40 48
* 50 107
*/
THREE.ConvexGeometry = function( vertices ) {
THREE.Geometry.call( this );
var faces = [ [ 0, 1, 2 ], [ 0, 2, 1 ] ];
for ( var i = 3; i < vertices.length; i++ ) {
addPoint( i );
}
function addPoint( vertexId ) {
var vertex = vertices[ vertexId ].clone();
var mag = vertex.length();
vertex.x += mag * randomOffset();
vertex.y += mag * randomOffset();
vertex.z += mag * randomOffset();
var hole = [];
for ( var f = 0; f < faces.length; ) {
var face = faces[ f ];
// for each face, if the vertex can see it,
// then we try to add the face's edges into the hole.
if ( visible( face, vertex ) ) {
for ( var e = 0; e < 3; e++ ) {
var edge = [ face[ e ], face[ ( e + 1 ) % 3 ] ];
var boundary = true;
// remove duplicated edges.
for ( var h = 0; h < hole.length; h++ ) {
if ( equalEdge( hole[ h ], edge ) ) {
hole[ h ] = hole[ hole.length - 1 ];
hole.pop();
boundary = false;
break;
}
}
if ( boundary ) {
hole.push( edge );
}
}
// remove faces[ f ]
faces[ f ] = faces[ faces.length - 1 ];
faces.pop();
} else { // not visible
f++;
}
}
// construct the new faces formed by the edges of the hole and the vertex
for ( var h = 0; h < hole.length; h++ ) {
faces.push( [
hole[ h ][ 0 ],
hole[ h ][ 1 ],
vertexId
] );
}
}
/**
* Whether the face is visible from the vertex
*/
function visible( face, vertex ) {
var va = vertices[ face[ 0 ] ];
var vb = vertices[ face[ 1 ] ];
var vc = vertices[ face[ 2 ] ];
var n = normal( va, vb, vc );
// distance from face to origin
var dist = n.dot( va );
return n.dot( vertex ) >= dist;
}
/**
* Face normal
*/
function normal( va, vb, vc ) {
var cb = new THREE.Vector3();
var ab = new THREE.Vector3();
cb.subVectors( vc, vb );
ab.subVectors( va, vb );
cb.cross( ab );
cb.normalize();
return cb;
}
/**
* Detect whether two edges are equal.
* Note that when constructing the convex hull, two same edges can only
* be of the negative direction.
*/
function equalEdge( ea, eb ) {
return ea[ 0 ] === eb[ 1 ] && ea[ 1 ] === eb[ 0 ];
}
/**
* Create a random offset between -1e-6 and 1e-6.
*/
function randomOffset() {
return ( Math.random() - 0.5 ) * 2 * 1e-6;
}
/**
* XXX: Not sure if this is the correct approach. Need someone to review.
*/
function vertexUv( vertex ) {
var mag = vertex.length();
return new THREE.Vector2( vertex.x / mag, vertex.y / mag );
}
// Push vertices into `this.vertices`, skipping those inside the hull
var id = 0;
var newId = new Array( vertices.length ); // map from old vertex id to new id
for ( var i = 0; i < faces.length; i++ ) {
var face = faces[ i ];
for ( var j = 0; j < 3; j++ ) {
if ( newId[ face[ j ] ] === undefined ) {
newId[ face[ j ] ] = id++;
this.vertices.push( vertices[ face[ j ] ] );
}
face[ j ] = newId[ face[ j ] ];
}
}
// Convert faces into instances of THREE.Face3
for ( var i = 0; i < faces.length; i++ ) {
this.faces.push( new THREE.Face3(
faces[ i ][ 0 ],
faces[ i ][ 1 ],
faces[ i ][ 2 ]
) );
}
// Compute UVs
for ( var i = 0; i < this.faces.length; i++ ) {
var face = this.faces[ i ];
this.faceVertexUvs[ 0 ].push( [
vertexUv( this.vertices[ face.a ] ),
vertexUv( this.vertices[ face.b ] ),
vertexUv( this.vertices[ face.c ])
] );
}
this.computeFaceNormals();
this.computeVertexNormals();
};
THREE.ConvexGeometry.prototype = Object.create( THREE.Geometry.prototype );
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