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271 lines
6.4 KiB
271 lines
6.4 KiB
/*
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* @author zz85
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*
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* Experimenting of primitive geometry creation using Surface Parametric equations
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*
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*/
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THREE.ParametricGeometries = {
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klein: function ( v, u ) {
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u *= Math.PI;
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v *= 2 * Math.PI;
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u = u * 2;
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var x, y, z;
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if ( u < Math.PI ) {
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x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( u ) * Math.cos( v );
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z = - 8 * Math.sin( u ) - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( u ) * Math.cos( v );
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} else {
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x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( v + Math.PI );
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z = - 8 * Math.sin( u );
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}
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y = - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( v );
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return new THREE.Vector3( x, y, z );
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},
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plane: function ( width, height ) {
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return function( u, v ) {
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var x = u * width;
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var y = 0;
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var z = v * height;
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return new THREE.Vector3( x, y, z );
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};
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},
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mobius: function( u, t ) {
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// flat mobius strip
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// http://www.wolframalpha.com/input/?i=M%C3%B6bius+strip+parametric+equations&lk=1&a=ClashPrefs_*Surface.MoebiusStrip.SurfaceProperty.ParametricEquations-
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u = u - 0.5;
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var v = 2 * Math.PI * t;
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var x, y, z;
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var a = 2;
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x = Math.cos( v ) * ( a + u * Math.cos( v / 2 ) );
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y = Math.sin( v ) * ( a + u * Math.cos( v / 2 ) );
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z = u * Math.sin( v / 2 );
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return new THREE.Vector3( x, y, z );
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},
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mobius3d: function( u, t ) {
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// volumetric mobius strip
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u *= Math.PI;
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t *= 2 * Math.PI;
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u = u * 2;
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var phi = u / 2;
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var major = 2.25, a = 0.125, b = 0.65;
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var x, y, z;
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x = a * Math.cos( t ) * Math.cos( phi ) - b * Math.sin( t ) * Math.sin( phi );
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z = a * Math.cos( t ) * Math.sin( phi ) + b * Math.sin( t ) * Math.cos( phi );
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y = ( major + x ) * Math.sin( u );
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x = ( major + x ) * Math.cos( u );
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return new THREE.Vector3( x, y, z );
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}
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};
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/*********************************************
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*
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* Parametric Replacement for TubeGeometry
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*
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*********************************************/
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THREE.ParametricGeometries.TubeGeometry = function( path, segments, radius, segmentsRadius, closed, debug ) {
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this.path = path;
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this.segments = segments || 64;
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this.radius = radius || 1;
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this.segmentsRadius = segmentsRadius || 8;
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this.closed = closed || false;
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if ( debug ) this.debug = new THREE.Object3D();
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var scope = this,
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tangent, normal, binormal,
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numpoints = this.segments + 1,
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x, y, z, tx, ty, tz, u, v,
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cx, cy, pos, pos2 = new THREE.Vector3(),
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i, j, ip, jp, a, b, c, d, uva, uvb, uvc, uvd;
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var frames = new THREE.TubeGeometry.FrenetFrames( path, segments, closed ),
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tangents = frames.tangents,
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normals = frames.normals,
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binormals = frames.binormals;
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// proxy internals
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this.tangents = tangents;
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this.normals = normals;
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this.binormals = binormals;
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var ParametricTube = function( u, v ) {
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v *= 2 * Math.PI;
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i = u * ( numpoints - 1 );
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i = Math.floor( i );
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pos = path.getPointAt( u );
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tangent = tangents[ i ];
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normal = normals[ i ];
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binormal = binormals[ i ];
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if ( scope.debug ) {
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scope.debug.add( new THREE.ArrowHelper( tangent, pos, radius, 0x0000ff ) );
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scope.debug.add( new THREE.ArrowHelper( normal, pos, radius, 0xff0000 ) );
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scope.debug.add( new THREE.ArrowHelper( binormal, pos, radius, 0x00ff00 ) );
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}
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cx = - scope.radius * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
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cy = scope.radius * Math.sin( v );
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pos2.copy( pos );
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pos2.x += cx * normal.x + cy * binormal.x;
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pos2.y += cx * normal.y + cy * binormal.y;
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pos2.z += cx * normal.z + cy * binormal.z;
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return pos2.clone();
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};
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THREE.ParametricGeometry.call( this, ParametricTube, segments, segmentsRadius );
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};
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THREE.ParametricGeometries.TubeGeometry.prototype = Object.create( THREE.Geometry.prototype );
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THREE.ParametricGeometries.TubeGeometry.prototype.constructor = THREE.ParametricGeometries.TubeGeometry;
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/*********************************************
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*
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* Parametric Replacement for TorusKnotGeometry
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*
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*********************************************/
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THREE.ParametricGeometries.TorusKnotGeometry = function ( radius, tube, segmentsR, segmentsT, p, q, heightScale ) {
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var scope = this;
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this.radius = radius || 200;
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this.tube = tube || 40;
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this.segmentsR = segmentsR || 64;
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this.segmentsT = segmentsT || 8;
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this.p = p || 2;
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this.q = q || 3;
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this.heightScale = heightScale || 1;
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var TorusKnotCurve = THREE.Curve.create(
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function() {
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},
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function( t ) {
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t *= Math.PI * 2;
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var r = 0.5;
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var tx = ( 1 + r * Math.cos( q * t ) ) * Math.cos( p * t ),
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ty = ( 1 + r * Math.cos( q * t ) ) * Math.sin( p * t ),
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tz = r * Math.sin( q * t );
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return new THREE.Vector3( tx, ty * heightScale, tz ).multiplyScalar( radius );
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}
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);
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var segments = segmentsR;
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var radiusSegments = segmentsT;
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var extrudePath = new TorusKnotCurve();
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THREE.ParametricGeometries.TubeGeometry.call( this, extrudePath, segments, tube, radiusSegments, true, false );
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};
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THREE.ParametricGeometries.TorusKnotGeometry.prototype = Object.create( THREE.Geometry.prototype );
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THREE.ParametricGeometries.TorusKnotGeometry.prototype.constructor = THREE.ParametricGeometries.TorusKnotGeometry;
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/*********************************************
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*
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* Parametric Replacement for SphereGeometry
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*
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*********************************************/
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THREE.ParametricGeometries.SphereGeometry = function( size, u, v ) {
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function sphere( u, v ) {
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u *= Math.PI;
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v *= 2 * Math.PI;
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var x = size * Math.sin( u ) * Math.cos( v );
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var y = size * Math.sin( u ) * Math.sin( v );
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var z = size * Math.cos( u );
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return new THREE.Vector3( x, y, z );
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}
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THREE.ParametricGeometry.call( this, sphere, u, v, ! true );
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};
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THREE.ParametricGeometries.SphereGeometry.prototype = Object.create( THREE.Geometry.prototype );
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THREE.ParametricGeometries.SphereGeometry.prototype.constructor = THREE.ParametricGeometries.SphereGeometry;
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/*********************************************
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*
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* Parametric Replacement for PlaneGeometry
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*
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*********************************************/
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THREE.ParametricGeometries.PlaneGeometry = function( width, depth, segmentsWidth, segmentsDepth ) {
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function plane( u, v ) {
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var x = u * width;
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var y = 0;
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var z = v * depth;
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return new THREE.Vector3( x, y, z );
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}
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THREE.ParametricGeometry.call( this, plane, segmentsWidth, segmentsDepth );
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};
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THREE.ParametricGeometries.PlaneGeometry.prototype = Object.create( THREE.Geometry.prototype );
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THREE.ParametricGeometries.PlaneGeometry.prototype.constructor = THREE.ParametricGeometries.PlaneGeometry;
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