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215 lines
5.4 KiB
215 lines
5.4 KiB
( function () {
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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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const ParametricGeometries = {
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klein: function ( v, u, target ) {
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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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let x, 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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const y = - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( v );
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target.set( x, y, z );
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},
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plane: function ( width, height ) {
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return function ( u, v, target ) {
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const x = u * width;
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const y = 0;
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const z = v * height;
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target.set( x, y, z );
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};
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},
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mobius: function ( u, t, target ) {
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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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const v = 2 * Math.PI * t;
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const a = 2;
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const x = Math.cos( v ) * ( a + u * Math.cos( v / 2 ) );
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const y = Math.sin( v ) * ( a + u * Math.cos( v / 2 ) );
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const z = u * Math.sin( v / 2 );
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target.set( x, y, z );
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},
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mobius3d: function ( u, t, target ) {
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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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const phi = u / 2;
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const major = 2.25,
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a = 0.125,
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b = 0.65;
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let x = a * Math.cos( t ) * Math.cos( phi ) - b * Math.sin( t ) * Math.sin( phi );
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const z = a * Math.cos( t ) * Math.sin( phi ) + b * Math.sin( t ) * Math.cos( phi );
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const y = ( major + x ) * Math.sin( u );
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x = ( major + x ) * Math.cos( u );
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target.set( 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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ParametricGeometries.TubeGeometry = class TubeGeometry extends THREE.ParametricGeometry {
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constructor( path, segments = 64, radius = 1, segmentsRadius = 8, closed = false ) {
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const numpoints = segments + 1;
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const frames = path.computeFrenetFrames( 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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const position = new THREE.Vector3();
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function ParametricTube( u, v, target ) {
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v *= 2 * Math.PI;
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const i = Math.floor( u * ( numpoints - 1 ) );
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path.getPointAt( u, position );
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const normal = normals[ i ];
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const binormal = binormals[ i ];
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const cx = - radius * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
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const cy = radius * Math.sin( v );
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position.x += cx * normal.x + cy * binormal.x;
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position.y += cx * normal.y + cy * binormal.y;
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position.z += cx * normal.z + cy * binormal.z;
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target.copy( position );
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}
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super( ParametricTube, segments, segmentsRadius ); // 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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this.path = path;
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this.segments = segments;
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this.radius = radius;
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this.segmentsRadius = segmentsRadius;
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this.closed = closed;
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}
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};
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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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ParametricGeometries.TorusKnotGeometry = class TorusKnotGeometry extends ParametricGeometries.TubeGeometry {
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constructor( radius = 200, tube = 40, segmentsT = 64, segmentsR = 8, p = 2, q = 3 ) {
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class TorusKnotCurve extends THREE.Curve {
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getPoint( t, optionalTarget = new THREE.Vector3() ) {
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const point = optionalTarget;
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t *= Math.PI * 2;
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const r = 0.5;
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const x = ( 1 + r * Math.cos( q * t ) ) * Math.cos( p * t );
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const y = ( 1 + r * Math.cos( q * t ) ) * Math.sin( p * t );
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const z = r * Math.sin( q * t );
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return point.set( x, y, z ).multiplyScalar( radius );
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}
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}
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const segments = segmentsT;
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const radiusSegments = segmentsR;
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const extrudePath = new TorusKnotCurve();
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super( extrudePath, segments, tube, radiusSegments, true, false );
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this.radius = radius;
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this.tube = tube;
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this.segmentsT = segmentsT;
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this.segmentsR = segmentsR;
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this.p = p;
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this.q = q;
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}
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};
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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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ParametricGeometries.SphereGeometry = class SphereGeometry extends THREE.ParametricGeometry {
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constructor( size, u, v ) {
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function sphere( u, v, target ) {
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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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target.set( x, y, z );
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}
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super( sphere, u, v );
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}
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};
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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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ParametricGeometries.PlaneGeometry = class PlaneGeometry extends THREE.ParametricGeometry {
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constructor( width, depth, segmentsWidth, segmentsDepth ) {
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function plane( u, v, target ) {
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const x = u * width;
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const y = 0;
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const z = v * depth;
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target.set( x, y, z );
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}
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super( plane, segmentsWidth, segmentsDepth );
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}
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};
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THREE.ParametricGeometries = ParametricGeometries;
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} )();
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