three/src/extras/geometries/TorusKnotBufferGeometry.js

JavaScript 3D library

/**
 * @author Mugen87 / https://github.com/Mugen87
 *
 * see: http://www.blackpawn.com/texts/pqtorus/
 */
THREE.TorusKnotBufferGeometry = function ( radius, tube, tubularSegments, radialSegments, p, q ) {

	THREE.BufferGeometry.call( this );

	this.type = 'TorusKnotBufferGeometry';

	this.parameters = {
		radius: radius,
		tube: tube,
		tubularSegments: tubularSegments,
		radialSegments: radialSegments,
		p: p,
		q: q
	};

	radius = radius || 100;
	tube = tube || 40;
	tubularSegments = Math.floor( tubularSegments ) || 64;
	radialSegments = Math.floor( radialSegments ) || 8;
	p = p || 2;
	q = q || 3;

	// used to calculate buffer length
	var vertexCount = ( ( radialSegments + 1 ) * ( tubularSegments + 1 ) );
	var indexCount = radialSegments * tubularSegments * 2 * 3;

	// buffers
	var indices = new THREE.BufferAttribute( new ( indexCount > 65535 ? Uint32Array : Uint16Array )( indexCount ) , 1 );
	var vertices = new THREE.BufferAttribute( new Float32Array( vertexCount * 3 ), 3 );
	var normals = new THREE.BufferAttribute( new Float32Array( vertexCount * 3 ), 3 );
	var uvs = new THREE.BufferAttribute( new Float32Array( vertexCount * 2 ), 2 );

	// helper variables
	var i, j, index = 0, indexOffset = 0;

	var vertex = new THREE.Vector3();
	var normal = new THREE.Vector3();
	var uv = new THREE.Vector2();

	var P1 = new THREE.Vector3();
	var P2 = new THREE.Vector3();

	var B = new THREE.Vector3();
	var T = new THREE.Vector3();
	var N = new THREE.Vector3();

	// generate vertices, normals and uvs

	for ( i = 0; i <= tubularSegments; ++ i ) {

		// the radian "u" is used to calculate the position on the torus curve of the current tubular segement

		var u = i / tubularSegments * p * Math.PI * 2;

		// now we calculate two points. P1 is our current position on the curve, P2 is a little farther ahead.
		// these points are used to create a special "coordinate space", which is necessary to calculate the correct vertex positions

		calculatePositionOnCurve( u, p, q, radius, P1 );
		calculatePositionOnCurve( u + 0.01, p, q, radius, P2 );

		// calculate orthonormal basis

		T.subVectors( P2, P1 );
		N.addVectors( P2, P1 );
		B.crossVectors( T, N );
		N.crossVectors( B, T );

		// normalize B, N. T can be ignored, we don't use it

		B.normalize();
		N.normalize();

		for ( j = 0; j <= radialSegments; ++ j ) {

			// now calculate the vertices. they are nothing more than an extrusion of the torus curve.
			// because we extrude a shape in the xy-plane, there is no need to calculate a z-value.

			var v = j / radialSegments * Math.PI * 2;
			var cx = - tube * Math.cos( v );
			var cy = tube * Math.sin( v );

			// now calculate the final vertex position.
			// first we orient the extrusion with our basis vectos, then we add it to the current position on the curve

			vertex.x = P1.x + ( cx * N.x + cy * B.x );
			vertex.y = P1.y + ( cx * N.y + cy * B.y );
			vertex.z = P1.z + ( cx * N.z + cy * B.z );

			// vertex
			vertices.setXYZ( index, vertex.x, vertex.y, vertex.z );

			// normal (P1 is always the center/origin of the extrusion, thus we can use it to calculate the normal)
			normal.subVectors( vertex, P1 ).normalize();
			normals.setXYZ( index, normal.x, normal.y, normal.z );

			// uv
			uv.x = i / tubularSegments;
			uv.y = j / radialSegments;
			uvs.setXY( index, uv.x, uv.y );

			// increase index
			index ++;

		}

	}

	// generate indices

	for ( j = 1; j <= tubularSegments; j ++ ) {

		for ( i = 1; i <= radialSegments; i ++ ) {

			// indices
			var a = ( radialSegments + 1 ) * ( j - 1 ) + ( i - 1 );
			var b = ( radialSegments + 1 ) * j + ( i - 1 );
			var c = ( radialSegments + 1 ) * j + i;
			var d = ( radialSegments + 1 ) * ( j - 1 ) + i;

			// face one
			indices.setX( indexOffset, a ); indexOffset++;
			indices.setX( indexOffset, b ); indexOffset++;
			indices.setX( indexOffset, d ); indexOffset++;

			// face two
			indices.setX( indexOffset, b ); indexOffset++;
			indices.setX( indexOffset, c ); indexOffset++;
			indices.setX( indexOffset, d ); indexOffset++;

		}

	}

	// build geometry

	this.setIndex( indices );
	this.addAttribute( 'position', vertices );
	this.addAttribute( 'normal', normals );
	this.addAttribute( 'uv', uvs );

	// this function calculates the current position on the torus curve

	function calculatePositionOnCurve( u, p, q, radius, position ) {

		var cu = Math.cos( u );
		var su = Math.sin( u );
		var quOverP = q / p * u;
		var cs = Math.cos( quOverP );

		position.x = radius * ( 2 + cs ) * 0.5 * cu;
		position.y = radius * ( 2 + cs ) * su * 0.5;
		position.z = radius * Math.sin( quOverP ) * 0.5;

	}

};

THREE.TorusKnotBufferGeometry.prototype = Object.create( THREE.BufferGeometry.prototype );
THREE.TorusKnotBufferGeometry.prototype.constructor = THREE.TorusKnotBufferGeometry;