three/src/geometries/TorusKnotGeometry.js

JavaScript 3D library

import { Geometry } from '../core/Geometry.js';
import { BufferGeometry } from '../core/BufferGeometry.js';
import { Float32BufferAttribute } from '../core/BufferAttribute.js';
import { Vector3 } from '../math/Vector3.js';

// TorusKnotGeometry

function TorusKnotGeometry( radius, tube, tubularSegments, radialSegments, p, q, heightScale ) {

	Geometry.call( this );

	this.type = 'TorusKnotGeometry';

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

	if ( heightScale !== undefined ) console.warn( 'THREE.TorusKnotGeometry: heightScale has been deprecated. Use .scale( x, y, z ) instead.' );

	this.fromBufferGeometry( new TorusKnotBufferGeometry( radius, tube, tubularSegments, radialSegments, p, q ) );
	this.mergeVertices();

}

TorusKnotGeometry.prototype = Object.create( Geometry.prototype );
TorusKnotGeometry.prototype.constructor = TorusKnotGeometry;

// TorusKnotBufferGeometry

function TorusKnotBufferGeometry( radius, tube, tubularSegments, radialSegments, p, q ) {

	BufferGeometry.call( this );

	this.type = 'TorusKnotBufferGeometry';

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

	radius = radius || 1;
	tube = tube || 0.4;
	tubularSegments = Math.floor( tubularSegments ) || 64;
	radialSegments = Math.floor( radialSegments ) || 8;
	p = p || 2;
	q = q || 3;

	// buffers

	const indices = [];
	const vertices = [];
	const normals = [];
	const uvs = [];

	// helper variables

	const vertex = new Vector3();
	const normal = new Vector3();

	const P1 = new Vector3();
	const P2 = new Vector3();

	const B = new Vector3();
	const T = new Vector3();
	const N = new Vector3();

	// generate vertices, normals and uvs

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

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

		const 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 ( let 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.

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

			vertices.push( 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.push( normal.x, normal.y, normal.z );

			// uv

			uvs.push( i / tubularSegments );
			uvs.push( j / radialSegments );

		}

	}

	// generate indices

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

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

			// indices

			const a = ( radialSegments + 1 ) * ( j - 1 ) + ( i - 1 );
			const b = ( radialSegments + 1 ) * j + ( i - 1 );
			const c = ( radialSegments + 1 ) * j + i;
			const d = ( radialSegments + 1 ) * ( j - 1 ) + i;

			// faces

			indices.push( a, b, d );
			indices.push( b, c, d );

		}

	}

	// build geometry

	this.setIndex( indices );
	this.setAttribute( 'position', new Float32BufferAttribute( vertices, 3 ) );
	this.setAttribute( 'normal', new Float32BufferAttribute( normals, 3 ) );
	this.setAttribute( 'uv', new Float32BufferAttribute( uvs, 2 ) );

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

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

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

	}

}

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


export { TorusKnotGeometry, TorusKnotBufferGeometry };