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/**
* @author oosmoxiecode
* @author Mugen87 / https://github.com/Mugen87
*
* based on http://www.blackpawn.com/texts/pqtorus/
*/
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
var indices = [];
var vertices = [];
var normals = [];
var uvs = [];
// helper variables
var i, j;
var vertex = new Vector3();
var normal = new Vector3();
var P1 = new Vector3();
var P2 = new Vector3();
var B = new Vector3();
var T = new Vector3();
var N = new 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 );
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 ( 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;
// faces
indices.push( a, b, d );
indices.push( b, c, d );
}
}
// build geometry
this.setIndex( indices );
this.addAttribute( 'position', new Float32BufferAttribute( vertices, 3 ) );
this.addAttribute( 'normal', new Float32BufferAttribute( normals, 3 ) );
this.addAttribute( 'uv', new Float32BufferAttribute( uvs, 2 ) );
// 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;
}
}
TorusKnotBufferGeometry.prototype = Object.create( BufferGeometry.prototype );
TorusKnotBufferGeometry.prototype.constructor = TorusKnotBufferGeometry;
export { TorusKnotGeometry, TorusKnotBufferGeometry };
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