three.js/src/extras/geometries/TubeGeometry.js

/**
 * @author WestLangley / https://github.com/WestLangley
 * @author zz85 / https://github.com/zz85
 * @author miningold / https://github.com/miningold
 * @author jonobr1 / https://github.com/jonobr1
 *
 * Modified from the TorusKnotGeometry by @oosmoxiecode
 *
 * Creates a tube which extrudes along a 3d spline
 *
 * Uses parallel transport frames as described in
 * http://www.cs.indiana.edu/pub/techreports/TR425.pdf
 */

THREE.TubeGeometry = function ( path, segments, radius, radialSegments, closed, taper ) {

	THREE.Geometry.call( this );

	this.type = 'TubeGeometry';

	this.parameters = {
		path: path,
		segments: segments,
		radius: radius,
		radialSegments: radialSegments,
		closed: closed,
		taper: taper
	};

	segments = segments || 64;
	radius = radius || 1;
	radialSegments = radialSegments || 8;
	closed = closed || false;
	taper = taper || THREE.TubeGeometry.NoTaper;

	var grid = [];

	var scope = this,

		tangent,
		normal,
		binormal,

		numpoints = segments + 1,

		u, v, r,

		cx, cy,
		pos, pos2 = new THREE.Vector3(),
		i, j,
		ip, jp,
		a, b, c, d,
		uva, uvb, uvc, uvd;

	var frames = new THREE.TubeGeometry.FrenetFrames( path, segments, closed ),
		tangents = frames.tangents,
		normals = frames.normals,
		binormals = frames.binormals;

	// proxy internals
	this.tangents = tangents;
	this.normals = normals;
	this.binormals = binormals;

	function vert( x, y, z ) {

		return scope.vertices.push( new THREE.Vector3( x, y, z ) ) - 1;

	}

	// construct the grid

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

		grid[ i ] = [];

		u = i / ( numpoints - 1 );

		pos = path.getPointAt( u );

		tangent = tangents[ i ];
		normal = normals[ i ];
		binormal = binormals[ i ];

		r = radius * taper( u );

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

			v = j / radialSegments * 2 * Math.PI;

			cx = - r * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
			cy = r * Math.sin( v );

			pos2.copy( pos );
			pos2.x += cx * normal.x + cy * binormal.x;
			pos2.y += cx * normal.y + cy * binormal.y;
			pos2.z += cx * normal.z + cy * binormal.z;

			grid[ i ][ j ] = vert( pos2.x, pos2.y, pos2.z );

		}

	}


	// construct the mesh

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

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

			ip = ( closed ) ? ( i + 1 ) % segments : i + 1;
			jp = ( j + 1 ) % radialSegments;

			a = grid[ i ][ j ];		// *** NOT NECESSARILY PLANAR ! ***
			b = grid[ ip ][ j ];
			c = grid[ ip ][ jp ];
			d = grid[ i ][ jp ];

			uva = new THREE.Vector2( i / segments, j / radialSegments );
			uvb = new THREE.Vector2( ( i + 1 ) / segments, j / radialSegments );
			uvc = new THREE.Vector2( ( i + 1 ) / segments, ( j + 1 ) / radialSegments );
			uvd = new THREE.Vector2( i / segments, ( j + 1 ) / radialSegments );

			this.faces.push( new THREE.Face3( a, b, d ) );
			this.faceVertexUvs[ 0 ].push( [ uva, uvb, uvd ] );

			this.faces.push( new THREE.Face3( b, c, d ) );
			this.faceVertexUvs[ 0 ].push( [ uvb.clone(), uvc, uvd.clone() ] );

		}

	}

	this.computeFaceNormals();
	this.computeVertexNormals();

};

THREE.TubeGeometry.prototype = Object.create( THREE.Geometry.prototype );
THREE.TubeGeometry.prototype.constructor = THREE.TubeGeometry;

THREE.TubeGeometry.NoTaper = function ( u ) {

	return 1;

};

THREE.TubeGeometry.SinusoidalTaper = function ( u ) {

	return Math.sin( Math.PI * u );

};

// For computing of Frenet frames, exposing the tangents, normals and binormals the spline
THREE.TubeGeometry.FrenetFrames = function ( path, segments, closed ) {

	var	normal = new THREE.Vector3(),

		tangents = [],
		normals = [],
		binormals = [],

		vec = new THREE.Vector3(),
		mat = new THREE.Matrix4(),

		numpoints = segments + 1,
		theta,
		smallest,

		tx, ty, tz,
		i, u;


	// expose internals
	this.tangents = tangents;
	this.normals = normals;
	this.binormals = binormals;

	// compute the tangent vectors for each segment on the path

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

		u = i / ( numpoints - 1 );

		tangents[ i ] = path.getTangentAt( u );
		tangents[ i ].normalize();

	}

	initialNormal3();

	/*
	function initialNormal1(lastBinormal) {
		// fixed start binormal. Has dangers of 0 vectors
		normals[ 0 ] = new THREE.Vector3();
		binormals[ 0 ] = new THREE.Vector3();
		if (lastBinormal===undefined) lastBinormal = new THREE.Vector3( 0, 0, 1 );
		normals[ 0 ].crossVectors( lastBinormal, tangents[ 0 ] ).normalize();
		binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] ).normalize();
	}

	function initialNormal2() {

		// This uses the Frenet-Serret formula for deriving binormal
		var t2 = path.getTangentAt( epsilon );

		normals[ 0 ] = new THREE.Vector3().subVectors( t2, tangents[ 0 ] ).normalize();
		binormals[ 0 ] = new THREE.Vector3().crossVectors( tangents[ 0 ], normals[ 0 ] );

		normals[ 0 ].crossVectors( binormals[ 0 ], tangents[ 0 ] ).normalize(); // last binormal x tangent
		binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] ).normalize();

	}
	*/

	function initialNormal3() {

		// select an initial normal vector perpendicular to the first tangent vector,
		// and in the direction of the smallest tangent xyz component

		normals[ 0 ] = new THREE.Vector3();
		binormals[ 0 ] = new THREE.Vector3();
		smallest = Number.MAX_VALUE;
		tx = Math.abs( tangents[ 0 ].x );
		ty = Math.abs( tangents[ 0 ].y );
		tz = Math.abs( tangents[ 0 ].z );

		if ( tx <= smallest ) {

			smallest = tx;
			normal.set( 1, 0, 0 );

		}

		if ( ty <= smallest ) {

			smallest = ty;
			normal.set( 0, 1, 0 );

		}

		if ( tz <= smallest ) {

			normal.set( 0, 0, 1 );

		}

		vec.crossVectors( tangents[ 0 ], normal ).normalize();

		normals[ 0 ].crossVectors( tangents[ 0 ], vec );
		binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] );

	}


	// compute the slowly-varying normal and binormal vectors for each segment on the path

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

		normals[ i ] = normals[ i - 1 ].clone();

		binormals[ i ] = binormals[ i - 1 ].clone();

		vec.crossVectors( tangents[ i - 1 ], tangents[ i ] );

		if ( vec.length() > Number.EPSILON ) {

			vec.normalize();

			theta = Math.acos( THREE.Math.clamp( tangents[ i - 1 ].dot( tangents[ i ] ), - 1, 1 ) ); // clamp for floating pt errors

			normals[ i ].applyMatrix4( mat.makeRotationAxis( vec, theta ) );

		}

		binormals[ i ].crossVectors( tangents[ i ], normals[ i ] );

	}


	// if the curve is closed, postprocess the vectors so the first and last normal vectors are the same

	if ( closed ) {

		theta = Math.acos( THREE.Math.clamp( normals[ 0 ].dot( normals[ numpoints - 1 ] ), - 1, 1 ) );
		theta /= ( numpoints - 1 );

		if ( tangents[ 0 ].dot( vec.crossVectors( normals[ 0 ], normals[ numpoints - 1 ] ) ) > 0 ) {

			theta = - theta;

		}

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

			// twist a little...
			normals[ i ].applyMatrix4( mat.makeRotationAxis( tangents[ i ], theta * i ) );
			binormals[ i ].crossVectors( tangents[ i ], normals[ i ] );

		}

	}

};