1 /**
  2  * Spline from Tween.js, slightly optimized (and trashed)
  3  * http://sole.github.com/tween.js/examples/05_spline.html
  4  *
  5  * @author mrdoob / http://mrdoob.com/
  6  * @author alteredq / http://alteredqualia.com/
  7  */
  8 
  9 /**@constructor*/
 10 THREE.Spline = function ( points ) {
 11 
 12 	this.points = points;
 13 
 14 	var c = [], v3 = { x: 0, y: 0, z: 0 },
 15 	point, intPoint, weight, w2, w3,
 16 	pa, pb, pc, pd;
 17 
 18 	this.initFromArray = function( a ) {
 19 
 20 		this.points = [];
 21 
 22 		for ( var i = 0; i < a.length; i++ ) {
 23 
 24 			this.points[ i ] = { x: a[ i ][ 0 ], y: a[ i ][ 1 ], z: a[ i ][ 2 ] };
 25 
 26 		}
 27 
 28 	};
 29 
 30 	this.getPoint = function ( k ) {
 31 
 32 		point = ( this.points.length - 1 ) * k;
 33 		intPoint = Math.floor( point );
 34 		weight = point - intPoint;
 35 
 36 		c[ 0 ] = intPoint === 0 ? intPoint : intPoint - 1;
 37 		c[ 1 ] = intPoint;
 38 		c[ 2 ] = intPoint  > this.points.length - 2 ? this.points.length - 1 : intPoint + 1;
 39 		c[ 3 ] = intPoint  > this.points.length - 3 ? this.points.length - 1 : intPoint + 2;
 40 
 41 		pa = this.points[ c[ 0 ] ];
 42 		pb = this.points[ c[ 1 ] ];
 43 		pc = this.points[ c[ 2 ] ];
 44 		pd = this.points[ c[ 3 ] ];
 45 
 46 		w2 = weight * weight;
 47 		w3 = weight * w2;
 48 
 49 		v3.x = interpolate( pa.x, pb.x, pc.x, pd.x, weight, w2, w3 );
 50 		v3.y = interpolate( pa.y, pb.y, pc.y, pd.y, weight, w2, w3 );
 51 		v3.z = interpolate( pa.z, pb.z, pc.z, pd.z, weight, w2, w3 );
 52 
 53 		return v3;
 54 
 55 	};
 56 
 57 	this.getControlPointsArray = function () {
 58 
 59 		var i, p, l = this.points.length,
 60 			coords = [];
 61 
 62 		for ( i = 0; i < l; i ++ ) {
 63 
 64 			p = this.points[ i ];
 65 			coords[ i ] = [ p.x, p.y, p.z ];
 66 
 67 		}
 68 
 69 		return coords;
 70 
 71 	};
 72 
 73 	// approximate length by summing linear segments
 74 
 75 	this.getLength = function ( nSubDivisions ) {
 76 
 77 		var i, index, nSamples, position,
 78 			point = 0, intPoint = 0, oldIntPoint = 0,
 79 			oldPosition = new THREE.Vector3(),
 80 			tmpVec = new THREE.Vector3(),
 81 			chunkLengths = [],
 82 			totalLength = 0;
 83 
 84 		// first point has 0 length
 85 
 86 		chunkLengths[ 0 ] = 0;
 87 
 88 		if ( !nSubDivisions ) nSubDivisions = 100;
 89 
 90 		nSamples = this.points.length * nSubDivisions;
 91 
 92 		oldPosition.copy( this.points[ 0 ] );
 93 
 94 		for ( i = 1; i < nSamples; i ++ ) {
 95 
 96 			index = i / nSamples;
 97 
 98 			position = this.getPoint( index );
 99 			tmpVec.copy( position );
100 
101 			totalLength += tmpVec.distanceTo( oldPosition );
102 
103 			oldPosition.copy( position );
104 
105 			point = ( this.points.length - 1 ) * index;
106 			intPoint = Math.floor( point );
107 
108 			if ( intPoint != oldIntPoint ) {
109 
110 				chunkLengths[ intPoint ] = totalLength;
111 				oldIntPoint = intPoint;
112 
113 			}
114 
115 		}
116 
117 		// last point ends with total length
118 
119 		chunkLengths[ chunkLengths.length ] = totalLength;
120 
121 		return { chunks: chunkLengths, total: totalLength };
122 
123 	};
124 
125 	this.reparametrizeByArcLength = function ( samplingCoef ) {
126 
127 		var i, j,
128 			index, indexCurrent, indexNext,
129 			linearDistance, realDistance,
130 			sampling, position,
131 			newpoints = [],
132 			tmpVec = new THREE.Vector3(),
133 			sl = this.getLength();
134 
135 		newpoints.push( tmpVec.copy( this.points[ 0 ] ).clone() );
136 
137 		for ( i = 1; i < this.points.length; i++ ) {
138 
139 			//tmpVec.copy( this.points[ i - 1 ] );
140 			//linearDistance = tmpVec.distanceTo( this.points[ i ] );
141 
142 			realDistance = sl.chunks[ i ] - sl.chunks[ i - 1 ];
143 
144 			sampling = Math.ceil( samplingCoef * realDistance / sl.total );
145 
146 			indexCurrent = ( i - 1 ) / ( this.points.length - 1 );
147 			indexNext = i / ( this.points.length - 1 );
148 
149 			for ( j = 1; j < sampling - 1; j++ ) {
150 
151 				index = indexCurrent + j * ( 1 / sampling ) * ( indexNext - indexCurrent );
152 
153 				position = this.getPoint( index );
154 				newpoints.push( tmpVec.copy( position ).clone() );
155 
156 			}
157 
158 			newpoints.push( tmpVec.copy( this.points[ i ] ).clone() );
159 
160 		}
161 
162 		this.points = newpoints;
163 
164 	};
165 
166 	// Catmull-Rom
167 
168 	function interpolate( p0, p1, p2, p3, t, t2, t3 ) {
169 
170 		var v0 = ( p2 - p0 ) * 0.5,
171 			v1 = ( p3 - p1 ) * 0.5;
172 
173 		return ( 2 * ( p1 - p2 ) + v0 + v1 ) * t3 + ( - 3 * ( p1 - p2 ) - 2 * v0 - v1 ) * t2 + v0 * t + p1;
174 
175 	};
176 
177 };
178 

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