initial commit

lib/math/interpolants/CubicInterpolant.js

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+import { ZeroCurvatureEnding } from '../../constants.js';
+import { Interpolant } from '../Interpolant.js';
+import { WrapAroundEnding, ZeroSlopeEnding } from '../../constants.js';
+
+/**
+ * Fast and simple cubic spline interpolant.
+ *
+ * It was derived from a Hermitian construction setting the first derivative
+ * at each sample position to the linear slope between neighboring positions
+ * over their parameter interval.
+ *
+ * @author tschw
+ */
+
+function CubicInterpolant( parameterPositions, sampleValues, sampleSize, resultBuffer ) {
+
+	Interpolant.call( this, parameterPositions, sampleValues, sampleSize, resultBuffer );
+
+	this._weightPrev = - 0;
+	this._offsetPrev = - 0;
+	this._weightNext = - 0;
+	this._offsetNext = - 0;
+
+}
+
+CubicInterpolant.prototype = Object.assign( Object.create( Interpolant.prototype ), {
+
+	constructor: CubicInterpolant,
+
+	DefaultSettings_: {
+
+		endingStart: ZeroCurvatureEnding,
+		endingEnd: ZeroCurvatureEnding
+
+	},
+
+	intervalChanged_: function ( i1, t0, t1 ) {
+
+		var pp = this.parameterPositions,
+			iPrev = i1 - 2,
+			iNext = i1 + 1,
+
+			tPrev = pp[ iPrev ],
+			tNext = pp[ iNext ];
+
+		if ( tPrev === undefined ) {
+
+			switch ( this.getSettings_().endingStart ) {
+
+				case ZeroSlopeEnding:
+
+					// f'(t0) = 0
+					iPrev = i1;
+					tPrev = 2 * t0 - t1;
+
+					break;
+
+				case WrapAroundEnding:
+
+					// use the other end of the curve
+					iPrev = pp.length - 2;
+					tPrev = t0 + pp[ iPrev ] - pp[ iPrev + 1 ];
+
+					break;
+
+				default: // ZeroCurvatureEnding
+
+					// f''(t0) = 0 a.k.a. Natural Spline
+					iPrev = i1;
+					tPrev = t1;
+
+			}
+
+		}
+
+		if ( tNext === undefined ) {
+
+			switch ( this.getSettings_().endingEnd ) {
+
+				case ZeroSlopeEnding:
+
+					// f'(tN) = 0
+					iNext = i1;
+					tNext = 2 * t1 - t0;
+
+					break;
+
+				case WrapAroundEnding:
+
+					// use the other end of the curve
+					iNext = 1;
+					tNext = t1 + pp[ 1 ] - pp[ 0 ];
+
+					break;
+
+				default: // ZeroCurvatureEnding
+
+					// f''(tN) = 0, a.k.a. Natural Spline
+					iNext = i1 - 1;
+					tNext = t0;
+
+			}
+
+		}
+
+		var halfDt = ( t1 - t0 ) * 0.5,
+			stride = this.valueSize;
+
+		this._weightPrev = halfDt / ( t0 - tPrev );
+		this._weightNext = halfDt / ( tNext - t1 );
+		this._offsetPrev = iPrev * stride;
+		this._offsetNext = iNext * stride;
+
+	},
+
+	interpolate_: function ( i1, t0, t, t1 ) {
+
+		var result = this.resultBuffer,
+			values = this.sampleValues,
+			stride = this.valueSize,
+
+			o1 = i1 * stride,		o0 = o1 - stride,
+			oP = this._offsetPrev, 	oN = this._offsetNext,
+			wP = this._weightPrev,	wN = this._weightNext,
+
+			p = ( t - t0 ) / ( t1 - t0 ),
+			pp = p * p,
+			ppp = pp * p;
+
+		// evaluate polynomials
+
+		var sP = - wP * ppp + 2 * wP * pp - wP * p;
+		var s0 = ( 1 + wP ) * ppp + ( - 1.5 - 2 * wP ) * pp + ( - 0.5 + wP ) * p + 1;
+		var s1 = ( - 1 - wN ) * ppp + ( 1.5 + wN ) * pp + 0.5 * p;
+		var sN = wN * ppp - wN * pp;
+
+		// combine data linearly
+
+		for ( var i = 0; i !== stride; ++ i ) {
+
+			result[ i ] =
+					sP * values[ oP + i ] +
+					s0 * values[ o0 + i ] +
+					s1 * values[ o1 + i ] +
+					sN * values[ oN + i ];
+
+		}
+
+		return result;
+
+	}
+
+} );
+
+
+export { CubicInterpolant };

lib/math/interpolants/DiscreteInterpolant.js

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+import { Interpolant } from '../Interpolant.js';
+
+/**
+ *
+ * Interpolant that evaluates to the sample value at the position preceeding
+ * the parameter.
+ *
+ * @author tschw
+ */
+
+function DiscreteInterpolant( parameterPositions, sampleValues, sampleSize, resultBuffer ) {
+
+	Interpolant.call( this, parameterPositions, sampleValues, sampleSize, resultBuffer );
+
+}
+
+DiscreteInterpolant.prototype = Object.assign( Object.create( Interpolant.prototype ), {
+
+	constructor: DiscreteInterpolant,
+
+	interpolate_: function ( i1 /*, t0, t, t1 */ ) {
+
+		return this.copySampleValue_( i1 - 1 );
+
+	}
+
+} );
+
+
+export { DiscreteInterpolant };

lib/math/interpolants/LinearInterpolant.js

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+import { Interpolant } from '../Interpolant.js';
+
+/**
+ * @author tschw
+ */
+
+function LinearInterpolant( parameterPositions, sampleValues, sampleSize, resultBuffer ) {
+
+	Interpolant.call( this, parameterPositions, sampleValues, sampleSize, resultBuffer );
+
+}
+
+LinearInterpolant.prototype = Object.assign( Object.create( Interpolant.prototype ), {
+
+	constructor: LinearInterpolant,
+
+	interpolate_: function ( i1, t0, t, t1 ) {
+
+		var result = this.resultBuffer,
+			values = this.sampleValues,
+			stride = this.valueSize,
+
+			offset1 = i1 * stride,
+			offset0 = offset1 - stride,
+
+			weight1 = ( t - t0 ) / ( t1 - t0 ),
+			weight0 = 1 - weight1;
+
+		for ( var i = 0; i !== stride; ++ i ) {
+
+			result[ i ] =
+					values[ offset0 + i ] * weight0 +
+					values[ offset1 + i ] * weight1;
+
+		}
+
+		return result;
+
+	}
+
+} );
+
+
+export { LinearInterpolant };

lib/math/interpolants/QuaternionLinearInterpolant.js

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+import { Interpolant } from '../Interpolant.js';
+import { Quaternion } from '../Quaternion.js';
+
+/**
+ * Spherical linear unit quaternion interpolant.
+ *
+ * @author tschw
+ */
+
+function QuaternionLinearInterpolant( parameterPositions, sampleValues, sampleSize, resultBuffer ) {
+
+	Interpolant.call( this, parameterPositions, sampleValues, sampleSize, resultBuffer );
+
+}
+
+QuaternionLinearInterpolant.prototype = Object.assign( Object.create( Interpolant.prototype ), {
+
+	constructor: QuaternionLinearInterpolant,
+
+	interpolate_: function ( i1, t0, t, t1 ) {
+
+		var result = this.resultBuffer,
+			values = this.sampleValues,
+			stride = this.valueSize,
+
+			offset = i1 * stride,
+
+			alpha = ( t - t0 ) / ( t1 - t0 );
+
+		for ( var end = offset + stride; offset !== end; offset += 4 ) {
+
+			Quaternion.slerpFlat( result, 0, values, offset - stride, values, offset, alpha );
+
+		}
+
+		return result;
+
+	}
+
+} );
+
+
+export { QuaternionLinearInterpolant };