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. */ class CubicInterpolant extends Interpolant { constructor(parameterPositions, sampleValues, sampleSize, resultBuffer) { super(parameterPositions, sampleValues, sampleSize, resultBuffer); this._weightPrev = -0; this._offsetPrev = -0; this._weightNext = -0; this._offsetNext = -0; this.DefaultSettings_ = { endingStart: ZeroCurvatureEnding, endingEnd: ZeroCurvatureEnding, }; } intervalChanged_(i1, t0, t1) { const pp = this.parameterPositions; let 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; } } const 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_(i1, t0, t, t1) { const 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 const sP = -wP * ppp + 2 * wP * pp - wP * p; const s0 = (1 + wP) * ppp + (-1.5 - 2 * wP) * pp + (-0.5 + wP) * p + 1; const s1 = (-1 - wN) * ppp + (1.5 + wN) * pp + 0.5 * p; const sN = wN * ppp - wN * pp; // combine data linearly for (let 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 };