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/**
* File: z_fcurve_data.c
* Description: Interpolation functions for use with Curve SkelAnime
*/
#include "curve.h"
#define FCURVE_INTERP_CUBIC 0 // Interpolate using a Hermite cubic spline
#define FCURVE_INTERP_NONE 1 // Return the value at the left endpoint instead of interpolating
#define FCURVE_INTERP_LINEAR 2 // Interpolate linearly
/**
* Hermite cubic spline interpolation between two endpoints, a,b. More information available at
* https://en.wikipedia.org/wiki/Cubic_Hermite_spline
*
* @param t interpolation parameter rescaled to lie in [0,1], (x-a)/(b-a)
* @param interval distance (b-a) between the endpoints
* @param y0 p(a)
* @param y1 p(b)
* @param m0 p'(a)
* @param m1 p'(b)
* @return f32 p(t), value of the cubic interpolating polynomial
*/
f32 Curve_CubicHermiteSpline(f32 t, f32 interval, f32 y0, f32 y1, f32 m0, f32 m1) {
f32 t2 = t * t;
f32 t3 = t2 * t;
f32 t3x2 = t3 * 2.0f;
f32 t2x3 = t2 * 3.0f;
// Hermite basis cubics h_{ij} satisfy h_{ij}^{(j)}(i) = 1, the other three values being 0
f32 h00 = t3x2 - t2x3 + 1.0f; // h_{00}(t) = 2t^3 - 3t^2 + 1
f32 h01 = t2x3 - t3x2; // h_{01}(t) = 3t^2 - 2t^3
f32 h10 = t3 - t2 * 2.0f + t; // h_{10}(t) = t^3 - 2t^2 + t
f32 h11 = t3 - t2; // h_{11}(t) = t^3 - t^2
f32 ret = h00 * y0;
ret += h01 * y1;
ret += h10 * m0 * interval;
ret += h11 * m1 * interval;
return ret;
}
/**
* Interpolates based on an array of CurveInterpKnot.
*
* @param x point at which to interpolate.
* @param knots Beginning of CurveInterpKnot array to use.
* @param knotCount number of knots to read from the array.
* @return f32 interpolated value
*/
f32 Curve_Interpolate(f32 x, CurveInterpKnot* knots, s32 knotCount) {
// If outside the entire interpolation interval, return the value at the near endpoint.
if (x <= knots[0].abscissa) {
return knots[0].ordinate;
} else if (x >= knots[knotCount - 1].abscissa) {
return knots[knotCount - 1].ordinate;
} else {
s32 cur;
for (cur = 0;; cur++) {
s32 next = cur + 1;
// Find the subinterval in which x lies
if (x < knots[next].abscissa) {
if (knots[cur].flags & FCURVE_INTERP_NONE) {
// No interpolation
return knots[cur].ordinate;
} else if (knots[cur].flags & FCURVE_INTERP_LINEAR) {
// Linear interpolation
return knots[cur].ordinate +
((x - (f32)knots[cur].abscissa) / ((f32)knots[next].abscissa - (f32)knots[cur].abscissa)) *
(knots[next].ordinate - knots[cur].ordinate);
} else {
// Cubic interpolation
f32 diff = (f32)knots[next].abscissa - (f32)knots[cur].abscissa;
f32 t = (x - (f32)knots[cur].abscissa) / ((f32)knots[next].abscissa - (f32)knots[cur].abscissa);
return Curve_CubicHermiteSpline(t, diff * (1.0f / 30.0f), knots[cur].ordinate, knots[next].ordinate,
knots[cur].rightGradient, knots[next].leftGradient);
}
}
}
}
}
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