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0e51a51fb1
* Rename and document SkelCurve * AVOID_UB in DemoTreLgt_OverrideLimbDraw * Rename code_8006C510 * Objdump flags in the makefile * Move CC_CHECK above compilation * Review 1 * Review 2 * Review 3 * Review Add doxygen comments to file head use angle macro, improve bug comment, make arguments of SkelCurve_Draw more consistent, Change this temp to pad in MagicWind
85 lines
3.2 KiB
C
85 lines
3.2 KiB
C
/**
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* File: z_fcurve_data.c
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* Description: Interpolation functions for use with Curve SkelAnime
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*/
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#include "global.h"
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#include "z64curve.h"
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#define FCURVE_INTERP_CUBIC 0 // Interpolate using a Hermite cubic spline
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#define FCURVE_INTERP_NONE 1 // Return the value at the left endpoint instead of interpolating
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#define FCURVE_INTERP_LINEAR 2 // Interpolate linearly
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/**
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* Hermite cubic spline interpolation between two endpoints, a,b. More information available at
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* https://en.wikipedia.org/wiki/Cubic_Hermite_spline
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*
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* @param t interpolation parameter rescaled to lie in [0,1], (x-a)/(b-a)
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* @param interval distance (b-a) between the endpoints
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* @param y0 p(a)
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* @param y1 p(b)
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* @param m0 p'(a)
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* @param m1 p'(b)
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* @return f32 p(t), value of the cubic interpolating polynomial
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*/
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f32 Curve_CubicHermiteSpline(f32 t, f32 interval, f32 y0, f32 y1, f32 m0, f32 m1) {
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f32 t2 = t * t;
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f32 t3 = t2 * t;
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f32 t3x2 = t3 * 2.0f;
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f32 t2x3 = t2 * 3.0f;
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// Hermite basis cubics h_{ij} satisfy h_{ij}^{(j)}(i) = 1, the other three values being 0
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f32 h00 = t3x2 - t2x3 + 1.0f; // h_{00}(t) = 2t^3 - 3t^2 + 1
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f32 h01 = t2x3 - t3x2; // h_{01}(t) = 3t^2 - 2t^3
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f32 h10 = t3 - t2 * 2.0f + t; // h_{10}(t) = t^3 - 2t^2 + t
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f32 h11 = t3 - t2; // h_{11}(t) = t^3 - t^2
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f32 ret = h00 * y0;
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ret += h01 * y1;
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ret += h10 * m0 * interval;
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ret += h11 * m1 * interval;
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return ret;
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}
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/**
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* Interpolates based on an array of CurveInterpKnot.
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*
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* @param x point at which to interpolate.
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* @param knots Beginning of CurveInterpKnot array to use.
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* @param knotCount number of knots to read from the array.
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* @return f32 interpolated value
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*/
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f32 Curve_Interpolate(f32 x, CurveInterpKnot* knots, s32 knotCount) {
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// If outside the entire interpolation interval, return the value at the near endpoint.
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if (x <= knots[0].abscissa) {
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return knots[0].ordinate;
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} else if (x >= knots[knotCount - 1].abscissa) {
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return knots[knotCount - 1].ordinate;
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} else {
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s32 cur;
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for (cur = 0;; cur++) {
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s32 next = cur + 1;
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// Find the subinterval in which x lies
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if (x < knots[next].abscissa) {
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if (knots[cur].flags & FCURVE_INTERP_NONE) {
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// No interpolation
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return knots[cur].ordinate;
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} else if (knots[cur].flags & FCURVE_INTERP_LINEAR) {
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// Linear interpolation
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return knots[cur].ordinate +
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((x - (f32)knots[cur].abscissa) / ((f32)knots[next].abscissa - (f32)knots[cur].abscissa)) *
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(knots[next].ordinate - knots[cur].ordinate);
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} else {
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// Cubic interpolation
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f32 diff = (f32)knots[next].abscissa - (f32)knots[cur].abscissa;
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f32 t = (x - (f32)knots[cur].abscissa) / ((f32)knots[next].abscissa - (f32)knots[cur].abscissa);
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return Curve_CubicHermiteSpline(t, diff * (1.0f / 30.0f), knots[cur].ordinate, knots[next].ordinate,
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knots[cur].rightGradient, knots[next].leftGradient);
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}
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}
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}
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}
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}
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