`z_fcurve_data` OK, match last function in `z_fcurve_data_skelanime`, document SkelCurve system (#776)

* Match SkelCurve_Update

Co-authored-by: Kelebek1 <34639600+Kelebek1@users.noreply.github.com>

* Match and document z_fcurve_data

* Begin documenting SkelCurve

* More documentation

* Deformat header

* Pluralise knotCount

* Sort out jointTable

* Rename frameCount

* Format

* More documentation

* Cleanup on DemoEffect

* Remove space on typedef

* Format, couple of fixes in the header

* Review

* Oops

* Fix EnBox, DemoTreLgt, use macros in EnTorch

Co-authored-by: Kelebek1 <34639600+Kelebek1@users.noreply.github.com>

1 files changed, 83 insertions, 2 deletions

diff --git a/src/code/z_fcurve_data.c b/src/code/z_fcurve_data.c
index a0bf887e1..5c0aa066a 100644
--- a/src/code/z_fcurve_data.c
+++ b/src/code/z_fcurve_data.c
@@ -1,5 +1,86 @@
+/**
+ * @file z_fcurve_data.c
+ * @brief Interpolation functions for use with Curve SkelAnime
+ */
 #include "global.h"
+#include "z64curve.h"
 
-#pragma GLOBAL_ASM("asm/non_matchings/code/z_fcurve_data/func_800F23E0.s")
+#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
 
-#pragma GLOBAL_ASM("asm/non_matchings/code/z_fcurve_data/func_800F2478.s")
+/**
+ * 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);
+                }
+            }
+        }
+    }
+}