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authorAaditya Dhruv <[email protected]>2026-01-25 15:10:37 -0600
committerAaditya Dhruv <[email protected]>2026-01-25 15:10:37 -0600
commit118980e02e59ff31871df59dce257075394f3533 (patch)
tree26fba4492bb4b561d21bf49b35d892a821d54fab /include/cglm/bezier.h
parent0e6e1245b70df4dfcba135d50e1b53d1a8ef7eb8 (diff)
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diff --git a/include/cglm/bezier.h b/include/cglm/bezier.h
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+/*
+ * Copyright (c), Recep Aslantas.
+ *
+ * MIT License (MIT), http://opensource.org/licenses/MIT
+ * Full license can be found in the LICENSE file
+ */
+
+#ifndef cglm_bezier_h
+#define cglm_bezier_h
+
+#include "common.h"
+
+#define GLM_BEZIER_MAT_INIT {{-1.0f, 3.0f, -3.0f, 1.0f}, \
+ { 3.0f, -6.0f, 3.0f, 0.0f}, \
+ {-3.0f, 3.0f, 0.0f, 0.0f}, \
+ { 1.0f, 0.0f, 0.0f, 0.0f}}
+#define GLM_HERMITE_MAT_INIT {{ 2.0f, -3.0f, 0.0f, 1.0f}, \
+ {-2.0f, 3.0f, 0.0f, 0.0f}, \
+ { 1.0f, -2.0f, 1.0f, 0.0f}, \
+ { 1.0f, -1.0f, 0.0f, 0.0f}}
+/* for C only */
+#define GLM_BEZIER_MAT ((mat4)GLM_BEZIER_MAT_INIT)
+#define GLM_HERMITE_MAT ((mat4)GLM_HERMITE_MAT_INIT)
+
+#define CGLM_DECASTEL_EPS 1e-9f
+#define CGLM_DECASTEL_MAX 1000
+#define CGLM_DECASTEL_SMALL 1e-20f
+
+/*!
+ * @brief cubic bezier interpolation
+ *
+ * Formula:
+ * B(s) = P0*(1-s)^3 + 3*C0*s*(1-s)^2 + 3*C1*s^2*(1-s) + P1*s^3
+ *
+ * similar result using matrix:
+ * B(s) = glm_smc(t, GLM_BEZIER_MAT, (vec4){p0, c0, c1, p1})
+ *
+ * glm_eq(glm_smc(...), glm_bezier(...)) should return TRUE
+ *
+ * @param[in] s parameter between 0 and 1
+ * @param[in] p0 begin point
+ * @param[in] c0 control point 1
+ * @param[in] c1 control point 2
+ * @param[in] p1 end point
+ *
+ * @return B(s)
+ */
+CGLM_INLINE
+float
+glm_bezier(float s, float p0, float c0, float c1, float p1) {
+ float x, xx, ss, xs3, a;
+
+ x = 1.0f - s;
+ xx = x * x;
+ ss = s * s;
+ xs3 = (s - ss) * 3.0f;
+ a = p0 * xx + c0 * xs3;
+
+ return a + s * (c1 * xs3 + p1 * ss - a);
+}
+
+/*!
+ * @brief cubic hermite interpolation
+ *
+ * Formula:
+ * H(s) = P0*(2*s^3 - 3*s^2 + 1) + T0*(s^3 - 2*s^2 + s)
+ * + P1*(-2*s^3 + 3*s^2) + T1*(s^3 - s^2)
+ *
+ * similar result using matrix:
+ * H(s) = glm_smc(t, GLM_HERMITE_MAT, (vec4){p0, p1, c0, c1})
+ *
+ * glm_eq(glm_smc(...), glm_hermite(...)) should return TRUE
+ *
+ * @param[in] s parameter between 0 and 1
+ * @param[in] p0 begin point
+ * @param[in] t0 tangent 1
+ * @param[in] t1 tangent 2
+ * @param[in] p1 end point
+ *
+ * @return H(s)
+ */
+CGLM_INLINE
+float
+glm_hermite(float s, float p0, float t0, float t1, float p1) {
+ float ss, d, a, b, c, e, f;
+
+ ss = s * s;
+ a = ss + ss;
+ c = a + ss;
+ b = a * s;
+ d = s * ss;
+ f = d - ss;
+ e = b - c;
+
+ return p0 * (e + 1.0f) + t0 * (f - ss + s) + t1 * f - p1 * e;
+}
+
+/*!
+ * @brief iterative way to solve cubic equation
+ *
+ * @param[in] prm parameter between 0 and 1
+ * @param[in] p0 begin point
+ * @param[in] c0 control point 1
+ * @param[in] c1 control point 2
+ * @param[in] p1 end point
+ *
+ * @return parameter to use in cubic equation
+ */
+CGLM_INLINE
+float
+glm_decasteljau(float prm, float p0, float c0, float c1, float p1) {
+ float u, v, a, b, c, d, e, f;
+ int i;
+
+ if (prm - p0 < CGLM_DECASTEL_SMALL)
+ return 0.0f;
+
+ if (p1 - prm < CGLM_DECASTEL_SMALL)
+ return 1.0f;
+
+ u = 0.0f;
+ v = 1.0f;
+
+ for (i = 0; i < CGLM_DECASTEL_MAX; i++) {
+ /* de Casteljau Subdivision */
+ a = (p0 + c0) * 0.5f;
+ b = (c0 + c1) * 0.5f;
+ c = (c1 + p1) * 0.5f;
+ d = (a + b) * 0.5f;
+ e = (b + c) * 0.5f;
+ f = (d + e) * 0.5f; /* this one is on the curve! */
+
+ /* The curve point is close enough to our wanted t */
+ if (fabsf(f - prm) < CGLM_DECASTEL_EPS)
+ return glm_clamp_zo((u + v) * 0.5f);
+
+ /* dichotomy */
+ if (f < prm) {
+ p0 = f;
+ c0 = e;
+ c1 = c;
+ u = (u + v) * 0.5f;
+ } else {
+ c0 = a;
+ c1 = d;
+ p1 = f;
+ v = (u + v) * 0.5f;
+ }
+ }
+
+ return glm_clamp_zo((u + v) * 0.5f);
+}
+
+#endif /* cglm_bezier_h */