diff options
| author | Aaditya Dhruv <[email protected]> | 2026-01-25 15:10:37 -0600 |
|---|---|---|
| committer | Aaditya Dhruv <[email protected]> | 2026-01-25 15:10:37 -0600 |
| commit | 118980e02e59ff31871df59dce257075394f3533 (patch) | |
| tree | 26fba4492bb4b561d21bf49b35d892a821d54fab /include/cglm/bezier.h | |
| parent | 0e6e1245b70df4dfcba135d50e1b53d1a8ef7eb8 (diff) | |
wip
Diffstat (limited to 'include/cglm/bezier.h')
| -rw-r--r-- | include/cglm/bezier.h | 154 |
1 files changed, 154 insertions, 0 deletions
diff --git a/include/cglm/bezier.h b/include/cglm/bezier.h new file mode 100644 index 0000000..a6e5f8a --- /dev/null +++ b/include/cglm/bezier.h @@ -0,0 +1,154 @@ +/* + * 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 */ |
