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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 */
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