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curve: cubic hermite intrpolation

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Recep Aslantas
2019-01-29 22:17:44 +03:00
parent 1e121a4855
commit 7848dda1dd
7 changed files with 102 additions and 12 deletions
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56
include/cglm/bezier.h
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@@ -8,13 +8,17 @@
#ifndef cglm_bezier_h
#define cglm_bezier_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_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_BEZIER_MAT ((mat4)GLM_BEZIER_MAT_INIT)
#define GLM_HERMITE_MAT ((mat4)GLM_HERMITE_MAT_INIT)
#define CGLM_DECASTEL_EPS 1e-9
#define CGLM_DECASTEL_MAX 1000
@@ -54,10 +58,46 @@ glm_bezier(float s, float p0, float c0, float c1, float p1) {
}
/*!
* @brief iterative way to solve cubic equation
* @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 B(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
@@ -112,7 +152,7 @@ glm_decasteljau(float prm, float p0, float c0, float c1, float p1) {
/*!
* @brief solve cubic bezier equation
*
* @param[in] s parameter between 0 and 1
* @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

4
include/cglm/call/bezier.h
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@@ -17,6 +17,10 @@ CGLM_EXPORT
float
glmc_bezier(float s, float p0, float c0, float c1, float p1);
CGLM_EXPORT
float
glmc_hermite(float s, float p0, float t0, float t1, float p1);
CGLM_EXPORT
float
glmc_decasteljau(float prm, float p0, float c0, float c1, float p1);