1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
|
.. default-domain:: C
Bezier
================================================================================
Header: cglm/bezier.h
Common helpers for cubic bezier and similar curves.
Table of contents (click to go):
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Functions:
1. :c:func:`glm_bezier`
2. :c:func:`glm_hermite`
3. :c:func:`glm_decasteljau`
Functions documentation
~~~~~~~~~~~~~~~~~~~~~~~
.. c:function:: float glm_bezier(float s, float p0, float c0, float c1, float p1)
| cubic bezier interpolation
| formula:
.. code-block:: text
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:
.. code-block:: text
B(s) = glm_smc(t, GLM_BEZIER_MAT, (vec4){p0, c0, c1, p1})
| glm_eq(glm_smc(...), glm_bezier(...)) should return TRUE
Parameters:
| *[in]* **s** parameter between 0 and 1
| *[in]* **p0** begin point
| *[in]* **c0** control point 1
| *[in]* **c1** control point 2
| *[in]* **p1** end point
Returns:
B(s)
.. c:function:: float glm_hermite(float s, float p0, float t0, float t1, float p1)
| cubic hermite interpolation
| formula:
.. code-block:: text
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:
.. code-block:: text
H(s) = glm_smc(t, GLM_HERMITE_MAT, (vec4){p0, p1, c0, c1})
| glm_eq(glm_smc(...), glm_hermite(...)) should return TRUE
Parameters:
| *[in]* **s** parameter between 0 and 1
| *[in]* **p0** begin point
| *[in]* **t0** tangent 1
| *[in]* **t1** tangent 2
| *[in]* **p1** end point
Returns:
B(s)
.. c:function:: float glm_decasteljau(float prm, float p0, float c0, float c1, float p1)
| iterative way to solve cubic equation
Parameters:
| *[in]* **prm** parameter between 0 and 1
| *[in]* **p0** begin point
| *[in]* **c0** control point 1
| *[in]* **c1** control point 2
| *[in]* **p1** end point
Returns:
parameter to use in cubic equation
|
