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
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
|
#pragma BLENDER_REQUIRE(common_math_lib.glsl)
/* ---------------------------------------------------------------------- */
/** \name Math intersection & projection functions.
* \{ */
float point_plane_projection_dist(vec3 lineorigin, vec3 planeorigin, vec3 planenormal)
{
return dot(planenormal, planeorigin - lineorigin);
}
float line_plane_intersect_dist(vec3 lineorigin,
vec3 linedirection,
vec3 planeorigin,
vec3 planenormal)
{
return dot(planenormal, planeorigin - lineorigin) / dot(planenormal, linedirection);
}
float line_plane_intersect_dist(vec3 lineorigin, vec3 linedirection, vec4 plane)
{
vec3 plane_co = plane.xyz * (-plane.w / len_squared(plane.xyz));
vec3 h = lineorigin - plane_co;
return -dot(plane.xyz, h) / dot(plane.xyz, linedirection);
}
vec3 line_plane_intersect(vec3 lineorigin, vec3 linedirection, vec3 planeorigin, vec3 planenormal)
{
float dist = line_plane_intersect_dist(lineorigin, linedirection, planeorigin, planenormal);
return lineorigin + linedirection * dist;
}
vec3 line_plane_intersect(vec3 lineorigin, vec3 linedirection, vec4 plane)
{
float dist = line_plane_intersect_dist(lineorigin, linedirection, plane);
return lineorigin + linedirection * dist;
}
float line_aligned_plane_intersect_dist(vec3 lineorigin, vec3 linedirection, vec3 planeorigin)
{
/* aligned plane normal */
vec3 L = planeorigin - lineorigin;
float diskdist = length(L);
vec3 planenormal = -normalize(L);
return -diskdist / dot(planenormal, linedirection);
}
vec3 line_aligned_plane_intersect(vec3 lineorigin, vec3 linedirection, vec3 planeorigin)
{
float dist = line_aligned_plane_intersect_dist(lineorigin, linedirection, planeorigin);
if (dist < 0) {
/* if intersection is behind we fake the intersection to be
* really far and (hopefully) not inside the radius of interest */
dist = 1e16;
}
return lineorigin + linedirection * dist;
}
float line_unit_sphere_intersect_dist(vec3 lineorigin, vec3 linedirection)
{
float a = dot(linedirection, linedirection);
float b = dot(linedirection, lineorigin);
float c = dot(lineorigin, lineorigin) - 1;
float dist = 1e15;
float determinant = b * b - a * c;
if (determinant >= 0) {
dist = (sqrt(determinant) - b) / a;
}
return dist;
}
float line_unit_box_intersect_dist(vec3 lineorigin, vec3 linedirection)
{
/* https://seblagarde.wordpress.com/2012/09/29/image-based-lighting-approaches-and-parallax-corrected-cubemap/
*/
vec3 firstplane = (vec3(1.0) - lineorigin) / linedirection;
vec3 secondplane = (vec3(-1.0) - lineorigin) / linedirection;
vec3 furthestplane = max(firstplane, secondplane);
return min_v3(furthestplane);
}
/** \} */
/* ---------------------------------------------------------------------- */
/** \name Other useful functions.
* \{ */
void make_orthonormal_basis(vec3 N, out vec3 T, out vec3 B)
{
vec3 UpVector = abs(N.z) < 0.99999 ? vec3(0.0, 0.0, 1.0) : vec3(1.0, 0.0, 0.0);
T = normalize(cross(UpVector, N));
B = cross(N, T);
}
/* ---- Encode / Decode Normal buffer data ---- */
/* From http://aras-p.info/texts/CompactNormalStorage.html
* Using Method #4: Spheremap Transform */
vec2 normal_encode(vec3 n, vec3 view)
{
float p = sqrt(n.z * 8.0 + 8.0);
return n.xy / p + 0.5;
}
vec3 normal_decode(vec2 enc, vec3 view)
{
vec2 fenc = enc * 4.0 - 2.0;
float f = dot(fenc, fenc);
float g = sqrt(1.0 - f / 4.0);
vec3 n;
n.xy = fenc * g;
n.z = 1 - f / 2;
return n;
}
/** \} */
|
