1 /*
2 * matrix.c
3 *
4 * Some useful matrix functions.
5 *
6 * Brian Paul
7 * 10 Feb 2004
8 */
9
10
11
12 #include <stdio.h>
13 #include <stdlib.h>
14 #include <math.h>
15
16
17 /**
18 * Pretty-print the given matrix.
19 */
20 void
PrintMatrix(const float p[16])21 PrintMatrix(const float p[16])
22 {
23 printf("[ %6.3f %6.3f %6.3f %6.3f ]\n", p[0], p[4], p[8], p[12]);
24 printf("[ %6.3f %6.3f %6.3f %6.3f ]\n", p[1], p[5], p[9], p[13]);
25 printf("[ %6.3f %6.3f %6.3f %6.3f ]\n", p[2], p[6], p[10], p[14]);
26 printf("[ %6.3f %6.3f %6.3f %6.3f ]\n", p[3], p[7], p[11], p[15]);
27 }
28
29
30 /**
31 * Build a glFrustum matrix.
32 */
33 void
Frustum(float left,float right,float bottom,float top,float nearZ,float farZ,float * m)34 Frustum(float left, float right, float bottom, float top, float nearZ, float farZ, float *m)
35 {
36 float x = (2.0F*nearZ) / (right-left);
37 float y = (2.0F*nearZ) / (top-bottom);
38 float a = (right+left) / (right-left);
39 float b = (top+bottom) / (top-bottom);
40 float c = -(farZ+nearZ) / ( farZ-nearZ);
41 float d = -(2.0F*farZ*nearZ) / (farZ-nearZ);
42
43 #define M(row,col) m[col*4+row]
44 M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F;
45 M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F;
46 M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d;
47 M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F;
48 #undef M
49 }
50
51
52 /**
53 * Build a glOrtho marix.
54 */
55 void
Ortho(float left,float right,float bottom,float top,float nearZ,float farZ,float * m)56 Ortho(float left, float right, float bottom, float top, float nearZ, float farZ, float *m)
57 {
58 #define M(row,col) m[col*4+row]
59 M(0,0) = 2.0F / (right-left);
60 M(0,1) = 0.0F;
61 M(0,2) = 0.0F;
62 M(0,3) = -(right+left) / (right-left);
63
64 M(1,0) = 0.0F;
65 M(1,1) = 2.0F / (top-bottom);
66 M(1,2) = 0.0F;
67 M(1,3) = -(top+bottom) / (top-bottom);
68
69 M(2,0) = 0.0F;
70 M(2,1) = 0.0F;
71 M(2,2) = -2.0F / (farZ-nearZ);
72 M(2,3) = -(farZ+nearZ) / (farZ-nearZ);
73
74 M(3,0) = 0.0F;
75 M(3,1) = 0.0F;
76 M(3,2) = 0.0F;
77 M(3,3) = 1.0F;
78 #undef M
79 }
80
81
82 /**
83 * Decompose a projection matrix to determine original glFrustum or
84 * glOrtho parameters.
85 */
86 void
DecomposeProjection(const float * m,int * isPerspective,float * leftOut,float * rightOut,float * botOut,float * topOut,float * nearOut,float * farOut)87 DecomposeProjection( const float *m,
88 int *isPerspective,
89 float *leftOut, float *rightOut,
90 float *botOut, float *topOut,
91 float *nearOut, float *farOut)
92 {
93 if (m[15] == 0.0) {
94 /* perspective */
95 float p[16];
96 const float x = m[0]; /* 2N / (R-L) */
97 const float y = m[5]; /* 2N / (T-B) */
98 const float a = m[8]; /* (R+L) / (R-L) */
99 const float b = m[9]; /* (T+B) / (T-B) */
100 const float c = m[10]; /* -(F+N) / (F-N) */
101 const float d = m[14]; /* -2FN / (F-N) */
102
103 /* These equations found with simple algebra, knowing the arithmetic
104 * use to set up a typical perspective projection matrix in OpenGL.
105 */
106 const float nearZ = -d / (1.0 - c);
107 const float farZ = (c - 1.0) * nearZ / (c + 1.0);
108 const float left = nearZ * (a - 1.0) / x;
109 const float right = 2.0 * nearZ / x + left;
110 const float bottom = nearZ * (b - 1.0) / y;
111 const float top = 2.0 * nearZ / y + bottom;
112
113 *isPerspective = 1;
114 *leftOut = left;
115 *rightOut = right;
116 *botOut = bottom;
117 *topOut = top;
118 *nearOut = nearZ;
119 *farOut = farZ;
120 }
121 else {
122 /* orthographic */
123 const float x = m[0]; /* 2 / (R-L) */
124 const float y = m[5]; /* 2 / (T-B) */
125 const float z = m[10]; /* -2 / (F-N) */
126 const float a = m[12]; /* -(R+L) / (R-L) */
127 const float b = m[13]; /* -(T+B) / (T-B) */
128 const float c = m[14]; /* -(F+N) / (F-N) */
129 /* again, simple algebra */
130 const float right = -(a - 1.0) / x;
131 const float left = right - 2.0 / x;
132 const float top = -(b - 1.0) / y;
133 const float bottom = top - 2.0 / y;
134 const float farZ = (c - 1.0) / z;
135 const float nearZ = farZ + 2.0 / z;
136
137 *isPerspective = 0;
138 *leftOut = left;
139 *rightOut = right;
140 *botOut = bottom;
141 *topOut = top;
142 *nearOut = nearZ;
143 *farOut = farZ;
144 }
145 }
146
147
148 #if 0
149 /* test harness */
150 int
151 main(int argc, char *argv[])
152 {
153 float m[16], p[16];
154 float l, r, b, t, n, f;
155 int persp;
156 int i;
157
158 #if 0
159 l = -.9;
160 r = 1.2;
161 b = -0.5;
162 t = 1.4;
163 n = 30;
164 f = 84;
165 printf(" Frustum(%f, %f, %f, %f, %f, %f\n",l+1, r+1.2, b+.5, t+.3, n, f);
166 Frustum(l+1, r+1.2, b+.5, t+.3, n, f, p);
167 DecomposeProjection(p, &persp, &l, &r, &b, &t, &n, &f);
168 printf("glFrustum(%f, %f, %f, %f, %f, %f)\n",
169 l, r, b, t, n, f);
170 PrintMatrix(p);
171 #else
172 printf("Ortho(-1, 1, -1, 1, 10, 84)\n");
173 Ortho(-1, 1, -1, 1, 10, 84, m);
174 PrintMatrix(m);
175 DecomposeProjection(m, &persp, &l, &r, &b, &t, &n, &f);
176 printf("Ortho(%f, %f, %f, %f, %f, %f) %d\n", l, r, b, t, n, f, persp);
177 #endif
178
179 return 0;
180 }
181 #endif
182