-
Notifications
You must be signed in to change notification settings - Fork 1
/
Mat4x4.cpp
293 lines (241 loc) · 8.72 KB
/
Mat4x4.cpp
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
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
#include "Mat4x4.h"
#include "Quat.h"
#include <math.h>
#define INDEX(x, y) ((x) * 4 + (y))
#define m00 m_v[INDEX(0, 0)]
#define m10 m_v[INDEX(1, 0)]
#define m20 m_v[INDEX(2, 0)]
#define m30 m_v[INDEX(3, 0)]
#define m01 m_v[INDEX(0, 1)]
#define m11 m_v[INDEX(1, 1)]
#define m21 m_v[INDEX(2, 1)]
#define m31 m_v[INDEX(3, 1)]
#define m02 m_v[INDEX(0, 2)]
#define m12 m_v[INDEX(1, 2)]
#define m22 m_v[INDEX(2, 2)]
#define m32 m_v[INDEX(3, 2)]
#define m03 m_v[INDEX(0, 3)]
#define m13 m_v[INDEX(1, 3)]
#define m23 m_v[INDEX(2, 3)]
#define m33 m_v[INDEX(3, 3)]
void Mat4x4::MakeRotationX(float angle, bool left)
{
MakeIdentity();
if (left)
{
m_v[INDEX(1, 1)] = +cosf(angle);
m_v[INDEX(2, 1)] = +sinf(angle);
m_v[INDEX(1, 2)] = -sinf(angle);
m_v[INDEX(2, 2)] = +cosf(angle);
}
else
{
m_v[INDEX(1, 1)] = +cosf(angle);
m_v[INDEX(2, 1)] = -sinf(angle);
m_v[INDEX(1, 2)] = +sinf(angle);
m_v[INDEX(2, 2)] = +cosf(angle);
}
}
void Mat4x4::MakeRotationY(float angle, bool left)
{
MakeIdentity();
if (left)
{
m_v[INDEX(0, 0)] = +cosf(angle);
m_v[INDEX(2, 0)] = -sinf(angle);
m_v[INDEX(0, 2)] = +sinf(angle);
m_v[INDEX(2, 2)] = +cosf(angle);
}
else
{
m_v[INDEX(0, 0)] = +cosf(angle);
m_v[INDEX(2, 0)] = +sinf(angle);
m_v[INDEX(0, 2)] = -sinf(angle);
m_v[INDEX(2, 2)] = +cosf(angle);
}
}
void Mat4x4::MakeRotationZ(float angle, bool left)
{
MakeIdentity();
if (left)
{
m_v[INDEX(0, 0)] = +cosf(angle);
m_v[INDEX(1, 0)] = +sinf(angle);
m_v[INDEX(0, 1)] = -sinf(angle);
m_v[INDEX(1, 1)] = +cosf(angle);
}
else
{
m_v[INDEX(0, 0)] = +cosf(angle);
m_v[INDEX(1, 0)] = -sinf(angle);
m_v[INDEX(0, 1)] = +sinf(angle);
m_v[INDEX(1, 1)] = +cosf(angle);
}
}
void Mat4x4::MakePerspectiveLH(float fov, float aspect, float nearCP, float farCP)
{
// left handed perspective matrix with clip space Z = (0, +1)
const float scaleY = 1.0f / tanf(fov / 2.0f);
const float scaleX = aspect * scaleY;
const float l_33 = farCP / ( farCP - nearCP );
const float l_43 = -nearCP * farCP / ( farCP - nearCP );
m00 = scaleX; m01 = 0.0f; m02 = 0.0f; m03 = 0.0f;
m10 = 0.0f; m11 = scaleY; m12 = 0.0f; m13 = 0.0f;
m20 = 0.0f; m21 = 0.0f; m22 = l_33; m23 =+1.0f;
m30 = 0.0f; m31 = 0.0f; m32 = l_43; m33 = 0.0f;
}
void Mat4x4::MakePerspectiveGL(float fov, float aspect, float nearCP, float farCP)
{
// right handed perspective matrix with clip space Z = (-1, +1)
const float scaleY = 1.0f / tanf(fov / 2.0f);
const float scaleX = aspect * scaleY;
const float l_33 = - (farCP + nearCP) / (nearCP - farCP);
const float l_43 = 2.f * (farCP * nearCP) / (nearCP - farCP);
m00 = scaleX; m01 = 0.0f; m02 = 0.0f; m03 = 0.0f;
m10 = 0.0f; m11 = scaleY; m12 = 0.0f; m13 = 0.0f;
m20 = 0.0f; m21 = 0.0f; m22 = l_33; m23 =+1.0f;
m30 = 0.0f; m31 = 0.0f; m32 = l_43; m33 = 0.0f;
}
void Mat4x4::MakeOrthoLH(float left, float right, float top, float bottom, float nearCP, float farCP)
{
// left handed orthographic matrix with clip space Z = (0, +1)
const float rl = 2.0f / (right - left);
const float tb = 2.0f / (top - bottom);
const float fn = 1.0f / (farCP - nearCP);
const float tx = (right + left) / (left - right);
const float ty = (top + bottom) / (bottom - top);
const float tz = nearCP / (nearCP - farCP);
m00 = rl; m01 = 0.0f; m02 = 0.0f; m03 = 0.0f;
m10 = 0.0f; m11 = tb; m12 = 0.0f; m13 = 0.0f;
m20 = 0.0f; m21 = 0.0f; m22 = fn; m23 = 0.0f;
m30 = tx; m31 = ty; m32 = tz; m33 = 1.0f;
}
void Mat4x4::MakeOrthoGL(float left, float right, float top, float bottom, float nearCP, float farCP)
{
// right handed orthographic matrix with clip space Z = (-1, +1)
const float rl = 2.0f / (right - left);
const float tb = 2.0f / (top - bottom);
const float fn = 2.0f / (farCP - nearCP);
const float tx = (right + left) / (left - right);
const float ty = (top + bottom) / (bottom - top);
const float tz = (farCP + nearCP) / (nearCP - farCP);
m00 = rl; m01 = 0.0f; m02 = 0.0f; m03 = 0.0f;
m10 = 0.0f; m11 = tb; m12 = 0.0f; m13 = 0.0f;
m20 = 0.0f; m21 = 0.0f; m22 = fn; m23 = 0.0f;
m30 = tx; m31 = ty; m32 = tz; m33 = 1.0f;
}
void Mat4x4::MakeLookat(const Vec3& position, const Vec3& target, const Vec3& up)
{
Mat4x4 orient;
orient.MakeIdentity();
Vec3 axisZ = target - position;
if (axisZ.CalcSizeSq() == 0.0f || (axisZ % up).CalcSizeSq() == 0.0f)
axisZ = Vec3(up[1], up[2], up[0]);
Vec3 axisX = up % axisZ;
Vec3 axisY = axisZ % axisX;
axisX = axisX.CalcNormalized();
axisY = axisY.CalcNormalized();
axisZ = axisZ.CalcNormalized();
for (int i = 0; i < 3; ++i)
{
orient(i, 0) = axisX[i];
orient(i, 1) = axisY[i];
orient(i, 2) = axisZ[i];
}
MakeTranslation(-position);
*this = orient * (*this);
}
void Mat4x4::MakeLookatInv(const Vec3& position, const Vec3& target, const Vec3& up)
{
Vec3 axisZ = target - position;
if (axisZ.CalcSizeSq() == 0.0f || (axisZ % up).CalcSizeSq() == 0.0f)
axisZ = Vec3(up[1], up[2], up[0]);
Vec3 axisX = up % axisZ;
Vec3 axisY = axisZ % axisX;
axisX = axisX.CalcNormalized();
axisY = axisY.CalcNormalized();
axisZ = axisZ.CalcNormalized();
for (int i = 0; i < 3; ++i)
{
m_v[INDEX(0, i)] = axisX[i];
m_v[INDEX(1, i)] = axisY[i];
m_v[INDEX(2, i)] = axisZ[i];
}
m_v[INDEX(0, 3)] = 0.f;
m_v[INDEX(1, 3)] = 0.f;
m_v[INDEX(2, 3)] = 0.f;
m_v[INDEX(3, 0)] = position[0];
m_v[INDEX(3, 1)] = position[1];
m_v[INDEX(3, 2)] = position[2];
m_v[INDEX(3, 3)] = 1.f;
}
float Mat4x4::CalcDet() const
{
float r;
r =
(m03 * m12 * m21 * m30) - (m02 * m13 * m21 * m30) - (m03 * m11 * m22 * m30) + (m01 * m13 * m22 * m30) +
(m02 * m11 * m23 * m30) - (m01 * m12 * m23 * m30) - (m03 * m12 * m20 * m31) + (m02 * m13 * m20 * m31) +
(m03 * m10 * m22 * m31) - (m00 * m13 * m22 * m31) - (m02 * m10 * m23 * m31) + (m00 * m12 * m23 * m31) +
(m03 * m11 * m20 * m32) - (m01 * m13 * m20 * m32) - (m03 * m10 * m21 * m32) + (m00 * m13 * m21 * m32) +
(m01 * m10 * m23 * m32) - (m00 * m11 * m23 * m32) - (m02 * m11 * m20 * m33) + (m01 * m12 * m20 * m33) +
(m02 * m10 * m21 * m33) - (m00 * m12 * m21 * m33) - (m01 * m10 * m22 * m33) + (m00 * m11 * m22 * m33);
return r;
}
Mat4x4 Mat4x4::CalcInv() const
{
Mat4x4 r;
r.m00 = (m12 * m23 * m31) - (m13 * m22 * m31) + (m13 * m21*m32) - (m11 * m23 * m32) - (m12 * m21 * m33) + (m11 * m22 * m33);
r.m01 = (m03 * m22 * m31) - (m02 * m23 * m31) - (m03 * m21*m32) + (m01 * m23 * m32) + (m02 * m21 * m33) - (m01 * m22 * m33);
r.m02 = (m02 * m13 * m31) - (m03 * m12 * m31) + (m03 * m11*m32) - (m01 * m13 * m32) - (m02 * m11 * m33) + (m01 * m12 * m33);
r.m03 = (m03 * m12 * m21) - (m02 * m13 * m21) - (m03 * m11*m22) + (m01 * m13 * m22) + (m02 * m11 * m23) - (m01 * m12 * m23);
r.m10 = (m13 * m22 * m30) - (m12 * m23 * m30) - (m13 * m20*m32) + (m10 * m23 * m32) + (m12 * m20 * m33) - (m10 * m22 * m33);
r.m11 = (m02 * m23 * m30) - (m03 * m22 * m30) + (m03 * m20*m32) - (m00 * m23 * m32) - (m02 * m20 * m33) + (m00 * m22 * m33);
r.m12 = (m03 * m12 * m30) - (m02 * m13 * m30) - (m03 * m10*m32) + (m00 * m13 * m32) + (m02 * m10 * m33) - (m00 * m12 * m33);
r.m13 = (m02 * m13 * m20) - (m03 * m12 * m20) + (m03 * m10*m22) - (m00 * m13 * m22) - (m02 * m10 * m23) + (m00 * m12 * m23);
r.m20 = (m11 * m23 * m30) - (m13 * m21 * m30) + (m13 * m20*m31) - (m10 * m23 * m31) - (m11 * m20 * m33) + (m10 * m21 * m33);
r.m21 = (m03 * m21 * m30) - (m01 * m23 * m30) - (m03 * m20*m31) + (m00 * m23 * m31) + (m01 * m20 * m33) - (m00 * m21 * m33);
r.m22 = (m01 * m13 * m30) - (m03 * m11 * m30) + (m03 * m10*m31) - (m00 * m13 * m31) - (m01 * m10 * m33) + (m00 * m11 * m33);
r.m23 = (m03 * m11 * m20) - (m01 * m13 * m20) - (m03 * m10*m21) + (m00 * m13 * m21) + (m01 * m10 * m23) - (m00 * m11 * m23);
r.m30 = (m12 * m21 * m30) - (m11 * m22 * m30) - (m12 * m20*m31) + (m10 * m22 * m31) + (m11 * m20 * m32) - (m10 * m21 * m32);
r.m31 = (m01 * m22 * m30) - (m02 * m21 * m30) + (m02 * m20*m31) - (m00 * m22 * m31) - (m01 * m20 * m32) + (m00 * m21 * m32);
r.m32 = (m02 * m11 * m30) - (m01 * m12 * m30) - (m02 * m10*m31) + (m00 * m12 * m31) + (m01 * m10 * m32) - (m00 * m11 * m32);
r.m33 = (m01 * m12 * m20) - (m02 * m11 * m20) + (m02 * m10*m21) - (m00 * m12 * m21) - (m01 * m10 * m22) + (m00 * m11 * m22);
const float scale = 1.0f / CalcDet();
for (int i = 0; i < 16; ++i)
r.m_v[i] *= scale;
return r;
}
Mat4x4 Mat4x4::Rotate(const Quat & q) const
{
Mat4x4 t = q.toMatrix();
return (*this) * t;
}
Mat4x4 Mat4x4::Rotate(const float angle, Vec3Arg axis) const
{
Quat q;
q.fromAngleAxis(angle, axis);
return Rotate(q);
}
Mat4x4 Mat4x4::Lookat(Vec3Arg position, Vec3Arg target, Vec3Arg up) const
{
Mat4x4 lookat;
lookat.MakeLookatInv(position, target, up);
return (*this) * lookat;
}
#undef INDEX
#undef m00
#undef m10
#undef m20
#undef m30
#undef m01
#undef m11
#undef m21
#undef m31
#undef m02
#undef m12
#undef m22
#undef m32
#undef m03
#undef m13
#undef m23
#undef m33