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
|
#define __NR_MATRIX_C__
/** \file
* Various matrix routines. Currently includes some NR::rotate etc. routines too.
*/
/*
* Authors:
* Lauris Kaplinski <lauris@kaplinski.com>
*
* This code is in public domain
*/
#include <cstdlib>
#include "nr-matrix.h"
#include "nr-matrix-fns.h"
/**
* Implement NR functions and methods
*/
namespace NR {
/**
* Multiply two matrices together
*/
Matrix operator*(Matrix const &m0, Matrix const &m1)
{
NR::Coord const d0 = m0[0] * m1[0] + m0[1] * m1[2];
NR::Coord const d1 = m0[0] * m1[1] + m0[1] * m1[3];
NR::Coord const d2 = m0[2] * m1[0] + m0[3] * m1[2];
NR::Coord const d3 = m0[2] * m1[1] + m0[3] * m1[3];
NR::Coord const d4 = m0[4] * m1[0] + m0[5] * m1[2] + m1[4];
NR::Coord const d5 = m0[4] * m1[1] + m0[5] * m1[3] + m1[5];
Matrix ret( d0, d1, d2, d3, d4, d5 );
return ret;
}
/**
* Return the inverse of this matrix. If an inverse is not defined,
* then return the identity matrix.
*/
Matrix Matrix::inverse() const
{
Matrix d(0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
NR::Coord const det = _c[0] * _c[3] - _c[1] * _c[2];
if (!NR_DF_TEST_CLOSE(det, 0.0, NR_EPSILON)) {
NR::Coord const idet = 1.0 / det;
NR::Coord *dest = d._c;
/*0*/ *dest++ = _c[3] * idet;
/*1*/ *dest++ = -_c[1] * idet;
/*2*/ *dest++ = -_c[2] * idet;
/*3*/ *dest++ = _c[0] * idet;
/*4*/ *dest++ = -_c[4] * d._c[0] - _c[5] * d._c[2];
/*5*/ *dest = -_c[4] * d._c[1] - _c[5] * d._c[3];
} else {
d.set_identity();
}
return d;
}
/**
* Set this matrix to Identity
*/
void Matrix::set_identity()
{
NR::Coord *dest = _c;
*dest++ = 1.0; //0
*dest++ = 0.0; //1
*dest++ = 0.0; //2
*dest++ = 1.0; //3
// translation
*dest++ = 0.0; //4
*dest = 0.0; //5
}
/**
* return an Identity matrix
*/
Matrix identity()
{
Matrix ret(1.0, 0.0,
0.0, 1.0,
0.0, 0.0);
return ret;
}
/**
*
*/
Matrix from_basis(Point const x_basis, Point const y_basis, Point const offset)
{
Matrix const ret(x_basis[X], y_basis[X],
x_basis[Y], y_basis[Y],
offset[X], offset[Y]);
return ret;
}
/**
* Returns a rotation matrix corresponding by the specified angle (in radians) about the origin.
*
* \see NR::rotate_degrees
*
* Angle direction in Inkscape code: If you use the traditional mathematics convention that y
* increases upwards, then positive angles are anticlockwise as per the mathematics convention. If
* you take the common non-mathematical convention that y increases downwards, then positive angles
* are clockwise, as is common outside of mathematics.
*/
rotate::rotate(NR::Coord const theta) :
vec(cos(theta),
sin(theta))
{
}
/**
* Return the determinant of the Matrix
*/
NR::Coord Matrix::det() const
{
return _c[0] * _c[3] - _c[1] * _c[2];
}
/**
* Return the scalar of the descriminant of the Matrix
*/
NR::Coord Matrix::descrim2() const
{
return fabs(det());
}
/**
* Return the descriminant of the Matrix
*/
NR::Coord Matrix::descrim() const
{
return sqrt(descrim2());
}
/**
*
*/
bool Matrix::is_translation(Coord const eps) const {
return ( fabs(_c[0] - 1.0) < eps &&
fabs(_c[3] - 1.0) < eps &&
fabs(_c[1]) < eps &&
fabs(_c[2]) < eps );
}
/**
*
*/
bool Matrix::is_scale(Coord const eps) const {
return ( (fabs(_c[0] - 1.0) > eps || fabs(_c[3] - 1.0) > eps) &&
fabs(_c[1]) < eps &&
fabs(_c[2]) < eps );
}
/**
*
*/
bool Matrix::is_rotation(Coord const eps) const {
return ( fabs(_c[1]) > eps &&
fabs(_c[2]) > eps &&
fabs(_c[1] + _c[2]) < 2 * eps);
}
/**
* test whether the matrix is the identity matrix (true). (2geom's Matrix::isIdentity() does the same)
*/
bool Matrix::test_identity() const {
return matrix_equalp(*this, NR_MATRIX_IDENTITY, NR_EPSILON);
}
/**
* calculates the descriminant of the matrix. (Geom::Coord Matrix::descrim() does the same)
*/
double expansion(Matrix const &m) {
return sqrt(fabs(m.det()));
}
/**
*
*/
bool transform_equalp(Matrix const &m0, Matrix const &m1, NR::Coord const epsilon) {
return
NR_DF_TEST_CLOSE(m0[0], m1[0], epsilon) &&
NR_DF_TEST_CLOSE(m0[1], m1[1], epsilon) &&
NR_DF_TEST_CLOSE(m0[2], m1[2], epsilon) &&
NR_DF_TEST_CLOSE(m0[3], m1[3], epsilon);
}
/**
*
*/
bool translate_equalp(Matrix const &m0, Matrix const &m1, NR::Coord const epsilon) {
return NR_DF_TEST_CLOSE(m0[4], m1[4], epsilon) && NR_DF_TEST_CLOSE(m0[5], m1[5], epsilon);
}
/**
*
*/
bool matrix_equalp(Matrix const &m0, Matrix const &m1, NR::Coord const epsilon) {
return transform_equalp(m0, m1, epsilon) && translate_equalp(m0, m1, epsilon);
}
} //namespace NR
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
|
