Mercurial > hg > orthanc-stone
annotate Framework/Toolbox/LinearAlgebra.cpp @ 166:4f661e2f7b6c wasm
cont
author | Sebastien Jodogne <s.jodogne@gmail.com> |
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date | Thu, 22 Feb 2018 19:36:23 +0100 |
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rev | line source |
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158 | 1 /** |
2 * Stone of Orthanc | |
3 * Copyright (C) 2012-2016 Sebastien Jodogne, Medical Physics | |
4 * Department, University Hospital of Liege, Belgium | |
5 * Copyright (C) 2017-2018 Osimis S.A., Belgium | |
6 * | |
7 * This program is free software: you can redistribute it and/or | |
8 * modify it under the terms of the GNU Affero General Public License | |
9 * as published by the Free Software Foundation, either version 3 of | |
10 * the License, or (at your option) any later version. | |
11 * | |
12 * This program is distributed in the hope that it will be useful, but | |
13 * WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
15 * Affero General Public License for more details. | |
16 * | |
17 * You should have received a copy of the GNU Affero General Public License | |
18 * along with this program. If not, see <http://www.gnu.org/licenses/>. | |
19 **/ | |
20 | |
21 | |
22 #include "LinearAlgebra.h" | |
23 | |
24 #include <Core/Logging.h> | |
25 #include <Core/OrthancException.h> | |
26 #include <Core/Toolbox.h> | |
27 | |
28 #include <stdio.h> | |
29 #include <boost/lexical_cast.hpp> | |
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30 #include <boost/numeric/ublas/lu.hpp> |
158 | 31 |
32 namespace OrthancStone | |
33 { | |
34 namespace LinearAlgebra | |
35 { | |
36 void Print(const Vector& v) | |
37 { | |
38 for (size_t i = 0; i < v.size(); i++) | |
39 { | |
40 printf("%g\n", v[i]); | |
41 //printf("%8.2f\n", v[i]); | |
42 } | |
43 printf("\n"); | |
44 } | |
45 | |
46 | |
47 void Print(const Matrix& m) | |
48 { | |
49 for (size_t i = 0; i < m.size1(); i++) | |
50 { | |
51 for (size_t j = 0; j < m.size2(); j++) | |
52 { | |
53 printf("%g ", m(i,j)); | |
54 //printf("%8.2f ", m(i,j)); | |
55 } | |
56 printf("\n"); | |
57 } | |
58 printf("\n"); | |
59 } | |
60 | |
61 | |
62 bool ParseVector(Vector& target, | |
63 const std::string& value) | |
64 { | |
65 std::vector<std::string> items; | |
66 Orthanc::Toolbox::TokenizeString(items, value, '\\'); | |
67 | |
68 target.resize(items.size()); | |
69 | |
70 for (size_t i = 0; i < items.size(); i++) | |
71 { | |
72 try | |
73 { | |
74 target[i] = boost::lexical_cast<double>(Orthanc::Toolbox::StripSpaces(items[i])); | |
75 } | |
76 catch (boost::bad_lexical_cast&) | |
77 { | |
78 target.clear(); | |
79 return false; | |
80 } | |
81 } | |
82 | |
83 return true; | |
84 } | |
85 | |
86 | |
87 bool ParseVector(Vector& target, | |
88 const Orthanc::DicomMap& dataset, | |
89 const Orthanc::DicomTag& tag) | |
90 { | |
91 std::string value; | |
92 return (dataset.CopyToString(value, tag, false) && | |
93 ParseVector(target, value)); | |
94 } | |
95 | |
96 | |
97 void AssignVector(Vector& v, | |
98 double v1, | |
99 double v2) | |
100 { | |
101 v.resize(2); | |
102 v[0] = v1; | |
103 v[1] = v2; | |
104 } | |
105 | |
106 | |
107 void AssignVector(Vector& v, | |
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108 double v1) |
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109 { |
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110 v.resize(1); |
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111 v[0] = v1; |
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112 } |
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113 |
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114 |
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115 void AssignVector(Vector& v, |
158 | 116 double v1, |
117 double v2, | |
118 double v3) | |
119 { | |
120 v.resize(3); | |
121 v[0] = v1; | |
122 v[1] = v2; | |
123 v[2] = v3; | |
124 } | |
125 | |
126 | |
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127 void AssignVector(Vector& v, |
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128 double v1, |
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129 double v2, |
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130 double v3, |
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131 double v4) |
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132 { |
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133 v.resize(4); |
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134 v[0] = v1; |
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135 v[1] = v2; |
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136 v[2] = v3; |
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137 v[3] = v4; |
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138 } |
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139 |
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140 |
165
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141 Vector CreateVector(double v1) |
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142 { |
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143 Vector v; |
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144 AssignVector(v, v1); |
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145 return v; |
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146 } |
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147 |
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148 |
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149 Vector CreateVector(double v1, |
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150 double v2) |
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151 { |
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152 Vector v; |
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153 AssignVector(v, v1, v2); |
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154 return v; |
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155 } |
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156 |
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157 |
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158 Vector CreateVector(double v1, |
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159 double v2, |
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160 double v3) |
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161 { |
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162 Vector v; |
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163 AssignVector(v, v1, v2, v3); |
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164 return v; |
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165 } |
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166 |
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167 |
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168 Vector CreateVector(double v1, |
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169 double v2, |
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170 double v3, |
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171 double v4) |
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172 { |
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173 Vector v; |
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174 AssignVector(v, v1, v2, v3, v4); |
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175 return v; |
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176 } |
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177 |
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178 |
158 | 179 bool IsNear(double x, |
180 double y) | |
181 { | |
182 // As most input is read as single-precision numbers, we take the | |
183 // epsilon machine for float32 into consideration to compare numbers | |
184 return IsNear(x, y, 10.0 * std::numeric_limits<float>::epsilon()); | |
185 } | |
186 | |
187 | |
188 void NormalizeVector(Vector& u) | |
189 { | |
190 double norm = boost::numeric::ublas::norm_2(u); | |
191 if (!IsCloseToZero(norm)) | |
192 { | |
193 u = u / norm; | |
194 } | |
195 } | |
196 | |
197 | |
198 void CrossProduct(Vector& result, | |
199 const Vector& u, | |
200 const Vector& v) | |
201 { | |
202 if (u.size() != 3 || | |
203 v.size() != 3) | |
204 { | |
205 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); | |
206 } | |
207 | |
208 result.resize(3); | |
209 | |
210 result[0] = u[1] * v[2] - u[2] * v[1]; | |
211 result[1] = u[2] * v[0] - u[0] * v[2]; | |
212 result[2] = u[0] * v[1] - u[1] * v[0]; | |
213 } | |
214 | |
215 | |
216 void FillMatrix(Matrix& target, | |
217 size_t rows, | |
218 size_t columns, | |
219 const double values[]) | |
220 { | |
221 target.resize(rows, columns); | |
222 | |
223 size_t index = 0; | |
224 | |
225 for (size_t y = 0; y < rows; y++) | |
226 { | |
227 for (size_t x = 0; x < columns; x++, index++) | |
228 { | |
229 target(y, x) = values[index]; | |
230 } | |
231 } | |
232 } | |
233 | |
234 | |
235 void FillVector(Vector& target, | |
236 size_t size, | |
237 const double values[]) | |
238 { | |
239 target.resize(size); | |
240 | |
241 for (size_t i = 0; i < size; i++) | |
242 { | |
243 target[i] = values[i]; | |
244 } | |
245 } | |
246 | |
247 | |
248 void Convert(Matrix& target, | |
249 const Vector& source) | |
250 { | |
251 const size_t n = source.size(); | |
252 | |
253 target.resize(n, 1); | |
254 | |
255 for (size_t i = 0; i < n; i++) | |
256 { | |
257 target(i, 0) = source[i]; | |
258 } | |
259 } | |
159
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260 |
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261 |
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262 double ComputeDeterminant(const Matrix& a) |
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263 { |
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264 if (a.size1() != a.size2()) |
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265 { |
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266 LOG(ERROR) << "Determinant only exists for square matrices"; |
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267 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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268 } |
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269 |
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270 // https://en.wikipedia.org/wiki/Rule_of_Sarrus |
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271 if (a.size1() == 1) |
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272 { |
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273 return a(0,0); |
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274 } |
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275 else if (a.size1() == 2) |
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276 { |
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277 return a(0,0) * a(1,1) - a(0,1) * a(1,0); |
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278 } |
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279 else if (a.size1() == 3) |
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280 { |
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281 return (a(0,0) * a(1,1) * a(2,2) + |
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282 a(0,1) * a(1,2) * a(2,0) + |
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283 a(0,2) * a(1,0) * a(2,1) - |
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284 a(2,0) * a(1,1) * a(0,2) - |
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285 a(2,1) * a(1,2) * a(0,0) - |
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286 a(2,2) * a(1,0) * a(0,1)); |
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287 } |
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288 else |
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289 { |
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290 throw Orthanc::OrthancException(Orthanc::ErrorCode_NotImplemented); |
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291 } |
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292 } |
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293 |
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294 |
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295 bool IsOrthogonalMatrix(const Matrix& q, |
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296 double threshold) |
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297 { |
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298 // https://en.wikipedia.org/wiki/Orthogonal_matrix |
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299 |
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300 using namespace boost::numeric::ublas; |
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301 |
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302 const Matrix check = prod(trans(q), q) - identity_matrix<double>(3); |
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303 |
160 | 304 type_traits<double>::real_type norm = norm_inf(check); |
159
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305 |
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306 return (norm <= threshold); |
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307 } |
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308 |
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309 |
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310 bool IsOrthogonalMatrix(const Matrix& q) |
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311 { |
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312 return IsOrthogonalMatrix(q, 10.0 * std::numeric_limits<float>::epsilon()); |
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313 } |
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314 |
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315 |
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316 bool IsRotationMatrix(const Matrix& r, |
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317 double threshold) |
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318 { |
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319 return (IsOrthogonalMatrix(r, threshold) && |
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320 IsNear(ComputeDeterminant(r), 1.0, threshold)); |
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321 } |
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322 |
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323 |
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324 bool IsRotationMatrix(const Matrix& r) |
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325 { |
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326 return IsRotationMatrix(r, 10.0 * std::numeric_limits<float>::epsilon()); |
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327 } |
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328 |
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329 |
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330 void InvertUpperTriangularMatrix(Matrix& output, |
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331 const Matrix& k) |
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332 { |
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333 if (k.size1() != k.size2()) |
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334 { |
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335 LOG(ERROR) << "Determinant only exists for square matrices"; |
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336 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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337 } |
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338 |
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339 output.resize(k.size1(), k.size2()); |
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340 |
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341 for (size_t i = 1; i < k.size1(); i++) |
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342 { |
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343 for (size_t j = 0; j < i; j++) |
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344 { |
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345 if (!IsCloseToZero(k(i, j))) |
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346 { |
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347 LOG(ERROR) << "Not an upper triangular matrix"; |
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348 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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349 } |
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350 |
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351 output(i, j) = 0; // The output is also upper triangular |
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352 } |
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353 } |
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354 |
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355 if (k.size1() == 3) |
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356 { |
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357 // https://math.stackexchange.com/a/1004181 |
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358 double a = k(0, 0); |
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359 double b = k(0, 1); |
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360 double c = k(0, 2); |
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361 double d = k(1, 1); |
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362 double e = k(1, 2); |
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363 double f = k(2, 2); |
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364 |
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365 if (IsCloseToZero(a) || |
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366 IsCloseToZero(d) || |
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367 IsCloseToZero(f)) |
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368 { |
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369 LOG(ERROR) << "Singular upper triangular matrix"; |
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370 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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371 } |
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372 else |
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373 { |
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374 output(0, 0) = 1.0 / a; |
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375 output(0, 1) = -b / (a * d); |
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376 output(0, 2) = (b * e - c * d) / (a * f * d); |
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377 output(1, 1) = 1.0 / d; |
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378 output(1, 2) = -e / (f * d); |
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379 output(2, 2) = 1.0 / f; |
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380 } |
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381 } |
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382 else |
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383 { |
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384 throw Orthanc::OrthancException(Orthanc::ErrorCode_NotImplemented); |
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385 } |
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386 } |
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387 |
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388 |
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389 static void GetGivensComponent(double& c, |
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390 double& s, |
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391 const Matrix& a, |
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392 size_t i, |
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393 size_t j) |
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394 { |
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395 assert(i < 3 && j < 3); |
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396 |
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397 double x = a(i, i); |
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398 double y = a(i, j); |
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399 double n = sqrt(x * x + y * y); |
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400 |
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401 if (IsCloseToZero(n)) |
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402 { |
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403 c = 1; |
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404 s = 0; |
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405 } |
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406 else |
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407 { |
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408 c = x / n; |
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409 s = -y / n; |
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410 } |
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411 } |
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412 |
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413 |
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414 /** |
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415 * This function computes the RQ decomposition of a 3x3 matrix, |
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416 * using Givens rotations. Reference: Algorithm A4.1 (page 579) of |
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417 * "Multiple View Geometry in Computer Vision" (2nd edition). The |
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418 * output matrix "Q" is a rotation matrix, and "R" is upper |
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419 * triangular. |
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420 **/ |
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421 void RQDecomposition3x3(Matrix& r, |
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422 Matrix& q, |
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423 const Matrix& a) |
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424 { |
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425 using namespace boost::numeric::ublas; |
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426 |
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427 if (a.size1() != 3 || |
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428 a.size2() != 3) |
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429 { |
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430 LOG(ERROR) << "Only applicable to a 3x3 matrix"; |
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431 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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432 } |
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433 |
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434 r.resize(3, 3); |
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435 q.resize(3, 3); |
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436 |
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437 r = a; |
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438 q = identity_matrix<double>(3); |
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439 |
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440 { |
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441 // Set A(2,1) to zero |
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442 double c, s; |
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443 GetGivensComponent(c, s, r, 2, 1); |
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444 |
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445 double v[9] = { 1, 0, 0, |
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446 0, c, -s, |
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447 0, s, c }; |
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448 |
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449 Matrix g; |
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450 FillMatrix(g, 3, 3, v); |
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451 |
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452 r = prod(r, g); |
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453 q = prod(trans(g), q); |
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454 } |
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455 |
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456 |
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457 { |
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458 // Set A(2,0) to zero |
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459 double c, s; |
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460 GetGivensComponent(c, s, r, 2, 0); |
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461 |
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462 double v[9] = { c, 0, -s, |
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463 0, 1, 0, |
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464 s, 0, c }; |
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465 |
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466 Matrix g; |
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467 FillMatrix(g, 3, 3, v); |
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468 |
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469 r = prod(r, g); |
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470 q = prod(trans(g), q); |
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471 } |
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472 |
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473 |
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474 { |
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475 // Set A(1,0) to zero |
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476 double c, s; |
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477 GetGivensComponent(c, s, r, 1, 0); |
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478 |
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479 double v[9] = { c, -s, 0, |
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480 s, c, 0, |
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481 0, 0, 1 }; |
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482 |
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483 Matrix g; |
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484 FillMatrix(g, 3, 3, v); |
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485 |
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486 r = prod(r, g); |
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487 q = prod(trans(g), q); |
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488 } |
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489 |
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490 if (!IsCloseToZero(norm_inf(prod(r, q) - a)) || |
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491 !IsRotationMatrix(q) || |
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492 !IsCloseToZero(r(1, 0)) || |
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493 !IsCloseToZero(r(2, 0)) || |
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494 !IsCloseToZero(r(2, 1))) |
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495 { |
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496 throw Orthanc::OrthancException(Orthanc::ErrorCode_InternalError); |
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497 } |
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498 } |
163
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499 |
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500 |
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501 void InvertMatrix(Matrix& target, |
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502 const Matrix& source) |
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503 { |
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504 if (source.size1() != source.size2()) |
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505 { |
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506 LOG(ERROR) << "Inverse only exists for square matrices"; |
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507 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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508 } |
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509 |
164
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510 if (source.size1() < 4) |
163
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511 { |
164
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512 // For matrices with size below 4, use direct computations |
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513 // instead of LU decomposition |
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514 |
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515 if (source.size1() == 0) |
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516 { |
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517 // By convention, the inverse of the empty matrix, is itself the empty matrix |
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518 target.resize(0, 0); |
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519 return; |
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520 } |
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521 |
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522 double determinant = ComputeDeterminant(source); |
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523 |
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524 if (IsCloseToZero(determinant)) |
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525 { |
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526 LOG(ERROR) << "Cannot invert singular matrix"; |
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527 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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528 } |
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529 |
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530 double denominator = 1.0 / determinant; |
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531 |
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532 target.resize(source.size1(), source.size2()); |
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533 |
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534 if (source.size1() == 1) |
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535 { |
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536 target(0, 0) = denominator; |
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537 } |
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538 else if (source.size1() == 2) |
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539 { |
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540 // https://en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_2_%C3%97_2_matrices |
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541 target(0, 0) = source(1, 1) * denominator; |
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542 target(0, 1) = -source(0, 1) * denominator; |
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543 target(1, 0) = -source(1, 0) * denominator; |
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544 target(1, 1) = source(0, 0) * denominator; |
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545 } |
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546 else if (source.size1() == 3) |
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547 { |
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548 // https://en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_3_%C3%97_3_matrices |
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549 const double a = source(0, 0); |
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550 const double b = source(0, 1); |
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551 const double c = source(0, 2); |
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552 const double d = source(1, 0); |
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553 const double e = source(1, 1); |
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554 const double f = source(1, 2); |
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555 const double g = source(2, 0); |
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556 const double h = source(2, 1); |
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557 const double i = source(2, 2); |
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558 |
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559 target(0, 0) = (e * i - f * h) * denominator; |
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560 target(0, 1) = -(b * i - c * h) * denominator; |
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561 target(0, 2) = (b * f - c * e) * denominator; |
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562 target(1, 0) = -(d * i - f * g) * denominator; |
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563 target(1, 1) = (a * i - c * g) * denominator; |
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564 target(1, 2) = -(a * f - c * d) * denominator; |
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565 target(2, 0) = (d * h - e * g) * denominator; |
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566 target(2, 1) = -(a * h - b * g) * denominator; |
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567 target(2, 2) = (a * e - b * d) * denominator; |
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568 } |
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569 else |
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570 { |
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571 throw Orthanc::OrthancException(Orthanc::ErrorCode_InternalError); |
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572 } |
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573 } |
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574 else |
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575 { |
164
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576 // General case, using LU decomposition |
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577 |
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578 Matrix a = source; // Copy the source matrix, as "lu_factorize()" modifies it |
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579 |
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580 boost::numeric::ublas::permutation_matrix<size_t> permutation(source.size1()); |
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581 |
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582 if (boost::numeric::ublas::lu_factorize(a, permutation) != 0) |
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583 { |
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584 LOG(ERROR) << "Cannot invert singular matrix"; |
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585 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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586 } |
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587 |
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588 target = boost::numeric::ublas::identity_matrix<double>(source.size1()); |
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589 lu_substitute(a, permutation, target); |
163
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590 } |
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591 } |
165
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592 |
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593 |
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594 void CreateSkewSymmetric(Matrix& s, |
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595 const Vector& v) |
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596 { |
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597 assert(v.size() == 3); |
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598 |
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599 s.resize(3, 3); |
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600 s(0,0) = 0; |
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601 s(0,1) = -v[2]; |
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602 s(0,2) = v[1]; |
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603 s(1,0) = v[2]; |
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604 s(1,1) = 0; |
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605 s(1,2) = -v[0]; |
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606 s(2,0) = -v[1]; |
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607 s(2,1) = v[0]; |
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608 s(2,2) = 0; |
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609 } |
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610 |
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611 |
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612 void AlignVectorsWithRotation(Matrix& r, |
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613 const Vector& a, |
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614 const Vector& b) |
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615 { |
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616 // This is Rodrigues' rotation formula: |
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617 // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula#Matrix_notation |
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618 |
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619 // Check also result A4.6 from "Multiple View Geometry in Computer |
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620 // Vision - 2nd edition" (p. 584) |
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621 |
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622 if (a.size() != 3 || |
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623 b.size() != 3) |
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624 { |
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625 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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626 } |
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627 |
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628 double aNorm = boost::numeric::ublas::norm_2(a); |
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629 double bNorm = boost::numeric::ublas::norm_2(b); |
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630 |
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631 if (LinearAlgebra::IsCloseToZero(aNorm) || |
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632 LinearAlgebra::IsCloseToZero(bNorm)) |
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633 { |
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634 LOG(ERROR) << "Vector with zero norm"; |
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635 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange); |
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636 } |
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637 |
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638 Vector aUnit, bUnit; |
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639 aUnit = a / aNorm; |
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640 bUnit = b / bNorm; |
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641 |
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642 Vector v; |
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643 LinearAlgebra::CrossProduct(v, aUnit, bUnit); |
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644 |
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645 double cosine = boost::numeric::ublas::inner_prod(aUnit, bUnit); |
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646 |
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647 if (LinearAlgebra::IsCloseToZero(1 + cosine)) |
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648 { |
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649 // "a == -b": TODO |
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650 throw Orthanc::OrthancException(Orthanc::ErrorCode_NotImplemented); |
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651 } |
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652 |
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653 Matrix k; |
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654 CreateSkewSymmetric(k, v); |
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655 |
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656 #if 0 |
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657 double sine = boost::numeric::ublas::norm_2(v); |
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658 |
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659 r = (boost::numeric::ublas::identity_matrix<double>(3) + |
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660 sine * k + |
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661 (1 - cosine) * boost::numeric::ublas::prod(k, k)); |
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662 #else |
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663 r = (boost::numeric::ublas::identity_matrix<double>(3) + |
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664 k + |
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665 boost::numeric::ublas::prod(k, k) / (1 + cosine)); |
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666 #endif |
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667 } |
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668 |
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669 |
166 | 670 Matrix InvertScalingTranslationMatrix(const Matrix& t) |
165
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671 { |
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672 if (t.size1() != 4 || |
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673 t.size2() != 4 || |
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674 !LinearAlgebra::IsCloseToZero(t(0,1)) || |
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675 !LinearAlgebra::IsCloseToZero(t(0,2)) || |
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676 !LinearAlgebra::IsCloseToZero(t(1,0)) || |
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677 !LinearAlgebra::IsCloseToZero(t(1,2)) || |
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678 !LinearAlgebra::IsCloseToZero(t(2,0)) || |
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679 !LinearAlgebra::IsCloseToZero(t(2,1)) || |
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680 !LinearAlgebra::IsCloseToZero(t(3,0)) || |
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681 !LinearAlgebra::IsCloseToZero(t(3,1)) || |
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682 !LinearAlgebra::IsCloseToZero(t(3,2))) |
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683 { |
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684 LOG(ERROR) << "This matrix is more than a zoom/translate transform"; |
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685 throw Orthanc::OrthancException(Orthanc::ErrorCode_InternalError); |
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686 } |
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687 |
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688 const double sx = t(0,0); |
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689 const double sy = t(1,1); |
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690 const double sz = t(2,2); |
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691 const double w = t(3,3); |
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692 |
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693 if (LinearAlgebra::IsCloseToZero(sx) || |
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694 LinearAlgebra::IsCloseToZero(sy) || |
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695 LinearAlgebra::IsCloseToZero(sz) || |
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696 LinearAlgebra::IsCloseToZero(w)) |
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697 { |
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698 LOG(ERROR) << "Singular transform"; |
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699 throw Orthanc::OrthancException(Orthanc::ErrorCode_InternalError); |
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700 } |
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701 |
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702 const double tx = t(0,3); |
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703 const double ty = t(1,3); |
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704 const double tz = t(2,3); |
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705 |
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706 Matrix m = IdentityMatrix(4); |
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707 |
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708 m(0,0) = 1.0 / sx; |
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709 m(1,1) = 1.0 / sy; |
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710 m(2,2) = 1.0 / sz; |
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711 m(3,3) = 1.0 / w; |
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712 |
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713 m(0,3) = -tx / (sx * w); |
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714 m(1,3) = -ty / (sy * w); |
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715 m(2,3) = -tz / (sz * w); |
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716 |
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717 return m; |
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718 } |
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719 |
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720 |
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721 bool IsShearMatrix(const Matrix& shear) |
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722 { |
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723 return (shear.size1() == 4 && |
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724 shear.size2() == 4 && |
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725 LinearAlgebra::IsNear(1.0, shear(0,0)) && |
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726 LinearAlgebra::IsNear(0.0, shear(0,1)) && |
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727 LinearAlgebra::IsNear(0.0, shear(0,3)) && |
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728 LinearAlgebra::IsNear(0.0, shear(1,0)) && |
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729 LinearAlgebra::IsNear(1.0, shear(1,1)) && |
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730 LinearAlgebra::IsNear(0.0, shear(1,3)) && |
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731 LinearAlgebra::IsNear(0.0, shear(2,0)) && |
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732 LinearAlgebra::IsNear(0.0, shear(2,1)) && |
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733 LinearAlgebra::IsNear(1.0, shear(2,2)) && |
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734 LinearAlgebra::IsNear(0.0, shear(2,3)) && |
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735 LinearAlgebra::IsNear(0.0, shear(3,0)) && |
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736 LinearAlgebra::IsNear(0.0, shear(3,1)) && |
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737 LinearAlgebra::IsNear(1.0, shear(3,3))); |
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738 } |
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739 |
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740 |
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741 Matrix InvertShearMatrix(const Matrix& shear) |
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742 { |
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743 if (!IsShearMatrix(shear)) |
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744 { |
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745 LOG(ERROR) << "Not a valid shear matrix"; |
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746 throw Orthanc::OrthancException(Orthanc::ErrorCode_InternalError); |
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747 } |
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748 |
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749 Matrix m = IdentityMatrix(4); |
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750 m(0,2) = -shear(0,2); |
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751 m(1,2) = -shear(1,2); |
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752 m(3,2) = -shear(3,2); |
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753 |
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754 return m; |
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755 } |
158 | 756 } |
757 } |