Point Cloud Library (PCL)  1.10.1-dev
eigen.hpp
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36 
37 // This file is part of Eigen, a lightweight C++ template library
38 // for linear algebra.
39 //
40 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
41 //
42 // Eigen is free software; you can redistribute it and/or
43 // modify it under the terms of the GNU Lesser General Public
44 // License as published by the Free Software Foundation; either
45 // version 3 of the License, or (at your option) any later version.
46 //
47 // Alternatively, you can redistribute it and/or
48 // modify it under the terms of the GNU General Public License as
49 // published by the Free Software Foundation; either version 2 of
50 // the License, or (at your option) any later version.
51 //
52 // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
53 // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
54 // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
55 // GNU General Public License for more details.
56 //
57 // You should have received a copy of the GNU Lesser General Public
58 // License and a copy of the GNU General Public License along with
59 // Eigen. If not, see <http://www.gnu.org/licenses/>.
60 
61 // The computeRoots function included in this is based on materials
62 // covered by the following copyright and license:
63 //
64 // Geometric Tools, LLC
65 // Copyright (c) 1998-2010
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89 
90 #ifndef PCL_GPU_FEATURES_EIGEN_HPP_
91 #define PCL_GPU_FEATURES_EIGEN_HPP_
92 
93 #include <limits>
94 
95 #include <pcl/gpu/utils/device/algorithm.hpp>
96 #include <pcl/gpu/utils/device/vector_math.hpp>
97 
98 namespace pcl
99 {
100  namespace device
101  {
102  __device__ __forceinline__ void computeRoots2(const float& b, const float& c, float3& roots)
103  {
104  roots.x = 0.f;
105  float d = b * b - 4.f * c;
106  if (d < 0.f) // no real roots!!!! THIS SHOULD NOT HAPPEN!
107  d = 0.f;
108 
109  float sd = sqrtf(d);
110 
111  roots.z = 0.5f * (b + sd);
112  roots.y = 0.5f * (b - sd);
113  }
114 
115  __device__ __forceinline__ void computeRoots3(float c0, float c1, float c2, float3& roots)
116  {
117  if ( std::abs(c0) < std::numeric_limits<float>::epsilon())// one root is 0 -> quadratic equation
118  {
119  computeRoots2 (c2, c1, roots);
120  }
121  else
122  {
123  const float s_inv3 = 1.f/3.f;
124  const float s_sqrt3 = sqrtf(3.f);
125  // Construct the parameters used in classifying the roots of the equation
126  // and in solving the equation for the roots in closed form.
127  float c2_over_3 = c2 * s_inv3;
128  float a_over_3 = (c1 - c2*c2_over_3)*s_inv3;
129  if (a_over_3 > 0.f)
130  a_over_3 = 0.f;
131 
132  float half_b = 0.5f * (c0 + c2_over_3 * (2.f * c2_over_3 * c2_over_3 - c1));
133 
134  float q = half_b * half_b + a_over_3 * a_over_3 * a_over_3;
135  if (q > 0.f)
136  q = 0.f;
137 
138  // Compute the eigenvalues by solving for the roots of the polynomial.
139  float rho = sqrtf(-a_over_3);
140  float theta = std::atan2 (sqrtf (-q), half_b)*s_inv3;
141  float cos_theta = __cosf (theta);
142  float sin_theta = __sinf (theta);
143  roots.x = c2_over_3 + 2.f * rho * cos_theta;
144  roots.y = c2_over_3 - rho * (cos_theta + s_sqrt3 * sin_theta);
145  roots.z = c2_over_3 - rho * (cos_theta - s_sqrt3 * sin_theta);
146 
147  // Sort in increasing order.
148  if (roots.x >= roots.y)
149  swap(roots.x, roots.y);
150 
151  if (roots.y >= roots.z)
152  {
153  swap(roots.y, roots.z);
154 
155  if (roots.x >= roots.y)
156  swap (roots.x, roots.y);
157  }
158  if (roots.x <= 0) // eigenval for symmetric positive semi-definite matrix can not be negative! Set it to 0
159  computeRoots2 (c2, c1, roots);
160  }
161  }
162 
163  struct Eigen33
164  {
165  public:
166  template<int Rows>
167  struct MiniMat
168  {
169  float3 data[Rows];
170  __device__ __host__ __forceinline__ float3& operator[](int i) { return data[i]; }
171  __device__ __host__ __forceinline__ const float3& operator[](int i) const { return data[i]; }
172  };
173  using Mat33 = MiniMat<3>;
174  using Mat43 = MiniMat<4>;
175 
176 
177  static __forceinline__ __device__ float3 unitOrthogonal (const float3& src)
178  {
179  float3 perp;
180  /* Let us compute the crossed product of *this with a vector
181  * that is not too close to being colinear to *this.
182  */
183 
184  /* unless the x and y coords are both close to zero, we can
185  * simply take ( -y, x, 0 ) and normalize it.
186  */
187  if(!isMuchSmallerThan(src.x, src.z) || !isMuchSmallerThan(src.y, src.z))
188  {
189  float invnm = rsqrtf(src.x*src.x + src.y*src.y);
190  perp.x = -src.y * invnm;
191  perp.y = src.x * invnm;
192  perp.z = 0.0f;
193  }
194  /* if both x and y are close to zero, then the vector is close
195  * to the z-axis, so it's far from colinear to the x-axis for instance.
196  * So we take the crossed product with (1,0,0) and normalize it.
197  */
198  else
199  {
200  float invnm = rsqrtf(src.z * src.z + src.y * src.y);
201  perp.x = 0.0f;
202  perp.y = -src.z * invnm;
203  perp.z = src.y * invnm;
204  }
205 
206  return perp;
207  }
208 
209  __device__ __forceinline__ Eigen33(volatile float* mat_pkg_arg) : mat_pkg(mat_pkg_arg) {}
210  __device__ __forceinline__ void compute(Mat33& tmp, Mat33& vec_tmp, Mat33& evecs, float3& evals)
211  {
212  // Scale the matrix so its entries are in [-1,1]. The scaling is applied
213  // only when at least one matrix entry has magnitude larger than 1.
214 
215  float max01 = fmaxf( std::abs(mat_pkg[0]), std::abs(mat_pkg[1]) );
216  float max23 = fmaxf( std::abs(mat_pkg[2]), std::abs(mat_pkg[3]) );
217  float max45 = fmaxf( std::abs(mat_pkg[4]), std::abs(mat_pkg[5]) );
218  float m0123 = fmaxf( max01, max23);
219  float scale = fmaxf( max45, m0123);
220 
221  if (scale <= std::numeric_limits<float>::min())
222  scale = 1.f;
223 
224  mat_pkg[0] /= scale;
225  mat_pkg[1] /= scale;
226  mat_pkg[2] /= scale;
227  mat_pkg[3] /= scale;
228  mat_pkg[4] /= scale;
229  mat_pkg[5] /= scale;
230 
231  // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The
232  // eigenvalues are the roots to this equation, all guaranteed to be
233  // real-valued, because the matrix is symmetric.
234  float c0 = m00() * m11() * m22()
235  + 2.f * m01() * m02() * m12()
236  - m00() * m12() * m12()
237  - m11() * m02() * m02()
238  - m22() * m01() * m01();
239  float c1 = m00() * m11() -
240  m01() * m01() +
241  m00() * m22() -
242  m02() * m02() +
243  m11() * m22() -
244  m12() * m12();
245  float c2 = m00() + m11() + m22();
246 
247  computeRoots3(c0, c1, c2, evals);
248 
249  if(evals.z - evals.x <= std::numeric_limits<float>::epsilon())
250  {
251  evecs[0] = make_float3(1.f, 0.f, 0.f);
252  evecs[1] = make_float3(0.f, 1.f, 0.f);
253  evecs[2] = make_float3(0.f, 0.f, 1.f);
254  }
255  else if (evals.y - evals.x <= std::numeric_limits<float>::epsilon() )
256  {
257  // first and second equal
258  tmp[0] = row0(); tmp[1] = row1(); tmp[2] = row2();
259  tmp[0].x -= evals.z; tmp[1].y -= evals.z; tmp[2].z -= evals.z;
260 
261  vec_tmp[0] = cross(tmp[0], tmp[1]);
262  vec_tmp[1] = cross(tmp[0], tmp[2]);
263  vec_tmp[2] = cross(tmp[1], tmp[2]);
264 
265  float len1 = dot (vec_tmp[0], vec_tmp[0]);
266  float len2 = dot (vec_tmp[1], vec_tmp[1]);
267  float len3 = dot (vec_tmp[2], vec_tmp[2]);
268 
269  if (len1 >= len2 && len1 >= len3)
270  {
271  evecs[2] = vec_tmp[0] * rsqrtf (len1);
272  }
273  else if (len2 >= len1 && len2 >= len3)
274  {
275  evecs[2] = vec_tmp[1] * rsqrtf (len2);
276  }
277  else
278  {
279  evecs[2] = vec_tmp[2] * rsqrtf (len3);
280  }
281 
282  evecs[1] = unitOrthogonal(evecs[2]);
283  evecs[0] = cross(evecs[1], evecs[2]);
284  }
285  else if (evals.z - evals.y <= std::numeric_limits<float>::epsilon() )
286  {
287  // second and third equal
288  tmp[0] = row0(); tmp[1] = row1(); tmp[2] = row2();
289  tmp[0].x -= evals.x; tmp[1].y -= evals.x; tmp[2].z -= evals.x;
290 
291  vec_tmp[0] = cross(tmp[0], tmp[1]);
292  vec_tmp[1] = cross(tmp[0], tmp[2]);
293  vec_tmp[2] = cross(tmp[1], tmp[2]);
294 
295  float len1 = dot(vec_tmp[0], vec_tmp[0]);
296  float len2 = dot(vec_tmp[1], vec_tmp[1]);
297  float len3 = dot(vec_tmp[2], vec_tmp[2]);
298 
299  if (len1 >= len2 && len1 >= len3)
300  {
301  evecs[0] = vec_tmp[0] * rsqrtf(len1);
302  }
303  else if (len2 >= len1 && len2 >= len3)
304  {
305  evecs[0] = vec_tmp[1] * rsqrtf(len2);
306  }
307  else
308  {
309  evecs[0] = vec_tmp[2] * rsqrtf(len3);
310  }
311 
312  evecs[1] = unitOrthogonal( evecs[0] );
313  evecs[2] = cross(evecs[0], evecs[1]);
314  }
315  else
316  {
317 
318  tmp[0] = row0(); tmp[1] = row1(); tmp[2] = row2();
319  tmp[0].x -= evals.z; tmp[1].y -= evals.z; tmp[2].z -= evals.z;
320 
321  vec_tmp[0] = cross(tmp[0], tmp[1]);
322  vec_tmp[1] = cross(tmp[0], tmp[2]);
323  vec_tmp[2] = cross(tmp[1], tmp[2]);
324 
325  float len1 = dot(vec_tmp[0], vec_tmp[0]);
326  float len2 = dot(vec_tmp[1], vec_tmp[1]);
327  float len3 = dot(vec_tmp[2], vec_tmp[2]);
328 
329  float mmax[3];
330 
331  unsigned int min_el = 2;
332  unsigned int max_el = 2;
333  if (len1 >= len2 && len1 >= len3)
334  {
335  mmax[2] = len1;
336  evecs[2] = vec_tmp[0] * rsqrtf (len1);
337  }
338  else if (len2 >= len1 && len2 >= len3)
339  {
340  mmax[2] = len2;
341  evecs[2] = vec_tmp[1] * rsqrtf (len2);
342  }
343  else
344  {
345  mmax[2] = len3;
346  evecs[2] = vec_tmp[2] * rsqrtf (len3);
347  }
348 
349  tmp[0] = row0(); tmp[1] = row1(); tmp[2] = row2();
350  tmp[0].x -= evals.y; tmp[1].y -= evals.y; tmp[2].z -= evals.y;
351 
352  vec_tmp[0] = cross(tmp[0], tmp[1]);
353  vec_tmp[1] = cross(tmp[0], tmp[2]);
354  vec_tmp[2] = cross(tmp[1], tmp[2]);
355 
356  len1 = dot(vec_tmp[0], vec_tmp[0]);
357  len2 = dot(vec_tmp[1], vec_tmp[1]);
358  len3 = dot(vec_tmp[2], vec_tmp[2]);
359 
360  if (len1 >= len2 && len1 >= len3)
361  {
362  mmax[1] = len1;
363  evecs[1] = vec_tmp[0] * rsqrtf (len1);
364  min_el = len1 <= mmax[min_el] ? 1 : min_el;
365  max_el = len1 > mmax[max_el] ? 1 : max_el;
366  }
367  else if (len2 >= len1 && len2 >= len3)
368  {
369  mmax[1] = len2;
370  evecs[1] = vec_tmp[1] * rsqrtf (len2);
371  min_el = len2 <= mmax[min_el] ? 1 : min_el;
372  max_el = len2 > mmax[max_el] ? 1 : max_el;
373  }
374  else
375  {
376  mmax[1] = len3;
377  evecs[1] = vec_tmp[2] * rsqrtf (len3);
378  min_el = len3 <= mmax[min_el] ? 1 : min_el;
379  max_el = len3 > mmax[max_el] ? 1 : max_el;
380  }
381 
382  tmp[0] = row0(); tmp[1] = row1(); tmp[2] = row2();
383  tmp[0].x -= evals.x; tmp[1].y -= evals.x; tmp[2].z -= evals.x;
384 
385  vec_tmp[0] = cross(tmp[0], tmp[1]);
386  vec_tmp[1] = cross(tmp[0], tmp[2]);
387  vec_tmp[2] = cross(tmp[1], tmp[2]);
388 
389  len1 = dot (vec_tmp[0], vec_tmp[0]);
390  len2 = dot (vec_tmp[1], vec_tmp[1]);
391  len3 = dot (vec_tmp[2], vec_tmp[2]);
392 
393 
394  if (len1 >= len2 && len1 >= len3)
395  {
396  mmax[0] = len1;
397  evecs[0] = vec_tmp[0] * rsqrtf (len1);
398  min_el = len3 <= mmax[min_el] ? 0 : min_el;
399  max_el = len3 > mmax[max_el] ? 0 : max_el;
400  }
401  else if (len2 >= len1 && len2 >= len3)
402  {
403  mmax[0] = len2;
404  evecs[0] = vec_tmp[1] * rsqrtf (len2);
405  min_el = len3 <= mmax[min_el] ? 0 : min_el;
406  max_el = len3 > mmax[max_el] ? 0 : max_el;
407  }
408  else
409  {
410  mmax[0] = len3;
411  evecs[0] = vec_tmp[2] * rsqrtf (len3);
412  min_el = len3 <= mmax[min_el] ? 0 : min_el;
413  max_el = len3 > mmax[max_el] ? 0 : max_el;
414  }
415 
416  unsigned mid_el = 3 - min_el - max_el;
417  evecs[min_el] = normalized( cross( evecs[(min_el+1) % 3], evecs[(min_el+2) % 3] ) );
418  evecs[mid_el] = normalized( cross( evecs[(mid_el+1) % 3], evecs[(mid_el+2) % 3] ) );
419  }
420  // Rescale back to the original size.
421  evals *= scale;
422  }
423  private:
424  volatile float* mat_pkg;
425 
426  __device__ __forceinline__ float m00() const { return mat_pkg[0]; }
427  __device__ __forceinline__ float m01() const { return mat_pkg[1]; }
428  __device__ __forceinline__ float m02() const { return mat_pkg[2]; }
429  __device__ __forceinline__ float m10() const { return mat_pkg[1]; }
430  __device__ __forceinline__ float m11() const { return mat_pkg[3]; }
431  __device__ __forceinline__ float m12() const { return mat_pkg[4]; }
432  __device__ __forceinline__ float m20() const { return mat_pkg[2]; }
433  __device__ __forceinline__ float m21() const { return mat_pkg[4]; }
434  __device__ __forceinline__ float m22() const { return mat_pkg[5]; }
435 
436  __device__ __forceinline__ float3 row0() const { return make_float3( m00(), m01(), m02() ); }
437  __device__ __forceinline__ float3 row1() const { return make_float3( m10(), m11(), m12() ); }
438  __device__ __forceinline__ float3 row2() const { return make_float3( m20(), m21(), m22() ); }
439 
440  __device__ __forceinline__ static bool isMuchSmallerThan (float x, float y)
441  {
442  // copied from <eigen>/include/Eigen/src/Core/NumTraits.h
443  constexpr float prec_sqr = std::numeric_limits<float>::epsilon() * std::numeric_limits<float>::epsilon();
444  return x * x <= prec_sqr * y * y;
445  }
446 
447  };
448  }
449 }
450 
451 #endif /* PCL_GPU_FEATURES_EIGEN_HPP_ */
__device__ __host__ __forceinline__ void swap(T &a, T &b)
Definition: utils.hpp:51
__device__ __forceinline__ float3 normalized(const float3 &v)
Definition: utils.hpp:99
__device__ __host__ __forceinline__ const float3 & operator[](int i) const
Definition: eigen.hpp:171
__device__ __host__ __forceinline__ float3 cross(const float3 &v1, const float3 &v2)
Definition: utils.hpp:105
__device__ __forceinline__ void compute(Mat33 &tmp, Mat33 &vec_tmp, Mat33 &evecs, float3 &evals)
Definition: eigen.hpp:210
__device__ __forceinline__ float dot(const float3 &v1, const float3 &v2)
Definition: utils.hpp:57
static __forceinline__ __device__ float3 unitOrthogonal(const float3 &src)
Definition: eigen.hpp:177
__device__ __forceinline__ void computeRoots2(const float &b, const float &c, float3 &roots)
Definition: eigen.hpp:102
__device__ __forceinline__ Eigen33(volatile float *mat_pkg_arg)
Definition: eigen.hpp:209
__device__ __host__ __forceinline__ float3 & operator[](int i)
Definition: eigen.hpp:170
__device__ __forceinline__ void computeRoots3(float c0, float c1, float c2, float3 &roots)
Definition: eigen.hpp:115