Point Cloud Library (PCL)  1.12.1-dev
auxiliary.h
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37 
38 #pragma once
39 
40 #include <Eigen/Core> // for Matrix
41 #include <Eigen/Geometry> // for AngleAxis
42 #include <pcl/point_types.h>
43 
44 #define AUX_PI_FLOAT 3.14159265358979323846f
45 #define AUX_HALF_PI 1.57079632679489661923f
46 #define AUX_DEG_TO_RADIANS (3.14159265358979323846f/180.0f)
47 
48 namespace pcl
49 {
50  namespace recognition
51  {
52  namespace aux
53  {
54  template<typename T> bool
55  compareOrderedPairs (const std::pair<T,T>& a, const std::pair<T,T>& b)
56  {
57  if ( a.first == b.first )
58  return a.second < b.second;
59 
60  return a.first < b.first;
61  }
62 
63  template<typename T> T
64  sqr (T a)
65  {
66  return (a*a);
67  }
68 
69  template<typename T> T
70  clamp (T value, T min, T max)
71  {
72  if ( value < min )
73  return min;
74  if ( value > max )
75  return max;
76 
77  return value;
78  }
79 
80  /** \brief Expands the destination bounding box 'dst' such that it contains 'src'. */
81  template<typename T> void
82  expandBoundingBox (T dst[6], const T src[6])
83  {
84  if ( src[0] < dst[0] ) dst[0] = src[0];
85  if ( src[2] < dst[2] ) dst[2] = src[2];
86  if ( src[4] < dst[4] ) dst[4] = src[4];
87 
88  if ( src[1] > dst[1] ) dst[1] = src[1];
89  if ( src[3] > dst[3] ) dst[3] = src[3];
90  if ( src[5] > dst[5] ) dst[5] = src[5];
91  }
92 
93  /** \brief Expands the bounding box 'bbox' such that it contains the point 'p'. */
94  template<typename T> void
95  expandBoundingBoxToContainPoint (T bbox[6], const T p[3])
96  {
97  if ( p[0] < bbox[0] ) bbox[0] = p[0];
98  else if ( p[0] > bbox[1] ) bbox[1] = p[0];
99 
100  if ( p[1] < bbox[2] ) bbox[2] = p[1];
101  else if ( p[1] > bbox[3] ) bbox[3] = p[1];
102 
103  if ( p[2] < bbox[4] ) bbox[4] = p[2];
104  else if ( p[2] > bbox[5] ) bbox[5] = p[2];
105  }
106 
107  /** \brief v[0] = v[1] = v[2] = value */
108  template <typename T> void
109  set3 (T v[3], T value)
110  {
111  v[0] = v[1] = v[2] = value;
112  }
113 
114  /** \brief dst = src */
115  template <typename T> void
116  copy3 (const T src[3], T dst[3])
117  {
118  dst[0] = src[0];
119  dst[1] = src[1];
120  dst[2] = src[2];
121  }
122 
123  /** \brief dst = src */
124  template <typename T> void
125  copy3 (const T src[3], pcl::PointXYZ& dst)
126  {
127  dst.x = src[0];
128  dst.y = src[1];
129  dst.z = src[2];
130  }
131 
132  /** \brief a = -a */
133  template <typename T> void
134  flip3 (T a[3])
135  {
136  a[0] = -a[0];
137  a[1] = -a[1];
138  a[2] = -a[2];
139  }
140 
141  /** \brief a = b */
142  template <typename T> bool
143  equal3 (const T a[3], const T b[3])
144  {
145  return (a[0] == b[0] && a[1] == b[1] && a[2] == b[2]);
146  }
147 
148  /** \brief a += b */
149  template <typename T> void
150  add3 (T a[3], const T b[3])
151  {
152  a[0] += b[0];
153  a[1] += b[1];
154  a[2] += b[2];
155  }
156 
157  /** \brief c = a + b */
158  template <typename T> void
159  sum3 (const T a[3], const T b[3], T c[3])
160  {
161  c[0] = a[0] + b[0];
162  c[1] = a[1] + b[1];
163  c[2] = a[2] + b[2];
164  }
165 
166  /** \brief c = a - b */
167  template <typename T> void
168  diff3 (const T a[3], const T b[3], T c[3])
169  {
170  c[0] = a[0] - b[0];
171  c[1] = a[1] - b[1];
172  c[2] = a[2] - b[2];
173  }
174 
175  template <typename T> void
176  cross3 (const T v1[3], const T v2[3], T out[3])
177  {
178  out[0] = v1[1]*v2[2] - v1[2]*v2[1];
179  out[1] = v1[2]*v2[0] - v1[0]*v2[2];
180  out[2] = v1[0]*v2[1] - v1[1]*v2[0];
181  }
182 
183  /** \brief Returns the length of v. */
184  template <typename T> T
185  length3 (const T v[3])
186  {
187  return (std::sqrt (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]));
188  }
189 
190  /** \brief Returns the Euclidean distance between a and b. */
191  template <typename T> T
192  distance3 (const T a[3], const T b[3])
193  {
194  T l[3] = {a[0]-b[0], a[1]-b[1], a[2]-b[2]};
195  return (length3 (l));
196  }
197 
198  /** \brief Returns the squared Euclidean distance between a and b. */
199  template <typename T> T
200  sqrDistance3 (const T a[3], const T b[3])
201  {
202  return (aux::sqr (a[0]-b[0]) + aux::sqr (a[1]-b[1]) + aux::sqr (a[2]-b[2]));
203  }
204 
205  /** \brief Returns the dot product a*b */
206  template <typename T> T
207  dot3 (const T a[3], const T b[3])
208  {
209  return (a[0]*b[0] + a[1]*b[1] + a[2]*b[2]);
210  }
211 
212  /** \brief Returns the dot product (x, y, z)*(u, v, w) = x*u + y*v + z*w */
213  template <typename T> T
214  dot3 (T x, T y, T z, T u, T v, T w)
215  {
216  return (x*u + y*v + z*w);
217  }
218 
219  /** \brief v = scalar*v. */
220  template <typename T> void
221  mult3 (T* v, T scalar)
222  {
223  v[0] *= scalar;
224  v[1] *= scalar;
225  v[2] *= scalar;
226  }
227 
228  /** \brief out = scalar*v. */
229  template <typename T> void
230  mult3 (const T* v, T scalar, T* out)
231  {
232  out[0] = v[0]*scalar;
233  out[1] = v[1]*scalar;
234  out[2] = v[2]*scalar;
235  }
236 
237  /** \brief Normalize v */
238  template <typename T> void
239  normalize3 (T v[3])
240  {
241  T inv_len = (static_cast<T> (1.0))/aux::length3 (v);
242  v[0] *= inv_len;
243  v[1] *= inv_len;
244  v[2] *= inv_len;
245  }
246 
247  /** \brief Returns the square length of v. */
248  template <typename T> T
249  sqrLength3 (const T v[3])
250  {
251  return (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
252  }
253 
254  /** Projects 'x' on the plane through 0 and with normal 'planeNormal' and saves the result in 'out'. */
255  template <typename T> void
256  projectOnPlane3 (const T x[3], const T planeNormal[3], T out[3])
257  {
258  T dot = aux::dot3 (planeNormal, x);
259  // Project 'x' on the plane normal
260  T nproj[3] = {-dot*planeNormal[0], -dot*planeNormal[1], -dot*planeNormal[2]};
261  aux::sum3 (x, nproj, out);
262  }
263 
264  /** \brief Sets 'm' to the 3x3 identity matrix. */
265  template <typename T> void
266  identity3x3 (T m[9])
267  {
268  m[0] = m[4] = m[8] = 1.0;
269  m[1] = m[2] = m[3] = m[5] = m[6] = m[7] = 0.0;
270  }
271 
272  /** \brief out = mat*v. 'm' is an 1D array of 9 elements treated as a 3x3 matrix (row major order). */
273  template <typename T> void
274  mult3x3(const T m[9], const T v[3], T out[3])
275  {
276  out[0] = v[0]*m[0] + v[1]*m[1] + v[2]*m[2];
277  out[1] = v[0]*m[3] + v[1]*m[4] + v[2]*m[5];
278  out[2] = v[0]*m[6] + v[1]*m[7] + v[2]*m[8];
279  }
280 
281  /** Let x, y, z be the columns of the matrix a = [x|y|z]. The method computes out = a*m.
282  * Note that 'out' is a 1D array of 9 elements and the resulting matrix is stored in row
283  * major order, i.e., the first matrix row is (out[0] out[1] out[2]), the second
284  * (out[3] out[4] out[5]) and the third (out[6] out[7] out[8]). */
285  template <typename T> void
286  mult3x3 (const T x[3], const T y[3], const T z[3], const T m[3][3], T out[9])
287  {
288  out[0] = x[0]*m[0][0] + y[0]*m[1][0] + z[0]*m[2][0];
289  out[1] = x[0]*m[0][1] + y[0]*m[1][1] + z[0]*m[2][1];
290  out[2] = x[0]*m[0][2] + y[0]*m[1][2] + z[0]*m[2][2];
291 
292  out[3] = x[1]*m[0][0] + y[1]*m[1][0] + z[1]*m[2][0];
293  out[4] = x[1]*m[0][1] + y[1]*m[1][1] + z[1]*m[2][1];
294  out[5] = x[1]*m[0][2] + y[1]*m[1][2] + z[1]*m[2][2];
295 
296  out[6] = x[2]*m[0][0] + y[2]*m[1][0] + z[2]*m[2][0];
297  out[7] = x[2]*m[0][1] + y[2]*m[1][1] + z[2]*m[2][1];
298  out[8] = x[2]*m[0][2] + y[2]*m[1][2] + z[2]*m[2][2];
299  }
300 
301  /** \brief The first 9 elements of 't' are treated as a 3x3 matrix (row major order) and the last 3 as a translation.
302  * First, 'p' is multiplied by that matrix and then translated. The result is saved in 'out'. */
303  template<class T> void
304  transform(const T t[12], const T p[3], T out[3])
305  {
306  out[0] = t[0]*p[0] + t[1]*p[1] + t[2]*p[2] + t[9];
307  out[1] = t[3]*p[0] + t[4]*p[1] + t[5]*p[2] + t[10];
308  out[2] = t[6]*p[0] + t[7]*p[1] + t[8]*p[2] + t[11];
309  }
310 
311  /** \brief The first 9 elements of 't' are treated as a 3x3 matrix (row major order) and the last 3 as a translation.
312  * First, (x, y, z) is multiplied by that matrix and then translated. The result is saved in 'out'. */
313  template<class T> void
314  transform(const T t[12], T x, T y, T z, T out[3])
315  {
316  out[0] = t[0]*x + t[1]*y + t[2]*z + t[9];
317  out[1] = t[3]*x + t[4]*y + t[5]*z + t[10];
318  out[2] = t[6]*x + t[7]*y + t[8]*z + t[11];
319  }
320 
321  /** \brief Compute out = (upper left 3x3 of mat)*p + last column of mat. */
322  template<class T> void
323  transform(const Eigen::Matrix<T,4,4>& mat, const pcl::PointXYZ& p, pcl::PointXYZ& out)
324  {
325  out.x = mat(0,0)*p.x + mat(0,1)*p.y + mat(0,2)*p.z + mat(0,3);
326  out.y = mat(1,0)*p.x + mat(1,1)*p.y + mat(1,2)*p.z + mat(1,3);
327  out.z = mat(2,0)*p.x + mat(2,1)*p.y + mat(2,2)*p.z + mat(2,3);
328  }
329 
330  /** \brief The first 9 elements of 't' are treated as a 3x3 matrix (row major order) and the last 3 as a translation.
331  * First, 'p' is multiplied by that matrix and then translated. The result is saved in 'out'. */
332  template<class T> void
333  transform(const T t[12], const pcl::PointXYZ& p, T out[3])
334  {
335  out[0] = t[0]*p.x + t[1]*p.y + t[2]*p.z + t[9];
336  out[1] = t[3]*p.x + t[4]*p.y + t[5]*p.z + t[10];
337  out[2] = t[6]*p.x + t[7]*p.y + t[8]*p.z + t[11];
338  }
339 
340  /** \brief Returns true if the points 'p1' and 'p2' are co-planar and false otherwise. The method assumes that 'n1'
341  * is a normal at 'p1' and 'n2' is a normal at 'p2'. 'max_angle' is the threshold used for the test. The bigger
342  * the value the larger the deviation between the normals can be which still leads to a positive test result. The
343  * angle has to be in radians. */
344  template<typename T> bool
345  pointsAreCoplanar (const T p1[3], const T n1[3], const T p2[3], const T n2[3], T max_angle)
346  {
347  // Compute the angle between 'n1' and 'n2' and compare it with 'max_angle'
348  if ( std::acos (aux::clamp (aux::dot3 (n1, n2), -1.0f, 1.0f)) > max_angle )
349  return (false);
350 
351  T cl[3] = {p2[0] - p1[0], p2[1] - p1[1], p2[2] - p1[2]};
352  aux::normalize3 (cl);
353 
354  // Compute the angle between 'cl' and 'n1'
355  T tmp_angle = std::acos (aux::clamp (aux::dot3 (n1, cl), -1.0f, 1.0f));
356 
357  // 'tmp_angle' should not deviate too much from 90 degrees
358  if ( std::fabs (tmp_angle - AUX_HALF_PI) > max_angle )
359  return (false);
360 
361  // All tests passed => the points are coplanar
362  return (true);
363  }
364 
365  template<typename Scalar> void
366  array12ToMatrix4x4 (const Scalar src[12], Eigen::Matrix<Scalar, 4, 4>& dst)
367  {
368  dst(0,0) = src[0]; dst(0,1) = src[1]; dst(0,2) = src[2]; dst(0,3) = src[9];
369  dst(1,0) = src[3]; dst(1,1) = src[4]; dst(1,2) = src[5]; dst(1,3) = src[10];
370  dst(2,0) = src[6]; dst(2,1) = src[7]; dst(2,2) = src[8]; dst(2,3) = src[11];
371  dst(3,0) = dst(3,1) = dst(3,2) = 0.0; dst(3,3) = 1.0;
372  }
373 
374  template<typename Scalar> void
375  matrix4x4ToArray12 (const Eigen::Matrix<Scalar, 4, 4>& src, Scalar dst[12])
376  {
377  dst[0] = src(0,0); dst[1] = src(0,1); dst[2] = src(0,2); dst[9] = src(0,3);
378  dst[3] = src(1,0); dst[4] = src(1,1); dst[5] = src(1,2); dst[10] = src(1,3);
379  dst[6] = src(2,0); dst[7] = src(2,1); dst[8] = src(2,2); dst[11] = src(2,3);
380  }
381 
382  /** \brief The method copies the input array 'src' to the eigen matrix 'dst' in row major order.
383  * dst[0] = src(0,0); dst[1] = src(0,1); dst[2] = src(0,2);
384  * dst[3] = src(1,0); dst[4] = src(1,1); dst[5] = src(1,2);
385  * dst[6] = src(2,0); dst[7] = src(2,1); dst[8] = src(2,2);
386  * */
387  template <typename T> void
388  eigenMatrix3x3ToArray9RowMajor (const Eigen::Matrix<T,3,3>& src, T dst[9])
389  {
390  dst[0] = src(0,0); dst[1] = src(0,1); dst[2] = src(0,2);
391  dst[3] = src(1,0); dst[4] = src(1,1); dst[5] = src(1,2);
392  dst[6] = src(2,0); dst[7] = src(2,1); dst[8] = src(2,2);
393  }
394 
395  /** \brief The method copies the input array 'src' to the eigen matrix 'dst' in row major order.
396  * dst(0,0) = src[0]; dst(0,1) = src[1]; dst(0,2) = src[2];
397  * dst(1,0) = src[3]; dst(1,1) = src[4]; dst(1,2) = src[5];
398  * dst(2,0) = src[6]; dst(2,1) = src[7]; dst(2,2) = src[8];
399  * */
400  template <typename T> void
401  toEigenMatrix3x3RowMajor (const T src[9], Eigen::Matrix<T,3,3>& dst)
402  {
403  dst(0,0) = src[0]; dst(0,1) = src[1]; dst(0,2) = src[2];
404  dst(1,0) = src[3]; dst(1,1) = src[4]; dst(1,2) = src[5];
405  dst(2,0) = src[6]; dst(2,1) = src[7]; dst(2,2) = src[8];
406  }
407 
408  /** brief Computes a rotation matrix from the provided input vector 'axis_angle'. The direction of 'axis_angle' is the rotation axis
409  * and its magnitude is the angle of rotation about that axis. 'rotation_matrix' is the output rotation matrix saved in row major order. */
410  template <typename T> void
411  axisAngleToRotationMatrix (const T axis_angle[3], T rotation_matrix[9])
412  {
413  // Get the angle of rotation
414  T angle = aux::length3 (axis_angle);
415  if ( angle == 0.0 )
416  {
417  // Undefined rotation -> set to identity
418  aux::identity3x3 (rotation_matrix);
419  return;
420  }
421 
422  // Normalize the input
423  T normalized_axis_angle[3];
424  aux::mult3 (axis_angle, static_cast<T> (1.0)/angle, normalized_axis_angle);
425 
426  // The eigen objects
427  Eigen::Matrix<T,3,1> mat_axis(normalized_axis_angle);
428  Eigen::AngleAxis<T> eigen_angle_axis (angle, mat_axis);
429 
430  // Save the output
431  aux::eigenMatrix3x3ToArray9RowMajor (eigen_angle_axis.toRotationMatrix (), rotation_matrix);
432  }
433 
434  /** brief Extracts the angle-axis representation from 'rotation_matrix', i.e., computes a rotation 'axis' and an 'angle'
435  * of rotation about that axis from the provided input. The output 'angle' is in the range [0, pi] and 'axis' is normalized. */
436  template <typename T> void
437  rotationMatrixToAxisAngle (const T rotation_matrix[9], T axis[3], T& angle)
438  {
439  // The eigen objects
440  Eigen::AngleAxis<T> angle_axis;
441  Eigen::Matrix<T,3,3> rot_mat;
442  // Copy the input matrix to the eigen matrix in row major order
443  aux::toEigenMatrix3x3RowMajor (rotation_matrix, rot_mat);
444 
445  // Do the computation
446  angle_axis.fromRotationMatrix (rot_mat);
447 
448  // Save the result
449  axis[0] = angle_axis.axis () (0,0);
450  axis[1] = angle_axis.axis () (1,0);
451  axis[2] = angle_axis.axis () (2,0);
452  angle = angle_axis.angle ();
453 
454  // Make sure that 'angle' is in the range [0, pi]
455  if ( angle > AUX_PI_FLOAT )
456  {
457  angle = 2.0f*AUX_PI_FLOAT - angle;
458  aux::flip3 (axis);
459  }
460  }
461  } // namespace aux
462  } // namespace recognition
463 } // namespace pcl
Defines all the PCL implemented PointT point type structures.
T sqrLength3(const T v[3])
Returns the square length of v.
Definition: auxiliary.h:249
void expandBoundingBoxToContainPoint(T bbox[6], const T p[3])
Expands the bounding box 'bbox' such that it contains the point 'p'.
Definition: auxiliary.h:95
void array12ToMatrix4x4(const Scalar src[12], Eigen::Matrix< Scalar, 4, 4 > &dst)
Definition: auxiliary.h:366
T distance3(const T a[3], const T b[3])
Returns the Euclidean distance between a and b.
Definition: auxiliary.h:192
void axisAngleToRotationMatrix(const T axis_angle[3], T rotation_matrix[9])
brief Computes a rotation matrix from the provided input vector 'axis_angle'.
Definition: auxiliary.h:411
T dot3(const T a[3], const T b[3])
Returns the dot product a*b.
Definition: auxiliary.h:207
T sqrDistance3(const T a[3], const T b[3])
Returns the squared Euclidean distance between a and b.
Definition: auxiliary.h:200
bool equal3(const T a[3], const T b[3])
a = b
Definition: auxiliary.h:143
T length3(const T v[3])
Returns the length of v.
Definition: auxiliary.h:185
void mult3(T *v, T scalar)
v = scalar*v.
Definition: auxiliary.h:221
void matrix4x4ToArray12(const Eigen::Matrix< Scalar, 4, 4 > &src, Scalar dst[12])
Definition: auxiliary.h:375
void add3(T a[3], const T b[3])
a += b
Definition: auxiliary.h:150
void transform(const T t[12], const T p[3], T out[3])
The first 9 elements of 't' are treated as a 3x3 matrix (row major order) and the last 3 as a transla...
Definition: auxiliary.h:304
void normalize3(T v[3])
Normalize v.
Definition: auxiliary.h:239
T clamp(T value, T min, T max)
Definition: auxiliary.h:70
void eigenMatrix3x3ToArray9RowMajor(const Eigen::Matrix< T, 3, 3 > &src, T dst[9])
The method copies the input array 'src' to the eigen matrix 'dst' in row major order.
Definition: auxiliary.h:388
void toEigenMatrix3x3RowMajor(const T src[9], Eigen::Matrix< T, 3, 3 > &dst)
The method copies the input array 'src' to the eigen matrix 'dst' in row major order.
Definition: auxiliary.h:401
void diff3(const T a[3], const T b[3], T c[3])
c = a - b
Definition: auxiliary.h:168
void set3(T v[3], T value)
v[0] = v[1] = v[2] = value
Definition: auxiliary.h:109
void projectOnPlane3(const T x[3], const T planeNormal[3], T out[3])
Projects 'x' on the plane through 0 and with normal 'planeNormal' and saves the result in 'out'.
Definition: auxiliary.h:256
void flip3(T a[3])
a = -a
Definition: auxiliary.h:134
bool pointsAreCoplanar(const T p1[3], const T n1[3], const T p2[3], const T n2[3], T max_angle)
Returns true if the points 'p1' and 'p2' are co-planar and false otherwise.
Definition: auxiliary.h:345
void copy3(const T src[3], T dst[3])
dst = src
Definition: auxiliary.h:116
void sum3(const T a[3], const T b[3], T c[3])
c = a + b
Definition: auxiliary.h:159
void cross3(const T v1[3], const T v2[3], T out[3])
Definition: auxiliary.h:176
void expandBoundingBox(T dst[6], const T src[6])
Expands the destination bounding box 'dst' such that it contains 'src'.
Definition: auxiliary.h:82
void identity3x3(T m[9])
Sets 'm' to the 3x3 identity matrix.
Definition: auxiliary.h:266
bool compareOrderedPairs(const std::pair< T, T > &a, const std::pair< T, T > &b)
Definition: auxiliary.h:55
void mult3x3(const T m[9], const T v[3], T out[3])
out = mat*v.
Definition: auxiliary.h:274
void rotationMatrixToAxisAngle(const T rotation_matrix[9], T axis[3], T &angle)
brief Extracts the angle-axis representation from 'rotation_matrix', i.e., computes a rotation 'axis'...
Definition: auxiliary.h:437
A point structure representing Euclidean xyz coordinates.