1 // Copyright (C) 2009-2012 OPEN CASCADE
3 // This library is free software; you can redistribute it and/or
4 // modify it under the terms of the GNU Lesser General Public
5 // License as published by the Free Software Foundation; either
6 // version 2.1 of the License.
8 // This library is distributed in the hope that it will be useful,
9 // but WITHOUT ANY WARRANTY; without even the implied warranty of
10 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
11 // Lesser General Public License for more details.
13 // You should have received a copy of the GNU Lesser General Public
14 // License along with this library; if not, write to the Free Software
15 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17 // See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
19 // File : DirectedBoundingBox.cxx
20 // Created : Mon Apr 12 14:41:22 2010
21 // Author : Edward AGAPOV (eap)
23 #include "DirectedBoundingBox.hxx"
25 #include "InterpolationUtils.hxx"
27 #define __TENSOR(i,j) tensor[(i)*_dim+(j)]
28 #define __AXIS(i) (&_axes[(i)*_dim])
29 #define __MIN(i) _minmax[i*2]
30 #define __MAX(i) _minmax[i*2+1]
31 #define __MYID (long(this)%10000)
33 // cout << msg << endl
39 //================================================================================
41 * \brief Add point coordinates to inertia tensor in 3D space
43 //================================================================================
45 inline void addPointToInertiaTensor3D(const double* coord,
47 vector<double>& tensor)
49 // we fill the upper triangle of tensor only
51 double x = coord[0] - gc[0], y = coord[1] - gc[1], z = coord[2] - gc[2];
52 __TENSOR(0,0) += y*y + z*z;
53 __TENSOR(1,1) += x*x + z*z;
54 __TENSOR(2,2) += x*x + y*y;
59 //================================================================================
61 * \brief Add point coordinates to inertia tensor in 2D space
63 //================================================================================
65 inline void addPointToInertiaTensor2D(const double* coord,
67 vector<double>& tensor)
69 // we fill the upper triangle of tensor only
71 double x = coord[0] - gc[0], y = coord[1] - gc[1];
77 //================================================================================
79 * \brief Find eigenvectors of tensor using Jacobi's method
81 //================================================================================
83 bool JacobiEigenvectorsSearch( const int _dim, vector<double>& tensor, vector<double>& _axes)
87 << "{ "<<__TENSOR(0,0) << ", "<<__TENSOR(0,1) << ", "<<__TENSOR(0,2) << "} "
88 << "{ "<<__TENSOR(1,0) << ", "<<__TENSOR(1,1) << ", "<<__TENSOR(1,2) << "} "
89 << "{ "<<__TENSOR(2,0) << ", "<<__TENSOR(2,1) << ", "<<__TENSOR(2,2) << "}} ");
92 << "{ "<<__TENSOR(0,0) << ", "<<__TENSOR(0,1) << "} "
93 << "{ "<<__TENSOR(1,0) << ", "<<__TENSOR(1,1) << "}} ");
95 const int maxRot = 5*_dim*_dim; // limit on number of rotations
96 const double tol = 1e-9;
98 // set _axes to identity
100 for ( i = 0; i < _dim; ++i )
101 for ( j = 0; j < _dim; ++j )
102 __AXIS(i)[j] = ( i==j ? 1. : 0 );
105 for ( int iRot = 0; iRot < maxRot; ++ iRot )
107 // find max off-diagonal element of the tensor
110 for ( i = 0; i < _dim-1; ++i )
111 for ( j = i+1; j < _dim; ++j )
112 if ( fabs( __TENSOR(i,j)) > max )
113 max = fabs( __TENSOR(i,j) ), k = i, l = j;
114 solved = ( max < tol );
118 // Rotate to make __TENSOR(k,l) == 0
120 double diff = __TENSOR(l,l) - __TENSOR(k,k);
121 double t; // tangent of rotation angle
122 if ( fabs(__TENSOR(k,l)) < abs(diff)*1.0e-36)
124 t = __TENSOR(k,l)/diff;
128 double phi = diff/(2.0*__TENSOR(k,l));
129 t = 1.0/(abs(phi) + sqrt(phi*phi + 1.0));
130 if ( phi < 0.0) t = -t;
132 double c = 1.0/sqrt(t*t + 1.0); // cosine of rotation angle
133 double s = t*c; // sine of rotation angle
134 double tau = s/(1.0 + c);
135 __TENSOR(k,k) -= t*__TENSOR(k,l);
136 __TENSOR(l,l) += t*__TENSOR(k,l);
139 #define __ROTATE(T,r1,c1,r2,c2) \
141 int i1 = r1*_dim+c1, i2 = r2*_dim+c2; \
142 double t1 = T[i1], t2 = T[i2]; \
143 T[i1] -= s * ( t2 + tau * t1);\
144 T[i2] += s * ( t1 - tau * t2);\
146 for ( i = 0; i < k; ++i ) // Case of i < k
147 __ROTATE(tensor, i,k,i,l);
149 for ( i = k+1; i < l; ++i ) // Case of k < i < l
150 __ROTATE(tensor, k,i,i,l);
152 for ( i = l + 1; i < _dim; ++i ) // Case of i > l
153 __ROTATE(tensor, k,i,l,i);
155 for ( i = 0; i < _dim; ++i ) // Update transformation matrix
156 __ROTATE(_axes, i,k,i,l);
159 __DMP( "Solved = " << solved );
161 __DMP( " Eigen " << __TENSOR(0,0)<<", "<<__TENSOR(1,1)<<", "<<__TENSOR(2,2) );
162 for ( int ii=0; ii <3; ++ii )
163 __DMP( ii << ": " << __AXIS(ii)[0] << ", " << __AXIS(ii)[1] << ", " << __AXIS(ii)[2] );
166 __DMP( " Eigen " << __TENSOR(0,0) << ", " << __TENSOR(1,1) );
167 for ( int ii=0; ii <2; ++ii )
168 __DMP( ii << ": " << __AXIS(ii)[0] << ", " << __AXIS(ii)[1] );
174 //================================================================================
176 * \brief Return true if two minmaxes do not intersect
178 //================================================================================
180 inline bool isMinMaxOut(const double* minmax1,
181 const double* minmax2,
184 for ( int i = 0; i < dim; ++i )
186 if ( minmax1[i*2] > minmax2[i*2+1] ||
187 minmax1[i*2+1] < minmax2[i*2] )
193 } // noname namespace
195 namespace INTERP_KERNEL
198 //================================================================================
200 * \brief Creates empty box intended to further initalization via setData()
202 //================================================================================
204 DirectedBoundingBox::DirectedBoundingBox():_dim(0)
208 //================================================================================
210 * \brief Creates bounding box of a mesh
211 * \param pts - coordinates of points in full interlace
212 * \param numPts - number of points in the mesh
213 * \param dim - space dimension
215 //================================================================================
217 DirectedBoundingBox::DirectedBoundingBox(const double* pts,
218 const unsigned numPts,
220 : _dim(dim), _axes(dim*dim), _minmax(2*dim)
222 // init box extremities
223 for ( unsigned i = 0; i < _dim; ++i )
224 _minmax[1+i*2] = -numeric_limits<double>::max(),
225 _minmax[i*2] = numeric_limits<double>::max();
227 if ( numPts < 1 ) return;
229 __DMP( "DirectedBoundingBox " << __MYID );
231 const double* coord = pts;
232 const double* coordEnd = coord + numPts * dim;
234 // compute gravity center of points
235 double gc[3] = {0,0,0};
238 for ( coord = pts; coord < coordEnd; )
239 for ( int i = 0; i < (int)dim; ++i )
241 for ( int j = 0; j < (int)dim; ++j )
246 // compute axes and box extremities
247 vector<double> tensor( dim * dim, 0.);
251 for ( coord = pts; coord < coordEnd; coord += dim )
252 addPointToInertiaTensor3D( coord, gc, tensor );
254 //computeAxes3D(tensor);
255 JacobiEigenvectorsSearch(_dim, tensor, _axes);
257 for ( coord = pts; coord < coordEnd; coord += dim )
258 addPointToBox( coord );
263 for ( coord = pts; coord < coordEnd; coord += dim )
264 addPointToInertiaTensor2D( coord, gc, tensor );
266 //computeAxes2D(tensor);
267 JacobiEigenvectorsSearch(_dim, tensor, _axes);
269 for ( coord = pts; coord < coordEnd; coord += dim )
270 addPointToBox( coord );
275 for ( coord = pts; coord < coordEnd; coord += dim )
277 if ( *coord < _minmax[0] ) _minmax[0] = *coord;
278 if ( *coord > _minmax[1] ) _minmax[1] = *coord;
283 //================================================================================
285 * \brief Creates bounding box of an element
286 * \param pts - coordinates of points of element
287 * \param numPts - number of points in the element
288 * \param dim - space dimension
290 //================================================================================
292 DirectedBoundingBox::DirectedBoundingBox(const double** pts,
293 const unsigned numPts,
295 : _dim(dim), _axes(dim*dim), _minmax(2*dim)
297 // init box extremities
298 for ( unsigned i = 0; i < _dim; ++i )
299 _minmax[1+i*2] = -numeric_limits<double>::max(),
300 _minmax[i*2] = numeric_limits<double>::max();
302 if ( numPts < 1 ) return;
304 __DMP( "DirectedBoundingBox " << __MYID );
306 // compute gravity center of points
307 double gc[3] = {0,0,0};
310 for ( unsigned i = 0; i < numPts; ++i )
311 for ( int j = 0; j < (int)dim; ++j )
313 for ( int j = 0; j < (int)dim; ++j )
317 // compute axes and box extremities
318 vector<double> tensor( dim * dim, 0.);
322 for ( unsigned i = 0; i < numPts; ++i )
323 addPointToInertiaTensor3D( pts[i], gc, tensor );
325 //computeAxes3D(tensor);
326 JacobiEigenvectorsSearch(_dim, tensor, _axes);
328 for ( unsigned i = 0; i < numPts; ++i )
329 addPointToBox( pts[i] );
333 for ( unsigned i = 0; i < numPts; ++i )
334 addPointToInertiaTensor2D( pts[i], gc, tensor );
336 //computeAxes2D(tensor);
337 JacobiEigenvectorsSearch(_dim, tensor, _axes);
339 for ( unsigned i = 0; i < numPts; ++i )
340 addPointToBox( pts[i] );
344 for ( unsigned i = 0; i < numPts; ++i )
346 if ( pts[i][0] < _minmax[0] ) _minmax[0] = pts[i][0];
347 if ( pts[i][0] > _minmax[1] ) _minmax[1] = pts[i][0];
353 //================================================================================
355 * \brief Compute eigenvectors of inertia tensor
357 //================================================================================
359 // void DirectedBoundingBox::computeAxes3D(const std::vector<double>& tensor)
361 // // compute principal moments of inertia which are eigenvalues of the tensor
364 // // coefficients of polynomial equation det(tensor-eig*I) = 0
366 // double b = __TENSOR(0,0)+__TENSOR(1,1)+__TENSOR(2,2);
368 // __TENSOR(0,1)*__TENSOR(0,1) +
369 // __TENSOR(0,2)*__TENSOR(0,2) +
370 // __TENSOR(1,2)*__TENSOR(1,2) -
371 // __TENSOR(0,0)*__TENSOR(1,1) -
372 // __TENSOR(0,0)*__TENSOR(2,2) -
373 // __TENSOR(1,1)*__TENSOR(2,2);
375 // __TENSOR(0,0)*__TENSOR(1,1)*__TENSOR(2,2) -
376 // __TENSOR(0,0)*__TENSOR(1,2)*__TENSOR(1,2) -
377 // __TENSOR(1,1)*__TENSOR(0,2)*__TENSOR(0,2) -
378 // __TENSOR(2,2)*__TENSOR(0,1)*__TENSOR(0,1) +
379 // __TENSOR(0,1)*__TENSOR(0,2)*__TENSOR(1,2)*2;
381 // // find eigenvalues which are roots of characteristic polynomial
382 // double x = (3*c/a - b*b/(a*a))/3;
383 // double y = (2*b*b*b/(a*a*a) - 9*b*c/(a*a) + 27*d/a)/27;
384 // double z = y*y/4 + x*x*x/27;
386 // double i = sqrt(y*y/4 - z) + 1e-300;
387 // double j = -pow(i,1/3.);
388 // double y2 = -y/(2*i);
389 // if ( y2 > 1.0) y2 = 1.; else if ( y2 < -1.0) y2 = -1.;
390 // double k = acos(y2);
391 // double m = cos(k/3);
392 // double n = sqrt(3)*sin(k/3);
393 // double p = -b/(3*a);
395 // eig[0] = -2*j*m + p;
396 // eig[1] = j *(m + n) + p;
397 // eig[2] = j *(m - n) + p;
399 // // compute eigenvector of the tensor at each eigenvalue
400 // // by solving system [tensor-eig*I]*[axis] = 0
402 // __DMP( "Tensor : {"
403 // << "{ "<<__TENSOR(0,0) << ", "<<__TENSOR(0,1) << ", "<<__TENSOR(0,2) << "} "
404 // << "{ "<<__TENSOR(1,0) << ", "<<__TENSOR(1,1) << ", "<<__TENSOR(1,2) << "} "
405 // << "{ "<<__TENSOR(2,0) << ", "<<__TENSOR(2,1) << ", "<<__TENSOR(2,2) << "}} ");
406 // for ( int i = 0; i < 3 && ok; ++i ) // loop on 3 eigenvalues
410 // {{ __TENSOR(0,0)-eig[i],__TENSOR(0,1), __TENSOR(0,2), },
411 // { __TENSOR(0,1), __TENSOR(1,1)-eig[i],__TENSOR(1,2), },
412 // { __TENSOR(0,2), __TENSOR(1,2), __TENSOR(2,2)-eig[i]}};
413 // // The determinant of T is zero, so that the equations are not linearly independent.
414 // // Therefore, we assign an arbitrary value (1.) to i-th component of eigenvector
415 // // and use two of the equations to compute the other two components
416 // double M[2][3], sol[2];
417 // for ( int j = 0, c = 0; j < 3; ++j )
419 // M[0][2] = -T[0][j], M[1][2] = -T[1][j];
421 // M[0][c] = T[0][j], M[1][c] = T[1][j], c++;
423 // ok = solveSystemOfEquations<2>( M, sol );
425 // double* eigenVec = __AXIS(i);
426 // for ( int j = 0, c = 0; j < 3; ++j )
427 // eigenVec[j] = ( i == j ) ? 1. : sol[c++];
430 // double size = sqrt(eigenVec[0]*eigenVec[0] +
431 // eigenVec[1]*eigenVec[1] +
432 // eigenVec[2]*eigenVec[2] );
433 // if ((ok = (size > numeric_limits<double>::min() )))
435 // eigenVec[0] /= size;
436 // eigenVec[1] /= size;
437 // eigenVec[2] /= size;
442 // __DMP( " solve3EquationSystem() - KO " );
443 // _axes = vector<double>( _dim*_dim, 0);
444 // __AXIS(0)[0] = __AXIS(1)[1] = __AXIS(2)[2] = 1.;
446 // __DMP( " Eigen " << eig[0] << ", " << eig[1] << ", " << eig[2] );
447 // for ( int i=0; i <3; ++i )
448 // __DMP( i << ": " << __AXIS(i)[0] << ", " << __AXIS(i)[1] << ", " << __AXIS(i)[2] );
450 // double* a0 = __AXIS(0), *a1 = __AXIS(1);
451 // double cross[3] = { a0[1]*a1[2]-a1[1]*a0[2],
452 // a0[2]*a1[0]-a1[2]*a0[0],
453 // a0[0]*a1[1]-a1[0]*a0[1] };
454 // __DMP( " Cross a1^a2 " << cross[0] << ", " << cross[1] << ", " << cross[2] );
457 //================================================================================
459 * \brief Compute eigenvectors of inertia tensor
461 //================================================================================
463 // void DirectedBoundingBox::computeAxes2D(const std::vector<double>& tensor)
465 // // compute principal moments of inertia which are eigenvalues of the tensor
466 // // by solving square equation det(tensor-eig*I)
467 // double X = (__TENSOR(0,0)+__TENSOR(1,1))/2;
468 // double Y = sqrt(4*__TENSOR(0,1)*__TENSOR(0,1) +
469 // (__TENSOR(0,0)-__TENSOR(1,1)) * (__TENSOR(0,0)-__TENSOR(1,1)))/2;
475 // // compute eigenvector of the tensor at each eigenvalue
476 // // by solving system [tensor-eig*I]*[axis] = 0
478 // for ( int i = 0; i < 2 && ok; ++i )
482 // {{ __TENSOR(0,0)-eig[i],__TENSOR(0,1) },
483 // { __TENSOR(0,1), __TENSOR(1,1)-eig[i] }};
485 // // The determinant of T is zero, so that the equations are not linearly independent.
486 // // Therefore, we assign an arbitrary value (1.) to i-th component of eigenvector
487 // // and use one equation to compute the other component
488 // double* eigenVec = __AXIS(i);
491 // if ((ok = ( fabs( T[j][j] ) > numeric_limits<double>::min() )))
492 // eigenVec[j] = -T[j][i] / T[j][j];
496 // _axes = vector<double>( _dim*_dim, 0);
497 // __AXIS(0)[0] = __AXIS(1)[1] = 1.;
501 //================================================================================
503 * \brief Convert point coordinates into local coordinate system of the box
505 //================================================================================
507 void DirectedBoundingBox::toLocalCS(const double* p, double* pLoc) const
512 pLoc[0] = dotprod<3>( p, __AXIS(0));
513 pLoc[1] = dotprod<3>( p, __AXIS(1));
514 pLoc[2] = dotprod<3>( p, __AXIS(2));
517 pLoc[0] = dotprod<2>( p, __AXIS(0));
518 pLoc[1] = dotprod<2>( p, __AXIS(1));
525 //================================================================================
527 * \brief Convert point coordinates from local coordinate system of the box to global CS
529 //================================================================================
531 void DirectedBoundingBox::fromLocalCS(const double* p, double* pGlob) const
536 pGlob[0] = p[0] * __AXIS(0)[0] + p[1] * __AXIS(1)[0] + p[2] * __AXIS(2)[0];
537 pGlob[1] = p[0] * __AXIS(0)[1] + p[1] * __AXIS(1)[1] + p[2] * __AXIS(2)[1];
538 pGlob[2] = p[0] * __AXIS(0)[2] + p[1] * __AXIS(1)[2] + p[2] * __AXIS(2)[2];
541 pGlob[0] = p[0] * __AXIS(0)[0] + p[1] * __AXIS(1)[0];
542 pGlob[1] = p[0] * __AXIS(0)[1] + p[1] * __AXIS(1)[1];
549 //================================================================================
551 * \brief Enlarge box size by given value
553 //================================================================================
555 void DirectedBoundingBox::enlarge(const double tol)
557 for ( unsigned i = 0; i < _dim; ++i )
558 __MIN(i) -= tol, __MAX(i) += tol;
561 //================================================================================
563 * \brief Return coordinates of corners of bounding box
565 //================================================================================
567 void DirectedBoundingBox::getCorners(std::vector<double>& corners,
568 const double* minmax) const
570 int iC, nbCorners = 1;
571 for ( int i=0;i<(int)_dim;++i ) nbCorners *= 2;
572 corners.resize( nbCorners * _dim );
573 // each coordinate is filled with either min or max, nbSwap is number of corners
574 // after which min and max swap
575 int nbSwap = nbCorners/2;
576 for ( unsigned i = 0; i < _dim; ++i )
579 while ( iC < nbCorners )
581 for (int j = 0; j < nbSwap; ++j, ++iC ) corners[iC*_dim+i] = minmax[i*2];
582 for (int j = 0; j < nbSwap; ++j, ++iC ) corners[iC*_dim+i] = minmax[i*2+1];
588 //================================================================================
590 * \brief Test if this box intersects with the other
591 * \retval bool - true if there is no intersection
593 //================================================================================
595 bool DirectedBoundingBox::isDisjointWith(const DirectedBoundingBox& box) const
597 if ( _dim < 1 || box._dim < 1 ) return false; // empty box includes all
599 return isMinMaxOut( &box._minmax[0], &this->_minmax[0], _dim );
601 // boxes are disjoined if their minmaxes in local CS of either of boxes do not intersect
602 for ( int isThisCS = 0; isThisCS < 2; ++isThisCS )
604 const DirectedBoundingBox* axisBox = isThisCS ? this : &box;
605 const DirectedBoundingBox* cornerBox = isThisCS ? &box : this;
607 // find minmax of cornerBox in the CS of axisBox
609 DirectedBoundingBox mmBox((double*)0,0,_dim); //!< empty box with CS == axisBox->_axes
610 mmBox._axes = axisBox->_axes;
612 vector<double> corners;
613 getCorners( corners, &cornerBox->_minmax[0] );
615 double globCorner[3];
616 for ( int iC = 0, nC = corners.size()/_dim; iC < nC; ++iC)
618 cornerBox->fromLocalCS( &corners[iC*_dim], globCorner );
619 mmBox.addPointToBox( globCorner );
621 if ( isMinMaxOut( &mmBox._minmax[0], &axisBox->_minmax[0], _dim ))
627 //================================================================================
629 * \brief Test if this box intersects with an non-directed box
630 * \retval bool - true if there is no intersection
632 //================================================================================
634 bool DirectedBoundingBox::isDisjointWith(const double* box) const
636 if ( _dim < 1 ) return false; // empty box includes all
638 return isMinMaxOut( &_minmax[0], box, _dim );
640 // boxes are disjoined if their minmaxes in local CS of either of boxes do not intersect
642 // compare minmaxes in locals CS of this directed box
644 vector<double> cornersOther;
645 getCorners( cornersOther, box );
646 DirectedBoundingBox mmBox((double*)0,0,_dim); //!< empty box with CS == this->_axes
647 mmBox._axes = this->_axes;
648 for ( int iC = 0, nC = cornersOther.size()/_dim; iC < nC; ++iC)
649 mmBox.addPointToBox( &cornersOther[iC*_dim] );
651 if ( isMinMaxOut( &mmBox._minmax[0], &this->_minmax[0], _dim ))
655 // compare minmaxes in global CS
657 vector<double> cornersThis;
658 getCorners( cornersThis, &_minmax[0] );
659 DirectedBoundingBox mmBox((double*)0,0,_dim); //!< initailized _minmax
660 double globCorner[3];
661 for ( int iC = 0, nC = cornersThis.size()/_dim; iC < nC; ++iC)
663 fromLocalCS( &cornersThis[iC*_dim], globCorner );
664 for ( int i = 0; i < (int)_dim; ++i )
666 if ( globCorner[i] < mmBox._minmax[i*2] ) mmBox._minmax[i*2] = globCorner[i];
667 if ( globCorner[i] > mmBox._minmax[i*2+1] ) mmBox._minmax[i*2+1] = globCorner[i];
670 if ( isMinMaxOut( &mmBox._minmax[0], box, _dim ))
676 //================================================================================
678 * \brief Return true if given point is out of this box
680 //================================================================================
682 bool DirectedBoundingBox::isOut(const double* point) const
684 if ( _dim < 1 ) return false; // empty box includes all
687 toLocalCS( point, pLoc );
688 bool out = isLocalOut( pLoc );
693 __DMP(__MYID<<": "<<point[0]<<", "<<point[1]<<", "<<point[2]<<" "<<(out?"OUT":"IN"));break;
695 __DMP(__MYID<<": "<<point[0]<<", "<<point[1]<<" "<<(out?"OUT":"IN"));break;
697 __DMP(__MYID<<": "<<point[0]<<" "<<(out?"OUT":"IN"));break;
703 //================================================================================
705 * \brief Return array of internal data
707 //================================================================================
709 vector<double> DirectedBoundingBox::getData() const
711 vector<double> data(1, _dim);
714 data.insert( data.end(), &_axes[0], &_axes[0] + _axes.size());
715 data.insert( data.end(), &_minmax[0], &_minmax[0] + _minmax.size());
717 if ( data.size() < (unsigned)dataSize( _dim ))
718 data.resize( dataSize( _dim ), 0 );
722 //================================================================================
724 * \brief Initializes self with data retrieved via getData()
726 //================================================================================
728 void DirectedBoundingBox::setData(const double* data)
730 _dim = unsigned( *data++ );
733 _axes.assign( data, data+_dim*_dim ); data += _dim*_dim;
734 _minmax.assign( data, data+2*_dim );
743 //================================================================================
745 * \brief Return size of internal data returned by getData() depending on space dim
747 //================================================================================
749 int DirectedBoundingBox::dataSize(int dim)
751 return 1 + dim*dim + 2*dim; // : _dim + _axes + _minmax