1 // Copyright (C) 2009-2021 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, or (at your option) any later version.
8 // This library is distributed in the hope that it will be useful,
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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
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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]
32 // cout << msg << endl
38 //================================================================================
40 * \brief Add point coordinates to inertia tensor in 3D space
42 //================================================================================
44 inline void addPointToInertiaTensor3D(const double* coord,
46 vector<double>& tensor)
48 // we fill the upper triangle of tensor only
50 double x = coord[0] - gc[0], y = coord[1] - gc[1], z = coord[2] - gc[2];
51 __TENSOR(0,0) += y*y + z*z;
52 __TENSOR(1,1) += x*x + z*z;
53 __TENSOR(2,2) += x*x + y*y;
58 //================================================================================
60 * \brief Add point coordinates to inertia tensor in 2D space
62 //================================================================================
64 inline void addPointToInertiaTensor2D(const double* coord,
66 vector<double>& tensor)
68 // we fill the upper triangle of tensor only
70 double x = coord[0] - gc[0], y = coord[1] - gc[1];
76 //================================================================================
78 * \brief Find eigenvectors of tensor using Jacobi's method
80 //================================================================================
82 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) << "}} ");
94 << "{ "<<__TENSOR(0,0) << ", "<<__TENSOR(0,1) << "} "
95 << "{ "<<__TENSOR(1,0) << ", "<<__TENSOR(1,1) << "}} ");
98 const int maxRot = 5*_dim*_dim; // limit on number of rotations
99 const double tol = 1e-9;
101 // set _axes to identity
103 for ( i = 0; i < _dim; ++i )
104 for ( j = 0; j < _dim; ++j )
105 __AXIS(i)[j] = ( i==j ? 1. : 0 );
108 for ( int iRot = 0; iRot < maxRot; ++ iRot )
110 // find max off-diagonal element of the tensor
113 for ( i = 0; i < _dim-1; ++i )
114 for ( j = i+1; j < _dim; ++j )
115 if ( fabs( __TENSOR(i,j)) > max )
116 max = fabs( __TENSOR(i,j) ), k = i, l = j;
117 solved = ( max < tol );
121 // Rotate to make __TENSOR(k,l) == 0
123 double diff = __TENSOR(l,l) - __TENSOR(k,k);
124 double t; // tangent of rotation angle
125 if ( fabs(__TENSOR(k,l)) < abs(diff)*1.0e-36)
127 t = __TENSOR(k,l)/diff;
131 double phi = diff/(2.0*__TENSOR(k,l));
132 t = 1.0/(abs(phi) + sqrt(phi*phi + 1.0));
133 if ( phi < 0.0) t = -t;
135 double c = 1.0/sqrt(t*t + 1.0); // cosine of rotation angle
136 double s = t*c; // sine of rotation angle
137 double tau = s/(1.0 + c);
138 __TENSOR(k,k) -= t*__TENSOR(k,l);
139 __TENSOR(l,l) += t*__TENSOR(k,l);
142 #define __ROTATE(T,r1,c1,r2,c2) \
144 int i1 = r1*_dim+c1, i2 = r2*_dim+c2; \
145 double t1 = T[i1], t2 = T[i2]; \
146 T[i1] -= s * ( t2 + tau * t1);\
147 T[i2] += s * ( t1 - tau * t2);\
149 for ( i = 0; i < k; ++i ) // Case of i < k
150 __ROTATE(tensor, i,k,i,l);
152 for ( i = k+1; i < l; ++i ) // Case of k < i < l
153 __ROTATE(tensor, k,i,i,l);
155 for ( i = l + 1; i < _dim; ++i ) // Case of i > l
156 __ROTATE(tensor, k,i,l,i);
158 for ( i = 0; i < _dim; ++i ) // Update transformation matrix
159 __ROTATE(_axes, i,k,i,l);
162 __DMP( "Solved = " << solved );
164 __DMP( " Eigen " << __TENSOR(0,0)<<", "<<__TENSOR(1,1)<<", "<<__TENSOR(2,2) );
165 for ( int ii=0; ii <3; ++ii )
166 __DMP( ii << ": " << __AXIS(ii)[0] << ", " << __AXIS(ii)[1] << ", " << __AXIS(ii)[2] );
169 __DMP( " Eigen " << __TENSOR(0,0) << ", " << __TENSOR(1,1) );
170 for ( int ii=0; ii <2; ++ii )
171 __DMP( ii << ": " << __AXIS(ii)[0] << ", " << __AXIS(ii)[1] );
177 //================================================================================
179 * \brief Return true if two minmaxes do not intersect
181 //================================================================================
183 inline bool isMinMaxOut(const double* minmax1,
184 const double* minmax2,
187 for ( int i = 0; i < dim; ++i )
189 if ( minmax1[i*2] > minmax2[i*2+1] ||
190 minmax1[i*2+1] < minmax2[i*2] )
196 } // noname namespace
198 namespace INTERP_KERNEL
201 //================================================================================
203 * \brief Creates empty box intended to further initialization via setData()
205 //================================================================================
207 DirectedBoundingBox::DirectedBoundingBox():_dim(0)
211 //================================================================================
213 * \brief Creates bounding box of a mesh
214 * \param pts - coordinates of points in full interlace
215 * \param numPts - number of points in the mesh
216 * \param dim - space dimension
218 //================================================================================
220 DirectedBoundingBox::DirectedBoundingBox(const double* pts,
221 const unsigned numPts,
223 : _dim(dim), _axes(dim*dim), _minmax(2*dim)
225 // init box extremities
226 for ( unsigned i = 0; i < _dim; ++i )
227 _minmax[1+i*2] = -numeric_limits<double>::max(),
228 _minmax[i*2] = numeric_limits<double>::max();
230 if ( numPts < 1 ) return;
232 __DMP( "DirectedBoundingBox " << __MYID );
234 const double* coord = pts;
235 const double* coordEnd = coord + numPts * dim;
237 // compute gravity center of points
238 double gc[3] = {0,0,0};
241 for ( coord = pts; coord < coordEnd; )
242 for ( int i = 0; i < (int)dim; ++i )
244 for ( int j = 0; j < (int)dim; ++j )
249 // compute axes and box extremities
250 vector<double> tensor( dim * dim, 0.);
254 for ( coord = pts; coord < coordEnd; coord += dim )
255 addPointToInertiaTensor3D( coord, gc, tensor );
257 //computeAxes3D(tensor);
258 JacobiEigenvectorsSearch(_dim, tensor, _axes);
260 for ( coord = pts; coord < coordEnd; coord += dim )
261 addPointToBox( coord );
266 for ( coord = pts; coord < coordEnd; coord += dim )
267 addPointToInertiaTensor2D( coord, gc, tensor );
269 //computeAxes2D(tensor);
270 JacobiEigenvectorsSearch(_dim, tensor, _axes);
272 for ( coord = pts; coord < coordEnd; coord += dim )
273 addPointToBox( coord );
278 for ( coord = pts; coord < coordEnd; coord += dim )
280 if ( *coord < _minmax[0] ) _minmax[0] = *coord;
281 if ( *coord > _minmax[1] ) _minmax[1] = *coord;
286 //================================================================================
288 * \brief Creates bounding box of an element
289 * \param pts - coordinates of points of element
290 * \param numPts - number of points in the element
291 * \param dim - space dimension
293 //================================================================================
295 DirectedBoundingBox::DirectedBoundingBox(const double** pts,
296 const unsigned numPts,
298 : _dim(dim), _axes(dim*dim), _minmax(2*dim)
300 // init box extremities
301 for ( unsigned i = 0; i < _dim; ++i )
302 _minmax[1+i*2] = -numeric_limits<double>::max(),
303 _minmax[i*2] = numeric_limits<double>::max();
305 if ( numPts < 1 ) return;
307 __DMP( "DirectedBoundingBox " << __MYID );
309 // compute gravity center of points
310 double gc[3] = {0,0,0};
313 for ( unsigned i = 0; i < numPts; ++i )
314 for ( int j = 0; j < (int)dim; ++j )
316 for ( int j = 0; j < (int)dim; ++j )
320 // compute axes and box extremities
321 vector<double> tensor( dim * dim, 0.);
325 for ( unsigned i = 0; i < numPts; ++i )
326 addPointToInertiaTensor3D( pts[i], gc, tensor );
328 //computeAxes3D(tensor);
329 JacobiEigenvectorsSearch(_dim, tensor, _axes);
331 for ( unsigned i = 0; i < numPts; ++i )
332 addPointToBox( pts[i] );
336 for ( unsigned i = 0; i < numPts; ++i )
337 addPointToInertiaTensor2D( pts[i], gc, tensor );
339 //computeAxes2D(tensor);
340 JacobiEigenvectorsSearch(_dim, tensor, _axes);
342 for ( unsigned i = 0; i < numPts; ++i )
343 addPointToBox( pts[i] );
347 for ( unsigned i = 0; i < numPts; ++i )
349 if ( pts[i][0] < _minmax[0] ) _minmax[0] = pts[i][0];
350 if ( pts[i][0] > _minmax[1] ) _minmax[1] = pts[i][0];
356 //================================================================================
358 * \brief Compute eigenvectors of inertia tensor
360 //================================================================================
362 // void DirectedBoundingBox::computeAxes3D(const std::vector<double>& tensor)
364 // // compute principal moments of inertia which are eigenvalues of the tensor
367 // // coefficients of polynomial equation det(tensor-eig*I) = 0
369 // double b = __TENSOR(0,0)+__TENSOR(1,1)+__TENSOR(2,2);
371 // __TENSOR(0,1)*__TENSOR(0,1) +
372 // __TENSOR(0,2)*__TENSOR(0,2) +
373 // __TENSOR(1,2)*__TENSOR(1,2) -
374 // __TENSOR(0,0)*__TENSOR(1,1) -
375 // __TENSOR(0,0)*__TENSOR(2,2) -
376 // __TENSOR(1,1)*__TENSOR(2,2);
378 // __TENSOR(0,0)*__TENSOR(1,1)*__TENSOR(2,2) -
379 // __TENSOR(0,0)*__TENSOR(1,2)*__TENSOR(1,2) -
380 // __TENSOR(1,1)*__TENSOR(0,2)*__TENSOR(0,2) -
381 // __TENSOR(2,2)*__TENSOR(0,1)*__TENSOR(0,1) +
382 // __TENSOR(0,1)*__TENSOR(0,2)*__TENSOR(1,2)*2;
384 // // find eigenvalues which are roots of characteristic polynomial
385 // double x = (3*c/a - b*b/(a*a))/3;
386 // double y = (2*b*b*b/(a*a*a) - 9*b*c/(a*a) + 27*d/a)/27;
387 // double z = y*y/4 + x*x*x/27;
389 // double i = sqrt(y*y/4 - z) + 1e-300;
390 // double j = -pow(i,1/3.);
391 // double y2 = -y/(2*i);
392 // if ( y2 > 1.0) y2 = 1.; else if ( y2 < -1.0) y2 = -1.;
393 // double k = acos(y2);
394 // double m = cos(k/3);
395 // double n = sqrt(3)*sin(k/3);
396 // double p = -b/(3*a);
398 // eig[0] = -2*j*m + p;
399 // eig[1] = j *(m + n) + p;
400 // eig[2] = j *(m - n) + p;
402 // // compute eigenvector of the tensor at each eigenvalue
403 // // by solving system [tensor-eig*I]*[axis] = 0
405 // __DMP( "Tensor : {"
406 // << "{ "<<__TENSOR(0,0) << ", "<<__TENSOR(0,1) << ", "<<__TENSOR(0,2) << "} "
407 // << "{ "<<__TENSOR(1,0) << ", "<<__TENSOR(1,1) << ", "<<__TENSOR(1,2) << "} "
408 // << "{ "<<__TENSOR(2,0) << ", "<<__TENSOR(2,1) << ", "<<__TENSOR(2,2) << "}} ");
409 // for ( int i = 0; i < 3 && ok; ++i ) // loop on 3 eigenvalues
413 // {{ __TENSOR(0,0)-eig[i],__TENSOR(0,1), __TENSOR(0,2), },
414 // { __TENSOR(0,1), __TENSOR(1,1)-eig[i],__TENSOR(1,2), },
415 // { __TENSOR(0,2), __TENSOR(1,2), __TENSOR(2,2)-eig[i]}};
416 // // The determinant of T is zero, so that the equations are not linearly independent.
417 // // Therefore, we assign an arbitrary value (1.) to i-th component of eigenvector
418 // // and use two of the equations to compute the other two components
419 // double M[2][3], sol[2];
420 // for ( int j = 0, c = 0; j < 3; ++j )
422 // M[0][2] = -T[0][j], M[1][2] = -T[1][j];
424 // M[0][c] = T[0][j], M[1][c] = T[1][j], c++;
426 // ok = solveSystemOfEquations<2>( M, sol );
428 // double* eigenVec = __AXIS(i);
429 // for ( int j = 0, c = 0; j < 3; ++j )
430 // eigenVec[j] = ( i == j ) ? 1. : sol[c++];
433 // double size = sqrt(eigenVec[0]*eigenVec[0] +
434 // eigenVec[1]*eigenVec[1] +
435 // eigenVec[2]*eigenVec[2] );
436 // if ((ok = (size > numeric_limits<double>::min() )))
438 // eigenVec[0] /= size;
439 // eigenVec[1] /= size;
440 // eigenVec[2] /= size;
445 // __DMP( " solve3EquationSystem() - KO " );
446 // _axes = vector<double>( _dim*_dim, 0);
447 // __AXIS(0)[0] = __AXIS(1)[1] = __AXIS(2)[2] = 1.;
449 // __DMP( " Eigen " << eig[0] << ", " << eig[1] << ", " << eig[2] );
450 // for ( int i=0; i <3; ++i )
451 // __DMP( i << ": " << __AXIS(i)[0] << ", " << __AXIS(i)[1] << ", " << __AXIS(i)[2] );
453 // double* a0 = __AXIS(0), *a1 = __AXIS(1);
454 // double cross[3] = { a0[1]*a1[2]-a1[1]*a0[2],
455 // a0[2]*a1[0]-a1[2]*a0[0],
456 // a0[0]*a1[1]-a1[0]*a0[1] };
457 // __DMP( " Cross a1^a2 " << cross[0] << ", " << cross[1] << ", " << cross[2] );
460 //================================================================================
462 * \brief Compute eigenvectors of inertia tensor
464 //================================================================================
466 // void DirectedBoundingBox::computeAxes2D(const std::vector<double>& tensor)
468 // // compute principal moments of inertia which are eigenvalues of the tensor
469 // // by solving square equation det(tensor-eig*I)
470 // double X = (__TENSOR(0,0)+__TENSOR(1,1))/2;
471 // double Y = sqrt(4*__TENSOR(0,1)*__TENSOR(0,1) +
472 // (__TENSOR(0,0)-__TENSOR(1,1)) * (__TENSOR(0,0)-__TENSOR(1,1)))/2;
478 // // compute eigenvector of the tensor at each eigenvalue
479 // // by solving system [tensor-eig*I]*[axis] = 0
481 // for ( int i = 0; i < 2 && ok; ++i )
485 // {{ __TENSOR(0,0)-eig[i],__TENSOR(0,1) },
486 // { __TENSOR(0,1), __TENSOR(1,1)-eig[i] }};
488 // // The determinant of T is zero, so that the equations are not linearly independent.
489 // // Therefore, we assign an arbitrary value (1.) to i-th component of eigenvector
490 // // and use one equation to compute the other component
491 // double* eigenVec = __AXIS(i);
494 // if ((ok = ( fabs( T[j][j] ) > numeric_limits<double>::min() )))
495 // eigenVec[j] = -T[j][i] / T[j][j];
499 // _axes = vector<double>( _dim*_dim, 0);
500 // __AXIS(0)[0] = __AXIS(1)[1] = 1.;
504 //================================================================================
506 * \brief Convert point coordinates into local coordinate system of the box
508 //================================================================================
510 void DirectedBoundingBox::toLocalCS(const double* p, double* pLoc) const
515 pLoc[0] = dotprod<3>( p, __AXIS(0));
516 pLoc[1] = dotprod<3>( p, __AXIS(1));
517 pLoc[2] = dotprod<3>( p, __AXIS(2));
520 pLoc[0] = dotprod<2>( p, __AXIS(0));
521 pLoc[1] = dotprod<2>( p, __AXIS(1));
528 //================================================================================
530 * \brief Convert point coordinates from local coordinate system of the box to global CS
532 //================================================================================
534 void DirectedBoundingBox::fromLocalCS(const double* p, double* pGlob) const
539 pGlob[0] = p[0] * __AXIS(0)[0] + p[1] * __AXIS(1)[0] + p[2] * __AXIS(2)[0];
540 pGlob[1] = p[0] * __AXIS(0)[1] + p[1] * __AXIS(1)[1] + p[2] * __AXIS(2)[1];
541 pGlob[2] = p[0] * __AXIS(0)[2] + p[1] * __AXIS(1)[2] + p[2] * __AXIS(2)[2];
544 pGlob[0] = p[0] * __AXIS(0)[0] + p[1] * __AXIS(1)[0];
545 pGlob[1] = p[0] * __AXIS(0)[1] + p[1] * __AXIS(1)[1];
552 //================================================================================
554 * \brief Enlarge box size by given value
556 //================================================================================
558 void DirectedBoundingBox::enlarge(const double tol)
560 for ( unsigned i = 0; i < _dim; ++i )
561 __MIN(i) -= tol, __MAX(i) += tol;
564 //================================================================================
566 * \brief Return coordinates of corners of bounding box
568 //================================================================================
570 void DirectedBoundingBox::getCorners(std::vector<double>& corners,
571 const double* minmax) const
573 int iC, nbCorners = 1;
574 for ( int i=0;i<(int)_dim;++i ) nbCorners *= 2;
575 corners.resize( nbCorners * _dim );
576 // each coordinate is filled with either min or max, nbSwap is number of corners
577 // after which min and max swap
578 int nbSwap = nbCorners/2;
579 for ( unsigned i = 0; i < _dim; ++i )
582 while ( iC < nbCorners )
584 for (int j = 0; j < nbSwap; ++j, ++iC ) corners[iC*_dim+i] = minmax[i*2];
585 for (int j = 0; j < nbSwap; ++j, ++iC ) corners[iC*_dim+i] = minmax[i*2+1];
591 //================================================================================
593 * \brief Test if this box intersects with the other
594 * \retval bool - true if there is no intersection
596 //================================================================================
598 bool DirectedBoundingBox::isDisjointWith(const DirectedBoundingBox& box) const
600 if ( _dim < 1 || box._dim < 1 ) return false; // empty box includes all
602 return isMinMaxOut( &box._minmax[0], &this->_minmax[0], _dim );
604 // boxes are disjoined if their minmaxes in local CS of either of boxes do not intersect
605 for ( int isThisCS = 0; isThisCS < 2; ++isThisCS )
607 const DirectedBoundingBox* axisBox = isThisCS ? this : &box;
608 const DirectedBoundingBox* cornerBox = isThisCS ? &box : this;
610 // find minmax of cornerBox in the CS of axisBox
612 DirectedBoundingBox mmBox((double*)0,0,_dim); //!< empty box with CS == axisBox->_axes
613 mmBox._axes = axisBox->_axes;
615 vector<double> corners;
616 getCorners( corners, &cornerBox->_minmax[0] );
618 double globCorner[3];
619 for ( std::size_t iC = 0, nC = corners.size()/_dim; iC < nC; ++iC)
621 cornerBox->fromLocalCS( &corners[iC*_dim], globCorner );
622 mmBox.addPointToBox( globCorner );
624 if ( isMinMaxOut( &mmBox._minmax[0], &axisBox->_minmax[0], _dim ))
630 //================================================================================
632 * \brief Test if this box intersects with an non-directed box
633 * \retval bool - true if there is no intersection
635 //================================================================================
637 bool DirectedBoundingBox::isDisjointWith(const double* box) const
639 if ( _dim < 1 ) return false; // empty box includes all
641 return isMinMaxOut( &_minmax[0], box, _dim );
643 // boxes are disjoined if their minmaxes in local CS of either of boxes do not intersect
645 // compare minmaxes in locals CS of this directed box
647 vector<double> cornersOther;
648 getCorners( cornersOther, box );
649 DirectedBoundingBox mmBox((double*)0,0,_dim); //!< empty box with CS == this->_axes
650 mmBox._axes = this->_axes;
651 for ( std::size_t iC = 0, nC = cornersOther.size()/_dim; iC < nC; ++iC)
652 mmBox.addPointToBox( &cornersOther[iC*_dim] );
654 if ( isMinMaxOut( &mmBox._minmax[0], &this->_minmax[0], _dim ))
658 // compare minmaxes in global CS
660 vector<double> cornersThis;
661 getCorners( cornersThis, &_minmax[0] );
662 DirectedBoundingBox mmBox((double*)0,0,_dim); //!< initailized _minmax
663 double globCorner[3];
664 for ( std::size_t iC = 0, nC = cornersThis.size()/_dim; iC < nC; ++iC)
666 fromLocalCS( &cornersThis[iC*_dim], globCorner );
667 for ( int i = 0; i < (int)_dim; ++i )
669 if ( globCorner[i] < mmBox._minmax[i*2] ) mmBox._minmax[i*2] = globCorner[i];
670 if ( globCorner[i] > mmBox._minmax[i*2+1] ) mmBox._minmax[i*2+1] = globCorner[i];
673 if ( isMinMaxOut( &mmBox._minmax[0], box, _dim ))
679 //================================================================================
681 * \brief Return true if given point is out of this box
683 //================================================================================
685 bool DirectedBoundingBox::isOut(const double* point) const
687 if ( _dim < 1 ) return false; // empty box includes all
690 toLocalCS( point, pLoc );
691 bool out = isLocalOut( pLoc );
696 __DMP(__MYID<<": "<<point[0]<<", "<<point[1]<<", "<<point[2]<<" "<<(out?"OUT":"IN"));break;
698 __DMP(__MYID<<": "<<point[0]<<", "<<point[1]<<" "<<(out?"OUT":"IN"));break;
700 __DMP(__MYID<<": "<<point[0]<<" "<<(out?"OUT":"IN"));break;
706 //================================================================================
708 * \brief Return array of internal data
710 //================================================================================
712 vector<double> DirectedBoundingBox::getData() const
714 vector<double> data(1, _dim);
717 data.insert( data.end(), &_axes[0], &_axes[0] + _axes.size());
718 data.insert( data.end(), &_minmax[0], &_minmax[0] + _minmax.size());
720 if ( data.size() < (unsigned)dataSize( _dim ))
721 data.resize( dataSize( _dim ), 0 );
725 //================================================================================
727 * \brief Initializes self with data retrieved via getData()
729 //================================================================================
731 void DirectedBoundingBox::setData(const double* data)
733 _dim = unsigned( *data++ );
736 _axes.assign( data, data+_dim*_dim ); data += _dim*_dim;
737 _minmax.assign( data, data+2*_dim );
746 //================================================================================
748 * \brief Return size of internal data returned by getData() depending on space dim
750 //================================================================================
752 int DirectedBoundingBox::dataSize(int dim)
754 return 1 + dim*dim + 2*dim; // : _dim + _axes + _minmax