G+Smo  25.01.0
Geometry + Simulation Modules
 
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gsGeometry.hpp
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1
14#pragma once
15
16#include <gsCore/gsBasis.h>
17#include <gsUtils/gsMesh/gsMesh.h>
18#include <gsCore/gsFuncData.h>
19#include <gsCore/gsFuncCoordinate.h>
20
21#include <gsCore/gsGeometrySlice.h>
22
23//#include <gsCore/gsMinimizer.h>
24#include <gsUtils/gsPointGrid.h>
25
26namespace gismo
27{
28
30template<class T>
31class gsSquaredDistance GISMO_FINAL : public gsFunction<T>
32{
33public:
34 gsSquaredDistance(const gsGeometry<T> & g, const gsVector<T> & pt)
35 : m_g(&g), m_pt(&pt), m_gd(2) { }
36
37 // f = (1/2)*||x-pt||^2
38 void eval_into(const gsMatrix<T>& u, gsMatrix<T>& result) const
39 {
40 m_g->eval_into(u, m_gd[0]);
41 result.resize(1, u.cols());
42 result.at(0) = 0.5 * (m_gd[0]-*m_pt).squaredNorm();
43 }
44
45 void evalAllDers_into(const gsMatrix<T> & u, int n,
46 std::vector<gsMatrix<T> > & result,
47 bool sameElement = false) const
48 {
49 GISMO_ASSERT(1==u.cols(), "Single argument assumed");
50 result.resize(n+1);
51 m_g->evalAllDers_into(u, n, m_gd, sameElement);
52
53 // f = (1/2)*||x-pt||^2
54 result[0].resize(1, 1);
55 result[0].at(0) = 0.5 * (m_gd[0]-*m_pt).squaredNorm();
56 if (n==0) return;
57
58 // f' = x'*(x-pt)
59 auto jacT = m_gd[1].reshaped(u.rows(),m_pt->rows());
60 result[1].noalias() = jacT * (m_gd[0] - *m_pt);
61 if (n==1) return;
62
63 // f'' = tr(x')*x' + sum_i[ (x_i-pt_i) * x_i'']
64 tmp.noalias() = jacT * jacT.transpose();
65 index_t d2 = u.rows() * (u.rows()+1) / 2;
66 gsMatrix<T> hm;
67 for ( index_t k=0; k < m_g->coefs().cols(); ++k )
68 {
69 hm = util::secDerToHessian(m_gd[2].block(k*d2,0,d2,1),u.rows()).reshaped(u.rows(),u.rows());
70 tmp += (m_gd[0].at(k)-m_pt->at(k)) * hm;
71 }
72 util::hessianToSecDer(tmp,u.rows(),result[2]);
73 }
74
75 // f' = x'*(x-pt)
76 void deriv_into(const gsMatrix<T>& u, gsMatrix<T>& result) const
77 {
78 result.resize(u.rows(), u.cols());
79 for ( index_t i=0; i != u.cols(); i++ )
80 {
81 tmp = u.col(i);
82 m_g->eval_into(tmp,m_gd[0]);
83 m_g->jacobian_into(tmp,m_gd[1]);
84 result.col(i).noalias() = m_gd[1].transpose() * (m_gd[0] - *m_pt);
85 }
86 }
87
88 // f'' = tr(x')*x' + sum_i[ (x_i-pt_i) * x_i'']
89 void hessian_into(const gsMatrix<T>& u, gsMatrix<T>& result,
90 index_t) const
91 {
92 m_g->eval_into(u,m_gd[0]);
93 m_g->jacobian_into(u,m_gd[1]);
94 result.noalias() = m_gd[1].transpose() * m_gd[1];
95 for ( index_t k=0; k < m_g->coefs().cols(); ++k )
96 {
97 tmp = m_g->hessian(u,k);
98 result.noalias() += (m_gd[0].at(k)-m_pt->at(k))*tmp;
99 }
100 }
101
102 gsMatrix<T> support() const {return m_g->support() ;}
103 short_t domainDim () const {return m_g->domainDim();}
104 short_t targetDim () const {return 1;}
105
106private:
107 const gsGeometry<T> * m_g;
108 const gsVector<T> * m_pt;
109 mutable std::vector<gsMatrix<T> > m_gd;
110 mutable gsMatrix<T> tmp;
111};
112
113 /*
114template<class T>
115boxSide gsGeometry<T>::sideOf( const gsVector<T> & u, )
116{
117 // get the indices of the coefficients which lie on the boundary
118 gsMatrix<index_t > allBnd = m_basis->allBoundary();
119 gsMatrix<T> bndCoeff(allBnd.rows(), m_coefs.rows());
120
121 // extract the indices of the boundary coefficients
122 for(index_t r = 0; r < allBnd.rows(); r++)
123 bndCoeff.row(r) = m_coefs.row(allBnd(r,0));
124
125
126 for(size_t size = 0; size < allBnd.rows(); size++)
127 if(boundaryPatch1[size] == 1)
128 interfaceIndicesPatch1.push_back(allBnd(size, 0)); // get the indices of the coefficients on patch 1 which lie on the common interface
129
130 boxSide side;
131
132 for(unsigned index = 1; index <= nBoundaries; index++) {
133 int contained = 0;
134 side.m_index = index;
135
136 gsMatrix<index_t> bnd = m_basis->boundary(side);
137
138 for(size_t i = 0; i < interfaceIndicesPatch1.size(); i++)
139 {
140 gsInfo << "index: " << interfaceIndicesPatch1[i] << "\n";
141 for (int j = 0; j < bnd.rows(); j++)
142 {
143 if(bnd(j, 0) == interfaceIndicesPatch1[i])
144 contained++;
145 }
146 }
147
148 if(contained == bnd.rows())
149 break;
150
151 //gsInfo << "indices of boundary : " << bnd << "\n";
152 }
153}
154 */
155
156template<class T>
157gsGeometry<T>::gsGeometry(const gsGeometry<T> & o)
158: m_coefs(o.m_coefs), m_basis(o.m_basis != NULL ? o.basis().clone().release() : NULL), m_id(o.m_id)
159{ }
160
161template<class T>
162gsGeometry<T>::~gsGeometry()
163{ delete m_basis; }
164
165template<class T>
166void gsGeometry<T>::eval_into(const gsMatrix<T>& u, gsMatrix<T>& result) const
167{ this->basis().evalFunc_into(u, m_coefs, result); }
168
169template<class T>
170void gsGeometry<T>::deriv_into(const gsMatrix<T>& u, gsMatrix<T>& result) const
171{ this->basis().derivFunc_into(u, m_coefs, result); }
172
173template<class T>
174void gsGeometry<T>::deriv2_into(const gsMatrix<T>& u, gsMatrix<T>& result) const
175{ this->basis().deriv2Func_into(u, m_coefs, result); }
176
177template<class T>
178void gsGeometry<T>::evalAllDers_into(const gsMatrix<T> & u, int n,
179 std::vector<gsMatrix<T> > & result,
180 bool sameElement) const
181{ this->basis().evalAllDersFunc_into(u, m_coefs, n, result, sameElement); }
182
183template<class T>
184short_t gsGeometry<T>::domainDim() const { return this->basis().domainDim(); }
185
186template<class T>
187short_t gsGeometry<T>::coDim() const { return coefDim()-this->basis().domainDim(); }
188
189template<class T>
190short_t gsGeometry<T>::parDim() const { return this->basis().domainDim(); }
191
192template<class T>
193gsMatrix<T> gsGeometry<T>::support() const
194{ return this->basis().support(); }
195
196template<class T>
198gsMatrix<T> gsGeometry<T>::parameterRange() const
199{ return this->basis().support(); }
200
201template<class T>
202gsGeometry<T>& gsGeometry<T>::operator=( const gsGeometry<T> & o)
203{
204 if ( this != &o )
205 {
206 m_coefs = o.m_coefs;
207 delete m_basis;
208 m_basis = o.basis().clone().release() ;
209 m_id = o.m_id;
210 }
211 return *this;
212}
213
214template<class T>
215typename gsGeometry<T>::uPtr
216gsGeometry<T>::boundary(boxSide const& s) const
217{
218 gsMatrix<index_t> ind = this->basis().boundary(s); // get indices of the boundary DOF
219 gsMatrix<T> coeffs (ind.size(), geoDim()); // create matrix for boundary coefficients
220
221 for (index_t i=0; i != ind.size(); i++ )
222 {
223 coeffs.row(i) = m_coefs.row( ind(i,0) );
224 }
225
226 typename gsBasis<T>::uPtr Bs = this->basis().boundaryBasis(s); // Basis for boundary side s
227 return Bs->makeGeometry( give(coeffs) );
228}
229
230template<class T>
231typename gsGeometry<T>::uPtr
237
238template<class T>
239typename gsGeometry<T>::uPtr
240gsGeometry<T>::component(boxComponent const& bc) const
241{
242 gsMatrix<index_t> ind;
243 typename gsBasis<T>::uPtr Bs = this->basis().componentBasis_withIndices(bc, ind, false);
244 gsMatrix<T> coefs (ind.size(), geoDim());
245
246 for (index_t i=0; i != ind.size(); i++ )
247 {
248 coefs.row(i) = m_coefs.row( ind(i,0) );
249 }
250
251 return Bs->makeGeometry( coefs );
252}
253
254template<class T>
255void gsGeometry<T>::evaluateMesh(gsMesh<T>& mesh) const
256{
257 const int pDim = parDim();
258 const int gDim = geoDim();
259
260 gsMatrix<T> tmp;
261
262 // For all vertices of the mesh, push forward the value by the
263 // geometry mapping
264 if (1==gDim && 3>pDim) // Plot a graph
265 for (size_t i = 0; i!= mesh.numVertices(); ++i)
266 {
267 eval_into( mesh.vertex(i).topRows(pDim), tmp );
268 mesh.vertex(i).middleRows(pDim, gDim) = tmp;
269 }
270 else // Plot mesh on a mapping
271 for (size_t i = 0; i!= mesh.numVertices(); ++i)
272 {
273 eval_into( mesh.vertex(i).topRows(pDim), tmp );
274 const index_t gd = math::min(3,gDim);
275 mesh.vertex(i).topRows(gd) = tmp.topRows(gd);
276 }
277
278}
279template<class T>
280std::vector<gsGeometry<T>* > gsGeometry<T>::uniformSplit(index_t) const
281{
282 GISMO_NO_IMPLEMENTATION
283}
284
285template<class T>
286gsGeometrySlice<T> gsGeometry<T>::getIsoParametricSlice(index_t dir_fixed, T par) const
287{
288 return gsGeometrySlice<T>(this,dir_fixed,par);
289}
290
291template<class T>
292typename gsMatrix<T>::RowXpr
293gsGeometry<T>::coefAtCorner(boxCorner const & c)
294{
295 return this->m_coefs.row(this->basis().functionAtCorner(c));
296}
297
298template<class T>
299typename gsMatrix<T>::ConstRowXpr
300gsGeometry<T>::coefAtCorner(boxCorner const & c) const
301{
302 return this->m_coefs.row(this->basis().functionAtCorner(c));
303}
304
305template<class T>
306void gsGeometry<T>::uniformRefine(int numKnots, int mul, short_t const dir)
307{
308 this->basis().uniformRefine_withCoefs( m_coefs, numKnots, mul, dir);
309}
310
311template<class T>
312void gsGeometry<T>::uniformCoarsen(int numKnots) // todo: int dir = -1
313{
314 this->basis().uniformCoarsen_withCoefs( m_coefs, numKnots);
315}
316
317template<class T>
318void gsGeometry<T>::refineElements( std::vector<index_t> const & boxes )
319{
320 this->basis().refineElements_withCoefs(this->m_coefs, boxes );
321}
322
323template<class T>
324void gsGeometry<T>::unrefineElements( std::vector<index_t> const & boxes )
325{
326 this->basis().unrefineElements_withCoefs(this->m_coefs, boxes );
327}
328
329template<class T>
330inline typename gsGeometry<T>::uPtr gsGeometry<T>::coord(const index_t c) const {return this->basis().makeGeometry( this->coefs().col(c) ); }
331
332template<class T>
333short_t gsGeometry<T>::degree(const short_t & i) const
334 //{ return this->basisComponent(i).degree(); };
335 { return this->basis().degree(i); }
336
337
338template<class T>
339T gsGeometry<T>::closestPointTo(const gsVector<T> & pt,
340 gsVector<T> & result,
341 const T accuracy,
342 const bool useInitialPoint) const
343{
344 GISMO_ASSERT( pt.rows() == targetDim(), "Invalid input point." <<
345 pt.rows() <<"!="<< targetDim() );
346#if false
347 gsSquaredDistance<T> dist2(*this, pt);
348 gsMinimizer<T> fmin(dist2);
349 fmin.solve();
350 result = fmin.currentDesign();
351#else
352 gsSquaredDistance<T> dist2(*this, pt);
353 result = useInitialPoint ? dist2.argMin(accuracy*accuracy, 100, result)
354 : dist2.argMin(accuracy*accuracy, 100) ;
355#endif
356 return math::sqrt( dist2.eval(result).value() );
357}
358
359template<class T>
360T gsGeometry<T>::directedHausdorffDistance(const gsGeometry & other, const index_t nsamples, const T accuracy) const
361{
362 // Sample points on *this
363 gsMatrix<T> uv = gsPointGrid<T>(this->support(),nsamples);
364 gsMatrix<T> pts;
365 this->eval_into(uv,pts);
366 // Find the maximum of the closest point on *other from the set of pts
367 T maxDist=std::numeric_limits<T>::min();
368 gsVector<T> tmp;
369 for (index_t k=0; k!=pts.cols(); k++)
370 {
371 maxDist = std::max(maxDist,other.closestPointTo(pts.col(k),tmp,accuracy,false));
372 }
373 return math::sqrt(2*maxDist); // euclidean distance since closestPointTo uses 1/2*||x-y||^2, see gsSquaredDistance
374}
375
376template<class T>
377T gsGeometry<T>::HausdorffDistance(const gsGeometry & other, const index_t nsamples, const T accuracy, bool directed) const
378{
379 T this2other, other2this;
380 this2other = this->directedHausdorffDistance(other,nsamples,accuracy);
381 if (directed)
382 return this2other;
383 else
384 {
385 other2this = other.directedHausdorffDistance(*this,nsamples,accuracy);
386 return std::max(other2this,this2other);
387 }
388}
389
390
391// Recovers the points of the geometry from the given points and parameters
392template<class T>
393void gsGeometry<T>::recoverPoints(gsMatrix<T> & xyz, gsMatrix<T> & uv, index_t k,
394 const T accuracy) const
395{
396 gsVector<index_t> ind(xyz.rows()-1);
397 for (index_t i = 0; i!= xyz.rows(); ++i)
398 if (i<k) ind[i]=i;
399 else if (i>k) ind[i-1]=i;
400
401 gsMatrix<T> pt = xyz(ind,gsEigen::all);
402 gsFuncCoordinate<T> fc(*this, give(ind));
403 fc.invertPoints(pt,uv,accuracy,false);
404 xyz = this->eval(uv);
405 //possible check: pt close to xyz
406}
407
408
409template<class T>
410std::ostream & gsGeometry<T>::print(std::ostream &os) const
411{
412 os << "Geometry "<< "R^"<< this->parDim() <<
413 " --> R^"<< this->geoDim()<< ", #control pnts= "<< coefsSize() <<
414 ": "<< coef(0) <<" ... "<< coef(this->coefsSize()-1);
415 os<<"\nBasis:\n" << this->basis();
416 return os;
417}
418
419template<class T>
422
423template<class T>
424void gsGeometry<T>::toMesh(gsMesh<T> &, int) const
425{ GISMO_NO_IMPLEMENTATION }
426
427template<class T>
428typename gsGeometry<T>::uPtr
429gsGeometry<T>::approximateLinearly() const
430{ GISMO_NO_IMPLEMENTATION }
431
432template<class T>
435
436template<class T>
437std::vector<gsGeometry<T> *> gsGeometry<T>::boundary() const
438{
439 // TO DO: get boundary curves, using basis().boundary();
440 GISMO_NO_IMPLEMENTATION
441}
442
443template<class T>
448
449template<class T>
450void gsGeometry<T>::degreeElevate(short_t const i, short_t const dir)
451{
452 typename gsBasis<T>::uPtr b = m_basis->clone();
453 b->degreeElevate(i, dir);
454 gsMatrix<T> iVals, iPts = b->anchors();
455 this->eval_into(iPts, iVals);
456 typename gsGeometry<T>::uPtr g = b->interpolateData(iVals, iPts);
457
458 std::swap(m_basis, g->m_basis);
459 g->coefs().swap(this->coefs());
460}
461
462template<class T>
463void gsGeometry<T>::degreeReduce(short_t const i, short_t const dir)
464{
465 typename gsBasis<T>::uPtr b = m_basis->clone();
466 b->degreeReduce(i, dir);
467 gsMatrix<T> iVals, iPts = b->anchors();
468 this->eval_into(iPts, iVals);
469 typename gsGeometry<T>::uPtr g = b->interpolateData(iVals, iPts);
470
471 std::swap(m_basis, g->m_basis);
472 g->coefs().swap(this->coefs());
473}
474
475template<class T>
476void gsGeometry<T>::degreeIncrease(short_t const i, short_t const dir)
477{
478 typename gsBasis<T>::uPtr b = m_basis->clone();
479 b->degreeIncrease(i, dir);
480 gsMatrix<T> iVals, iPts = b->anchors();
481 this->eval_into(iPts, iVals);
482 typename gsGeometry<T>::uPtr g = b->interpolateData(iVals, iPts);
483
484 std::swap(m_basis, g->m_basis);
485 g->coefs().swap(this->coefs());
486}
487
488template<class T>
489void gsGeometry<T>::degreeDecrease(short_t const i, short_t const dir)
490{
491 typename gsBasis<T>::uPtr b = m_basis->clone();
492 b->degreeDecrease(i, dir);
493 gsMatrix<T> iVals, iPts = b->anchors();
494 this->eval_into(iPts, iVals);
495 typename gsGeometry<T>::uPtr g = b->interpolateData(iVals, iPts);
496
497 std::swap(m_basis, g->m_basis);
498 g->coefs().swap(this->coefs());
499}
500
501template<class T> void
502gsGeometry<T>::hessian_into(const gsMatrix<T>& u, gsMatrix<T> & result,
503 index_t coord) const
504{
505 const unsigned d = this->domainDim();
506 GISMO_ASSERT( coord<targetDim(),"Invalid coordinate function "<<coord);
507
508 gsMatrix<T> B, tmp(d,d);
509 gsMatrix<index_t> ind;
510
511 // coefficient matrix row k = coef. of basis function k
512 const gsMatrix<T>& C = this->m_coefs;
513 // col j = nonzero second derivatives at column point u(..,j)
514 m_basis->deriv2_into(u, B) ;
515 // col j = indices of active functions at column point u(..,j)
516 m_basis->active_into(u, ind);
517
518 result.setZero(d,d);
519 static const index_t j = 0;// just one column
520 //for ( unsigned j=0; j< u.cols(); j++ ) // for all points (columns of u)
521
522 for ( index_t i=0; i< ind.rows() ; i++ ) // for all non-zero basis functions)
523 {
524 unsigned r = i*d*(d+1)/2;
525 unsigned m = d;
526 //construct the Hessian of basis function ind(i,0)
527 for (unsigned k=0; k<d; ++k ) // for all rows
528 {
529 tmp(k,k) = B(r+k,j);
530 for (unsigned l=k+1; l<d; ++l ) // for all cols
531 tmp(k,l) = tmp(l,k) = B(r + m++,0);
532 }
533 result += C(ind(i,j), coord) * tmp;
534 }
535}
536
537template<class T>
538void gsGeometry<T>::controlNet( gsMesh<T> & mesh) const
539{ basis().connectivity(m_coefs, mesh); }
540
541
542
543template <typename T>
544void extractRows( const gsMatrix<T> &in, typename gsMatrix<index_t>::constColumn actives, gsMatrix<T> &out)
545{
546 out.resize(actives.rows(), in.cols());
547 for (index_t r=0; r<actives.rows();++r)
548 out.row(r)=in.row(actives(r,0));
549}
550
551template <class T>
552void
553gsGeometry<T>::compute(const gsMatrix<T> & in, gsFuncData<T> & out) const
554{
555 const unsigned flags = out.flags | NEED_ACTIVE;
556 const index_t numPt = in.cols();
557 const index_t numCo = m_coefs.cols();
558
559 gsFuncData<T> tmp(flags);
560 this->basis().compute(in, tmp);
561
562 out.values.resize(out.maxDeriv()+1);
563 out.dim.first = tmp.dim.first;
564 out.dim.second = numCo;
565 if ( flags & SAME_ELEMENT )
566 {
567 gsMatrix<T> coefM;
568 extractRows(m_coefs,tmp.active(0),coefM);
569
570 if (flags & NEED_VALUE)
571 out.values[0].noalias()=coefM.transpose()*tmp.values[0];
572 if (flags & NEED_DERIV)
573 {
574 const index_t derS = tmp.derivSize();
575 out.values[1].resize(derS*numCo,numPt);
576 for (index_t p=0; p< numPt; ++p)
577 out.values[1].reshapeCol(p, derS, numCo).noalias() = tmp.deriv(p)*coefM;
578 }
579 if (flags & NEED_DERIV2)
580 {
581 const index_t derS = tmp.deriv2Size();
582 out.values[2].resize(derS*numCo,numPt);
583 for (index_t p=0; p< numPt; ++p)
584 out.values[2].reshapeCol(p, derS, numCo).noalias() = tmp.deriv2(p)*coefM;
585 }
586 if (flags & NEED_ACTIVE)
587 this->active_into(in.col(0), out.actives);
588 }
589 else
590 {
591 gsMatrix<T> coefM;
592 const index_t derS = tmp.derivSize();
593 const index_t der2S = tmp.deriv2Size();
594
595 if (flags & NEED_VALUE) out.values[0].resize(numCo,numPt);
596 if (flags & NEED_DERIV) out.values[1].resize(numCo*derS,numPt);
597 if (flags & NEED_DERIV2) out.values[2].resize(numCo*der2S,numPt);
598 if (flags & NEED_ACTIVE) this->active_into(in, out.actives);
599
600 for (index_t p=0; p<numPt;++p)
601 {
602 extractRows(m_coefs,tmp.active(p),coefM);
603 if (flags & NEED_VALUE)
604 out.values[0].reshapeCol(p,1,numCo).noalias() = tmp.eval(p)*coefM;
605 if (flags & NEED_DERIV)
606 out.values[1].reshapeCol(p, derS, numCo).noalias() = tmp.deriv(p)*coefM;
607 if (flags & NEED_DERIV2)
608 out.values[2].reshapeCol(p, der2S, numCo).noalias() = tmp.deriv2(p)*coefM;
609 }
610 }
611}
612
613template<class T>
614void gsGeometry<T>::toggleOrientation()
615{
616 GISMO_NO_IMPLEMENTATION
617}
618
619template<class T>
620std::vector<boxSide> gsGeometry<T>::locateOn(const gsMatrix<T> & u, gsVector<bool> & onGeo, gsMatrix<T> & preIm, bool lookForBoundary, real_t tol) const
621{
622 onGeo.resize(u.cols());
623 std::vector<boxSide> sides(u.cols());
624
625 for(index_t i = 0; i < onGeo.size(); i++)
626 onGeo(i) = false;
627
628 preIm.resize(geoDim(), u.cols());
629 gsMatrix<T> pr = this->parameterRange(), tmp;
630
631 for(index_t i = 0; i < u.cols(); i++)
632 {
633 this->invertPoints(u.col(i), tmp, tol);
634 pr = this->parameterRange();
635 //if ((tmp.array() >= pr.col(0).array()).all()
636 // && (tmp.array() <= pr.col(1).array()).all())
637 if ((tmp.array() >= pr.col(0).array() - 1.e-4).all()
638 && (tmp.array() <= pr.col(1).array() + 1.e-4).all()) // be careful! if u is on the boundary then we may get a wrong result
639 // the tolerance is due to imprecisions in the geometry map. E.g. If a circle is rotated then the corner need
640 // not to lie exactly on the interface of the neighbour patch since we use only B-splines for the modelling
641 // TODO: Maybe find a better solution!
642 {
643 onGeo(i) = true;
644 preIm.col(i) = tmp;
645
646 if (lookForBoundary == true)
647 {
648 boxSide s;
649 for (int d = 0; d < geoDim(); d++) {
650 if ((math::abs(tmp(d, 0) - pr(d, 0)) < tol))
651 {
652 s.m_index = 2*d+1; // lower
653 break;
654 }
655
656 if ((math::abs(tmp(d, 0) - pr(d, 1)) < tol))
657 {
658 s.m_index = 2 * d + 2; // upper
659 break;
660 }
661 }
662 sides[i] = s;
663 }
664 }
665 }
666
667 return sides;
668}
669
670
671} // namespace gismo
gismo::boxSide
Struct which represents a certain side of a box.
Definition gsBoundary.h:85
gismo::boxSide::m_index
short_t m_index
Index of the side.
Definition gsBoundary.h:92
gismo::gsBasis::degreeDecrease
virtual void degreeDecrease(short_t const &i=1, short_t const dir=-1)
Lower the degree of the basis by the given amount, preserving knots multiplicity.
Definition gsBasis.hpp:641
gismo::gsBasis::interpolateData
memory::unique_ptr< gsGeometry< T > > interpolateData(gsMatrix< T > const &vals, gsMatrix< T > const &pts) const
Applies interpolation given the parameter values pts and values vals.
Definition gsBasis.hpp:240
gismo::gsBasis::degreeReduce
virtual void degreeReduce(short_t const &i=1, short_t const dir=-1)
Reduce the degree of the basis by the given amount, preserve smoothness.
Definition gsBasis.hpp:633
gismo::gsBasis::degreeIncrease
virtual void degreeIncrease(short_t const &i=1, short_t const dir=-1)
Elevate the degree of the basis by the given amount, preserve knots multiplicity.
Definition gsBasis.hpp:637
gismo::gsBasis::uPtr
memory::unique_ptr< gsBasis > uPtr
Unique pointer for gsBasis.
Definition gsBasis.h:89
gismo::gsBasis::anchors
gsMatrix< T > anchors() const
Returns the anchor points that represent the members of the basis. There is exactly one anchor point ...
Definition gsBasis.h:437
gismo::gsBasis::makeGeometry
virtual memory::unique_ptr< gsGeometry< T > > makeGeometry(gsMatrix< T > coefs) const =0
Create a gsGeometry of proper type for this basis with the given coefficient matrix.
gismo::gsBasis::degreeElevate
virtual void degreeElevate(short_t const &i=1, short_t const dir=-1)
Elevate the degree of the basis by the given amount, preserve smoothness.
Definition gsBasis.hpp:629
gismo::gsFuncCoordinate
Represents a certain component of a vector-valued function.
Definition gsFuncCoordinate.h:35
gismo::gsFunctionSet::clone
uPtr clone()
Clone methode. Produceds a deep copy inside a uPtr.
gismo::gsFunctionSet::eval
gsMatrix< T > eval(const gsMatrix< T > &u) const
Evaluate the function,.
Definition gsFunctionSet.hpp:120
gismo::gsFunction
A function from a n-dimensional domain to an m-dimensional image.
Definition gsFunction.h:60
gismo::gsFunction::invertPoints
virtual void invertPoints(const gsMatrix< T > &points, gsMatrix< T > &result, const T accuracy=1e-6, const bool useInitialPoint=false) const
Definition gsFunction.hpp:199
gismo::gsGeometrySlice
gsGeometrySlice is a class representing an iso parametric slice of a geometry object....
Definition gsGeometrySlice.h:28
gismo::gsGeometry
Abstract base class representing a geometry map.
Definition gsGeometry.h:93
gismo::gsGeometry::deriv2_into
virtual void deriv2_into(const gsMatrix< T > &u, gsMatrix< T > &result) const
Evaluate second derivatives of the function at points u into result.
Definition gsGeometry.hpp:174
gismo::gsGeometry::coefs
gsMatrix< T > & coefs()
Definition gsGeometry.h:340
gismo::gsGeometry::HausdorffDistance
T HausdorffDistance(const gsGeometry &other, const index_t nsamples=1000, const T accuracy=1e-6, const bool directed=false) const
Computes the Hausdorff distance between *this to other.
Definition gsGeometry.hpp:377
gismo::gsGeometry::boundary
std::vector< gsGeometry * > boundary() const
Get boundary of this geometry as a vector of new gsGeometry instances.
Definition gsGeometry.hpp:437
gismo::gsGeometry::uniformCoarsen
virtual void uniformCoarsen(int numKnots=1)
Coarsen the geometry uniformly, removing numKnots new knots into each knot span.
Definition gsGeometry.hpp:312
gismo::gsGeometry::coefAtCorner
gsMatrix< T >::RowXpr coefAtCorner(boxCorner const &c)
Returns the control point at corner c.
Definition gsGeometry.hpp:293
gismo::gsGeometry::degreeElevate
virtual void degreeElevate(short_t const i=1, short_t const dir=-1)
Elevate the degree by the given amount i for the direction dir. If dir is -1 then degree elevation is...
Definition gsGeometry.hpp:450
gismo::gsGeometry::degreeIncrease
virtual void degreeIncrease(short_t const i=1, short_t const dir=-1)
Elevate the degree by the given amount i for the direction dir. If dir is -1 then degree elevation is...
Definition gsGeometry.hpp:476
gismo::gsGeometry::degree
short_t degree(const short_t &i) const
Returns the degree wrt direction i.
Definition gsGeometry.hpp:333
gismo::gsGeometry::coDim
short_t coDim() const
Co-dimension of the geometric object.
Definition gsGeometry.hpp:187
gismo::gsGeometry::evaluateMesh
void evaluateMesh(gsMesh< T > &mesh) const
Definition gsGeometry.hpp:255
gismo::gsGeometry::uPtr
memory::unique_ptr< gsGeometry > uPtr
Unique pointer for gsGeometry.
Definition gsGeometry.h:100
gismo::gsGeometry::locateOn
std::vector< boxSide > locateOn(const gsMatrix< T > &u, gsVector< bool > &onG2, gsMatrix< T > &preIm, bool lookForBoundary=false, real_t tol=1.e-6) const
Get back the side of point u.
Definition gsGeometry.hpp:620
gismo::gsGeometry::evalAllDers_into
virtual void evalAllDers_into(const gsMatrix< T > &u, int n, std::vector< gsMatrix< T > > &result, bool sameElement=false) const
Evaluate the nonzero functions and their derivatives up to order n at points u into result.
Definition gsGeometry.hpp:178
gismo::gsGeometry::eval_into
void eval_into(const gsMatrix< T > &u, gsMatrix< T > &result) const
Evaluate the function at points u into result.
Definition gsGeometry.hpp:166
gismo::gsGeometry::merge
virtual void merge(gsGeometry *other)
Merge the given other geometry into this one.
Definition gsGeometry.hpp:420
gismo::gsGeometry::gsGeometry
gsGeometry()
Default constructor. Note: Derived constructors (except for the default) should assign m_basis to a v...
Definition gsGeometry.h:111
gismo::gsGeometry::hessian_into
virtual void hessian_into(const gsMatrix< T > &u, gsMatrix< T > &result, index_t coord) const
Definition gsGeometry.hpp:502
gismo::gsGeometry::compute
virtual void compute(const gsMatrix< T > &in, gsFuncData< T > &out) const
Computes function data.
Definition gsGeometry.hpp:553
gismo::gsGeometry::uniformSplit
virtual std::vector< gsGeometry< T > * > uniformSplit(index_t dir=-1) const
Definition gsGeometry.hpp:280
gismo::gsGeometry::outerNormal_into
void outerNormal_into(const gsMatrix< T > &u, gsMatrix< T > &result) const
Computes the outer normals at parametric points u.
Definition gsGeometry.hpp:433
gismo::gsGeometry::recoverPoints
void recoverPoints(gsMatrix< T > &xyz, gsMatrix< T > &uv, index_t k, const T accuracy) const
Recovers the points of the geometry from the given points xyz and parameters uv.
Definition gsGeometry.hpp:393
gismo::gsGeometry::degreeReduce
virtual void degreeReduce(short_t const i=1, short_t const dir=-1)
Reduces the degree by the given amount i for the direction dir. If dir is -1 then degree reduction is...
Definition gsGeometry.hpp:463
gismo::gsGeometry::directedHausdorffDistance
T directedHausdorffDistance(const gsGeometry &other, const index_t nsamples=1000, const T accuracy=1e-6) const
Definition gsGeometry.hpp:360
gismo::gsGeometry::domainDim
virtual short_t domainDim() const
Dimension d of the parameter domain (overriding gsFunction::domainDim()).
Definition gsGeometry.hpp:184
gismo::gsGeometry::basis
virtual const gsBasis< T > & basis() const =0
Returns a const reference to the basis of the geometry.
gismo::gsGeometry::iface
virtual gsGeometry::uPtr iface(const boundaryInterface &bi, const gsGeometry &other) const
Computes and returns the interface with other as a new geometry.
Definition gsGeometry.hpp:232
gismo::gsGeometry::component
gsGeometry::uPtr component(boxComponent const &bc) const
Get parametrization of box component bc as a new gsGeometry uPtr.
Definition gsGeometry.hpp:240
gismo::gsGeometry::uniformRefine
virtual void uniformRefine(int numKnots=1, int mul=1, short_t const dir=-1)
Refine the geometry uniformly, inserting numKnots new knots into each knot span.
Definition gsGeometry.hpp:306
gismo::gsGeometry::parDim
short_t parDim() const
Dimension d of the parameter domain (same as domainDim()).
Definition gsGeometry.hpp:190
gismo::gsGeometry::deriv_into
virtual void deriv_into(const gsMatrix< T > &u, gsMatrix< T > &result) const
Evaluate derivatives of the function at points u into result.
Definition gsGeometry.hpp:170
gismo::gsGeometry::m_basis
gsBasis< T > * m_basis
Pointer to the basis of this geometry.
Definition gsGeometry.h:632
gismo::gsGeometry::support
gsMatrix< T > support() const
Returns the range of parameters (same as parameterRange())
Definition gsGeometry.hpp:193
gismo::gsGeometry::closestPointTo
T closestPointTo(const gsVector< T > &pt, gsVector< T > &result, const T accuracy=1e-6, const bool useInitialPoint=false) const
Definition gsGeometry.hpp:339
gismo::gsGeometry::m_coefs
gsMatrix< T > m_coefs
Coefficient matrix of size coefsSize() x geoDim()
Definition gsGeometry.h:629
gismo::gsGeometry::m_id
size_t m_id
Definition gsGeometry.h:636
gismo::gsGeometry::print
virtual std::ostream & print(std::ostream &os) const
Prints the object as a string.
Definition gsGeometry.hpp:410
gismo::gsGeometry::controlNet
void controlNet(gsMesh< T > &mesh) const
Return the control net of the geometry.
Definition gsGeometry.hpp:538
gismo::gsGeometry::getIsoParametricSlice
gsGeometrySlice< T > getIsoParametricSlice(index_t dir_fixed, T par) const
Definition gsGeometry.hpp:286
gismo::gsGeometry::refineElements
void refineElements(std::vector< index_t > const &boxes)
Refines the basis and adjusts the coefficients to keep the geometry the same.
Definition gsGeometry.hpp:318
gismo::gsGeometry::insertKnot
virtual void insertKnot(T knot, index_t dir, index_t i=1)
Inserts knot knot at direction dir, i times.
Definition gsGeometry.hpp:444
gismo::gsGeometry::degreeDecrease
virtual void degreeDecrease(short_t const i=1, short_t const dir=-1)
Reduces the degree by the given amount i for the direction dir. If dir is -1 then degree reduction is...
Definition gsGeometry.hpp:489
gismo::gsGeometry::parameterRange
gsMatrix< T > parameterRange() const
Returns the range of parameters as a matrix with two columns, [lower upper].
Definition gsGeometry.hpp:198
gismo::gsMatrix
A matrix with arbitrary coefficient type and fixed or dynamic size.
Definition gsMatrix.h:41
gismo::gsMatrix::reshapeCol
gsAsMatrix< T, Dynamic, Dynamic > reshapeCol(index_t c, index_t n, index_t m)
Returns column c of the matrix resized to n x m matrix This function assumes that the matrix is size ...
Definition gsMatrix.h:231
gismo::gsMatrix::at
T at(index_t i) const
Returns the i-th element of the vectorization of the matrix.
Definition gsMatrix.h:211
gismo::gsMesh
Class Representing a triangle mesh with 3D vertices.
Definition gsMesh.h:32
gismo::gsSquaredDistance
Squared distance function from a fixed point to a gsGeometry.
Definition gsGeometry.hpp:32
gismo::gsSquaredDistance::evalAllDers_into
void evalAllDers_into(const gsMatrix< T > &u, int n, std::vector< gsMatrix< T > > &result, bool sameElement=false) const
Evaluate the nonzero functions and their derivatives up to order n at points u into result.
Definition gsGeometry.hpp:45
gismo::gsSquaredDistance::targetDim
short_t targetDim() const
Dimension of the target space.
Definition gsGeometry.hpp:104
gismo::gsSquaredDistance::eval_into
void eval_into(const gsMatrix< T > &u, gsMatrix< T > &result) const
Evaluate the function at points u into result.
Definition gsGeometry.hpp:38
gismo::gsSquaredDistance::domainDim
short_t domainDim() const
Dimension of the (source) domain.
Definition gsGeometry.hpp:103
gismo::gsSquaredDistance::deriv_into
void deriv_into(const gsMatrix< T > &u, gsMatrix< T > &result) const
Evaluate derivatives of the function at points u into result.
Definition gsGeometry.hpp:76
gismo::gsVector
A vector with arbitrary coefficient type and fixed or dynamic size.
Definition gsVector.h:37
gismo::gsVector::at
T at(index_t i) const
Returns the i-th element of the vector.
Definition gsVector.h:177
gsBasis.h
Provides declaration of Basis abstract interface.
short_t
#define short_t
Definition gsConfig.h:35
index_t
#define index_t
Definition gsConfig.h:32
GISMO_NO_IMPLEMENTATION
#define GISMO_NO_IMPLEMENTATION
Definition gsDebug.h:129
GISMO_ASSERT
#define GISMO_ASSERT(cond, message)
Definition gsDebug.h:89
gsFuncCoordinate.h
Provides definition of the FuncCoordinate class.
gsFuncData.h
This object is a cache for computed values from an evaluator.
gsGeometrySlice.h
Provides declaration of the gsGeometrySlice class.
gsMesh.h
Provides declaration of the Mesh class.
gsPointGrid.h
Provides functions to generate structured point data.
gismo
The G+Smo namespace, containing all definitions for the library.
gismo::SAME_ELEMENT
@ SAME_ELEMENT
Enable optimizations based on the assumption that all evaluation points are in the same bezier domain...
Definition gsForwardDeclarations.h:89
gismo::NEED_VALUE
@ NEED_VALUE
Value of the object.
Definition gsForwardDeclarations.h:72
gismo::NEED_DERIV2
@ NEED_DERIV2
Second derivatives.
Definition gsForwardDeclarations.h:80
gismo::NEED_DERIV
@ NEED_DERIV
Gradient of the object.
Definition gsForwardDeclarations.h:73
gismo::NEED_ACTIVE
@ NEED_ACTIVE
Active function ids.
Definition gsForwardDeclarations.h:84
gismo::give
S give(S &x)
Definition gsMemory.h:266
gismo::boundaryInterface
Struct which represents an interface between two patches.
Definition gsBoundary.h:650
gismo::boxComponent
Struct which represents a certain component (interior, face, egde, corner).
Definition gsBoundary.h:445
gismo::boxCorner
Struct which represents a certain corner of a hyper-cube.
Definition gsBoundary.h:292