/
gsGeoUtils.hpp
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/
gsGeoUtils.hpp
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/** @file gsGeoUtils.hpp
@brief Provides isogeometric meshing and modelling routines.
This file is part of the G+Smo library.
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
Author(s):
A.Shamanskiy (2016 - ...., TU Kaiserslautern)
*/
#pragma once
#include <gsElasticity/gsGeoUtils.h>
#include <gsCore/gsField.h>
#include <gsCore/gsFuncData.h>
#include <gsCore/gsFunctionExpr.h>
#include <gsNurbs/gsBSpline.h>
#include <gsNurbs/gsTensorBSplineBasis.h>
#include <gsNurbs/gsTensorNurbs.h>
#include <gsAssembler/gsQuadRule.h>
#include <gsAssembler/gsQuadrature.h>
#include <gsModeling/gsCoonsPatch.h>
#include <gsElasticity/gsElasticityAssembler.h>
#include <gsElasticity/gsElasticityFunctions.h>
#include <gsElasticity/gsWriteParaviewMultiPhysics.h>
#include <gsUtils/gsMesh/gsMesh.h>
#include <gsIO/gsWriteParaview.h>
namespace gismo
{
//-----------------------------------//
//--------- Mesh Analysis -----------//
//-----------------------------------//
template <class T>
void plotGeometry(gsMultiPatch<T> const & domain, std::string fileName, index_t numSamples)
{
std::string fileNameOnly = gsFileManager::getFilename(fileName);
gsParaviewCollection collectionMesh(fileName + "_mesh");
gsParaviewCollection collectionJac(fileName + "_jac");
index_t res;
bool plotJac = true;
if (numSamples == 0)
plotJac = false;
gsPiecewiseFunction<T> dets;
for (size_t p = 0; p < domain.nPatches(); ++p)
dets.addPiecePointer(new gsDetFunction<T>(domain,p));
gsField<> detField(domain,dets,true);
std::map<std::string,const gsField<> *> fields;
fields["Jacobian"] = &detField;
gsWriteParaviewMultiPhysics(fields,fileName,numSamples,true);
for (size_t p = 0; p < domain.nPatches(); ++p)
{
collectionMesh.addPart(fileNameOnly + "_mesh.vtp",0,"Mesh",p);
if (plotJac)
collectionJac.addPart(fileNameOnly + ".vts",0,"Jac",p);
else
res = system(("rm " + fileName + util::to_string(p) + ".vts").c_str());
GISMO_ENSURE(res == 0, "Problems with deleting files\n");
}
res = system(("rm " + fileName + ".pvd").c_str());
GISMO_ENSURE(res == 0, "Problems with deleting files\n");
(void)res;
collectionMesh.save();
if (plotJac)
collectionJac.save();
}
template <class T>
void plotGeometry(const gsMultiPatch<T> & domain, std::string const & fileName,
gsParaviewCollection & collection, index_t step)
{
for (size_t p = 0; p < domain.nPatches(); ++p)
{
gsMesh<T> mesh(domain.basis(p),8);
domain.patch(p).evaluateMesh(mesh);
std::string patchFileName = fileName + util::to_string(step) + "_" + util::to_string(p);
gsWriteParaview(mesh,patchFileName,false);
collection.addPart(gsFileManager::getFilename(patchFileName),step,"",p);
}
}
template <class T>
void plotDeformation(const gsMultiPatch<T> & initDomain, const std::vector<gsMultiPatch<T> > & displacements,
std::string fileName, index_t numSamplingPoints)
{
gsInfo << "Plotting deformed configurations...\n";
std::string fileNameOnly = gsFileManager::getFilename(fileName);
gsParaviewCollection collectionMesh(fileName + "_mesh");
gsParaviewCollection collectionJac(fileName + "_jac");
index_t res;
gsMultiPatch<T> configuration;
for (size_t p = 0; p < initDomain.nPatches(); ++p)
configuration.addPatch(initDomain.patch(p).clone());
gsPiecewiseFunction<T> dets;
for (size_t p = 0; p < configuration.nPatches(); ++p)
dets.addPiecePointer(new gsDetFunction<T>(configuration,p));
bool plotJac = true;
if (numSamplingPoints == 0)
plotJac = false;
gsProgressBar bar;
bar.display(0, displacements.size());
gsField<T> detField(configuration,dets,true);
std::map<std::string,const gsField<T> *> fields;
fields["Jacobian"] = &detField;
gsWriteParaviewMultiPhysics(fields,fileName+util::to_string(0),numSamplingPoints == 0 ? 1 : numSamplingPoints,true);
for (size_t p = 0; p < configuration.nPatches(); ++p)
{
collectionMesh.addPart(fileNameOnly + util::to_string(0) + util::to_string(p) + "_mesh.vtp",0,"Mesh",p);
if (plotJac)
collectionJac.addPart(fileNameOnly + util::to_string(0) + util::to_string(p) + ".vts",0,"Jac",p);
else
{
res = system(("rm " + fileName + util::to_string(0) + util::to_string(p) + ".vts").c_str());
GISMO_ENSURE(res == 0, "Problems with deleting files\n");
}
}
res = system(("rm " + fileName + util::to_string(0) + ".pvd").c_str());
GISMO_ENSURE(res == 0, "Problems with deleting files\n");
for (size_t s = 0; s < displacements.size(); ++s)
{
bar.display(s+1, displacements.size());
for (size_t p = 0; p < configuration.nPatches(); ++p)
{
configuration.patch(p).coefs() += displacements[s].patch(p).coefs();
if (s > 0)
configuration.patch(p).coefs() -= displacements[s-1].patch(p).coefs();
}
gsWriteParaviewMultiPhysics(fields,fileName+util::to_string(s+1),numSamplingPoints == 0 ? 1 : numSamplingPoints,true);
for (size_t p = 0; p < configuration.nPatches(); ++p)
{
collectionMesh.addPart(fileNameOnly + util::to_string(s+1) + util::to_string(p) + "_mesh.vtp",s+1,"Mesh",p);
if (plotJac)
collectionJac.addPart(fileNameOnly + util::to_string(s+1) + util::to_string(p) + ".vts",s+1,"Jac",p);
else
{
res = system(("rm " + fileName + util::to_string(s+1) + util::to_string(p) + ".vts").c_str());
GISMO_ENSURE(res == 0, "Problems with deleting files\n");
}
}
res = system(("rm " + fileName + util::to_string(s+1) + ".pvd").c_str());
GISMO_ENSURE(res == 0, "Problems with deleting files\n");
}
collectionMesh.save();
if (plotJac)
collectionJac.save();
(void)res;
}
template <class T>
void plotDeformation(const gsMultiPatch<T> & initDomain, const gsMultiPatch<T> & displacement,
std::string const & fileName, gsParaviewCollection & collection, index_t step)
{
GISMO_ENSURE(initDomain.nPatches() == displacement.nPatches(), "Wrong number of patches! Geometry has " +
util::to_string(initDomain.nPatches()) + " patches. Displacement has " + util::to_string(displacement.nPatches()) + " patches.");
gsMultiPatch<T> configuration;
for (size_t p = 0; p < initDomain.nPatches(); ++p)
{
configuration.addPatch(initDomain.patch(p).clone());
configuration.patch(p).coefs() += displacement.patch(p).coefs();
}
for (size_t p = 0; p < configuration.nPatches(); ++p)
{
gsMesh<T> mesh(configuration.basis(p),8);
configuration.patch(p).evaluateMesh(mesh);
std::string patchFileName = fileName + util::to_string(step) + "_" + util::to_string(p);
gsWriteParaview(mesh,patchFileName,false);
collection.addPart(gsFileManager::getFilename(patchFileName),step,"",p);
}
}
template <class T>
index_t checkGeometry(gsMultiPatch<T> const & domain)
{
index_t corruptedPatch = -1;
bool continueIt = true;
for (size_t p = 0; p < domain.nPatches() && continueIt; ++p)
{
#pragma omp parallel
{
gsMapData<T> md;
md.flags = NEED_DERIV;
gsMatrix<T> points;
gsVector<index_t> numNodes(domain.dim());
for (short_t i = 0; i < domain.dim(); ++i)
numNodes.at(i) = domain.basis(p).degree(i)+1;
gsQuadRule<T> quRule = gsQuadrature::get<T>(gsQuadrature::GaussLegendre,numNodes);
typename gsBasis<T>::domainIter domIt = domain.basis(p).makeDomainIterator(boundary::none);
#ifdef _OPENMP
const int tid = omp_get_thread_num();
const int nt = omp_get_num_threads();
for ( domIt->next(tid); domIt->good() && continueIt; domIt->next(nt) )
#else
for (; domIt->good() && continueIt; domIt->next() )
#endif
{
genSamplingPoints(domIt->lowerCorner(),domIt->upperCorner(),quRule,points);
md.points = points;
domain.patch(p).computeMap(md);
for (index_t q = 0; q < points.cols() && continueIt; ++q)
if (md.jacobian(q).determinant() <= 0)
{
gsInfo << "Bad patch: " << p << "\nBad point:\n" << points.col(q) << "\nDet: " << md.jacobian(q).determinant() << std::endl;
corruptedPatch = p;
continueIt = false;
}
}
}
}
return corruptedPatch;
}
template <class T>
index_t checkDisplacement(gsMultiPatch<T> const & domain, gsMultiPatch<T> const & displacement)
{
index_t corruptedPatch = -1;
bool continueIt = true;
for (size_t p = 0; p < domain.nPatches() && continueIt; ++p)
{
#pragma omp parallel
{
gsMapData<T> mdG, mdU;
mdG.flags = NEED_DERIV;
mdU.flags = NEED_DERIV;
gsMatrix<T> points;
gsVector<index_t> numNodes(domain.dim());
for (short_t i = 0; i < domain.dim(); ++i)
numNodes.at(i) = displacement.basis(p).degree(i)+1;
gsQuadRule<T> quRule = gsQuadrature::get<T>(gsQuadrature::GaussLegendre,numNodes);
typename gsBasis<T>::domainIter domIt = displacement.basis(p).makeDomainIterator(boundary::none);
#ifdef _OPENMP
const int tid = omp_get_thread_num();
const int nt = omp_get_num_threads();
for ( domIt->next(tid); domIt->good() && continueIt; domIt->next(nt) )
#else
for (; domIt->good() && continueIt; domIt->next() )
#endif
{
genSamplingPoints(domIt->lowerCorner(),domIt->upperCorner(),quRule,points);
mdG.points = points;
mdU.points = points;
domain.patch(p).computeMap(mdG);
displacement.patch(p).computeMap(mdU);
for (index_t q = 0; q < points.cols() && continueIt; ++q)
{
gsMatrix<T> physDispJac = mdU.jacobian(q)*(mdG.jacobian(q).cramerInverse());
gsMatrix<T> F = gsMatrix<T>::Identity(domain.dim(),domain.dim()) + physDispJac;
if (F.determinant() <= 0)
{
gsInfo << "Bad patch: " << p << "\nBad point:\n" << points.col(q) << "\nDet: " << F.determinant() << std::endl;
corruptedPatch = p;
continueIt = false;
}
}
}
}
}
return corruptedPatch;
}
template <class T>
T normL2(gsMultiPatch<T> const & domain, gsMultiPatch<T> const & solution)
{
T norm = 0;
for (size_t p = 0; p < domain.nPatches(); ++p)
{
#pragma omp parallel
{
gsMapData<T> mdGeo(NEED_MEASURE);
gsMatrix<T> values, quNodes;
gsVector<T> quWeights;
gsVector<index_t> numNodes(domain.dim());
for (short_t i = 0; i < domain.dim(); ++i)
numNodes.at(i) = solution.basis(p).degree(i)+1;
gsQuadRule<T> quRule = gsQuadrature::get<T>(gsQuadrature::GaussLegendre,numNodes);
typename gsBasis<T>::domainIter domIt = solution.basis(p).makeDomainIterator(boundary::none);
#ifdef _OPENMP
const int tid = omp_get_thread_num();
const int nt = omp_get_num_threads();
for ( domIt->next(tid); domIt->good(); domIt->next(nt) )
#else
for (; domIt->good(); domIt->next() )
#endif
{
quRule.mapTo( domIt->lowerCorner(), domIt->upperCorner(), quNodes, quWeights );
mdGeo.points = quNodes;
domain.patch(p).computeMap(mdGeo);
solution.patch(p).eval_into(quNodes,values);
T tempNorm = 0;
for (index_t q = 0; q < quNodes.cols(); ++q)
tempNorm += mdGeo.measure(q)*quWeights.at(q)*(values.col(q).transpose()*values.col(q))(0,0);
#pragma omp critical
norm += tempNorm;
}
}
}
return sqrt(norm);
}
template <class T>
T geometryJacRatio(gsMultiPatch<T> const & domain)
{
std::vector<T> maxs, mins;
gsMapData<T> md;
md.flags = NEED_DERIV;
gsMatrix<T> points;
for (size_t p = 0; p < domain.nPatches(); ++p)
{
gsVector<index_t> numNodes(domain.dim());
for (short_t i = 0; i < domain.dim(); ++i)
numNodes.at(i) = domain.basis(p).degree(i)+1;
gsQuadRule<T> quRule = gsQuadrature::get<T>(gsQuadrature::GaussLegendre,numNodes);
typename gsBasis<T>::domainIter domIt = domain.basis(p).makeDomainIterator(boundary::none);
for (; domIt->good(); domIt->next())
{
genSamplingPoints(domIt->lowerCorner(),domIt->upperCorner(),quRule,points);
md.points = points;
domain.patch(p).computeMap(md);
T min = md.jacobian(0).determinant();
T max = min;
for (index_t q = 1; q < points.cols(); ++q)
{
T jac = md.jacobian(q).determinant();
if (jac > max)
max = jac;
if (jac < min)
min = jac;
}
maxs.push_back(max);
mins.push_back(min);
}
}
return *(std::min_element(mins.begin(),mins.end())) / *(std::max_element(maxs.begin(),maxs.end()));
}
template <class T>
T displacementJacRatio(const gsMultiPatch<T> & domain,const gsMultiPatch<T> & displacement)
{
std::vector<T> maxs, mins;
gsMapData<T> mdG, mdU;
mdG.flags = NEED_DERIV;
mdU.flags = NEED_DERIV;
gsMatrix<T> points;
size_t dim = domain.parDim();
for (size_t p = 0; p < displacement.nPatches(); ++p)
{
gsVector<index_t> numNodes(domain.dim());
for (short_t i = 0; i < domain.dim(); ++i)
numNodes.at(i) = displacement.basis(p).degree(i)+1;
gsQuadRule<T> quRule = gsQuadrature::get<T>(gsQuadrature::GaussLegendre,numNodes);
typename gsBasis<T>::domainIter domIt = domain.basis(p).makeDomainIterator(boundary::none);
for (; domIt->good(); domIt->next())
{
genSamplingPoints(domIt->lowerCorner(),domIt->upperCorner(),quRule,points);
mdG.points = points;
mdU.points = points;
domain.patch(p).computeMap(mdG);
displacement.patch(p).computeMap(mdU);
T minJ = (gsMatrix<T>::Identity(dim,dim) + mdU.jacobian(0)*(mdG.jacobian(0).cramerInverse())).determinant();
T maxJ = minJ;
for (int q = 1; q < points.cols(); ++q)
{
T J = (gsMatrix<T>::Identity(dim,dim) + mdU.jacobian(q)*(mdG.jacobian(q).cramerInverse())).determinant();
if (J > maxJ)
maxJ = J;
if (J < minJ)
minJ = J;
}
maxs.push_back(maxJ);
mins.push_back(minJ);
}
}
return *(std::min_element(mins.begin(),mins.end())) / *(std::max_element(maxs.begin(),maxs.end()));
}
template <class T>
void genSamplingPoints(const gsVector<T> & lower, const gsVector<T> & upper,
const gsQuadRule<T> & quRule, gsMatrix<T> & points)
{
gsMatrix<T> quadPoints;
gsVector<T> tempVector; // temporary argument for the gsQuadrule::mapTo function
quRule.mapTo(lower,upper,quadPoints,tempVector);
gsVector<unsigned> nPoints(quadPoints.rows());
for (index_t d = 0; d < quadPoints.rows(); ++d)
nPoints.at(d) = 2;
gsMatrix<T> corners = gsPointGrid(lower,upper,nPoints);
points.resize(quadPoints.rows(),quadPoints.cols()+corners.cols());
points << quadPoints,corners;
}
template <class T>
T patchLength(const gsGeometry<T> & geo, short_t dir)
{
GISMO_ENSURE(dir >= 0 && dir <= geo.parDim(),"Invalid parametric direction: " + util::to_string(dir)+
", geometry dimension: " + util::to_string(geo.parDim()));
switch (geo.parDim())
{
case 1: return curveLength<T>(geo);
case 2:
{
switch (dir)
{
case 0:
{
typename gsGeometry<T>::uPtr sideS = geo.boundary(boundary::south);
typename gsGeometry<T>::uPtr sideN = geo.boundary(boundary::north);
return (curveLength<T>(*sideS) + curveLength<T>(*sideN))/2;
}
case 1:
{
typename gsGeometry<T>::uPtr sideW = geo.boundary(boundary::west);
typename gsGeometry<T>::uPtr sideE = geo.boundary(boundary::east);
return (curveLength<T>(*sideW) + curveLength<T>(*sideE))/2;
}
default: return 0.;
}
}
case 3:
{
switch (dir)
{
case 0:
{
typename gsGeometry<T>::uPtr sideB = geo.boundary(boundary::back);
typename gsGeometry<T>::uPtr sideF = geo.boundary(boundary::front);
typename gsGeometry<T>::uPtr edgeBS = sideB->boundary(boundary::south);
typename gsGeometry<T>::uPtr edgeBN = sideB->boundary(boundary::north);
typename gsGeometry<T>::uPtr edgeFS = sideF->boundary(boundary::south);
typename gsGeometry<T>::uPtr edgeFN = sideF->boundary(boundary::north);
return (curveLength<T>(*edgeBS) + curveLength<T>(*edgeBN) +
curveLength<T>(*edgeFS) + curveLength<T>(*edgeFN))/4;
}
case 1:
{
typename gsGeometry<T>::uPtr sideB = geo.boundary(boundary::back);
typename gsGeometry<T>::uPtr sideF = geo.boundary(boundary::front);
typename gsGeometry<T>::uPtr edgeBW = sideB->boundary(boundary::west);
typename gsGeometry<T>::uPtr edgeBE = sideB->boundary(boundary::east);
typename gsGeometry<T>::uPtr edgeFW = sideF->boundary(boundary::west);
typename gsGeometry<T>::uPtr edgeFE = sideF->boundary(boundary::east);
return (curveLength<T>(*edgeBW) + curveLength<T>(*edgeBE) +
curveLength<T>(*edgeFW) + curveLength<T>(*edgeFE))/4;
}
case 2:
{
typename gsGeometry<T>::uPtr sideN = geo.boundary(boundary::north);
typename gsGeometry<T>::uPtr sideS = geo.boundary(boundary::south);
typename gsGeometry<T>::uPtr edgeNW = sideN->boundary(boundary::west);
typename gsGeometry<T>::uPtr edgeNE = sideN->boundary(boundary::east);
typename gsGeometry<T>::uPtr edgeSW = sideS->boundary(boundary::west);
typename gsGeometry<T>::uPtr edgeSE = sideS->boundary(boundary::east);
return (curveLength<T>(*edgeNW) + curveLength<T>(*edgeNE) +
curveLength<T>(*edgeSW) + curveLength<T>(*edgeSE))/4;
}
default: return 0.;
}
}
default: return 0.;
}
}
template <class T>
T curveLength(const gsGeometry<T> & geo)
{
GISMO_ENSURE(geo.parDim() == 1,"This is not a curve! Dim: " + util::to_string(geo.parDim()));
T length = 0.;
gsVector<index_t> numNodes(1);
numNodes << geo.basis().degree(0)+1;
gsQuadRule<T> quRule = gsQuadrature::get<T>(gsQuadrature::GaussLegendre,numNodes);
gsMatrix<T> qPoints;
gsVector<T> qWeights;
gsMapData<T> md;
md.flags = NEED_DERIV;
typename gsBasis<>::domainIter domIt = geo.basis().makeDomainIterator(boundary::none);
for (; domIt->good(); domIt->next())
{
quRule.mapTo(domIt->lowerCorner(),domIt->upperCorner(),qPoints,qWeights);
md.points = qPoints;
geo.computeMap(md);
for (index_t q = 0; q < qWeights.rows(); ++q)
length += qWeights.at(q)*md.jacobian(q).norm();
}
return length;
}
template <class T>
gsVector<unsigned> distributePoints(const gsGeometry<T> & geo, unsigned numPoints)
{
short_t dim = geo.parDim();
GISMO_ENSURE(dim >= 1 && dim <= 3,"Invalid patch dimension: " + util::to_string(dim));
gsVector<unsigned> numPointsPerDir(dim);
gsVector<T> parLengths(dim);
T volume = 1.;
for (short_t d = 0; d < dim; ++d)
{
parLengths.at(d) = patchLength<T>(geo,d);
volume *= parLengths.at(d);
}
T unit = pow(1.0*numPoints/volume,1./geo.parDim());
for (short_t d = 0; d < geo.parDim(); ++d)
numPointsPerDir.at(d) = math::ceil(unit*parLengths.at(d)) > 1 ? math::ceil(unit*parLengths.at(d)) : 2;
return numPointsPerDir;
}
//--------------------------------------------------------------------//
//------------------------ Modelling ---------------------------------//
//--------------------------------------------------------------------//
template<class T>
typename gsGeometry<T>::uPtr simplifyCurve(gsGeometry<T> const & curve,
index_t additionalPoints, index_t degree,
index_t numSamples)
{
GISMO_ENSURE(curve.domainDim() == 1 ,"That's not a curve.\n");
index_t deg = degree == 0 ? curve.degree(0) : degree;
index_t num = deg + 1 + additionalPoints;
gsKnotVector<T> knots(0.0,1.0, num - deg - 1, deg + 1);
gsKnotVector<T> knotVector(knots);
gsBSplineBasis<T> basis(knotVector);
gsMatrix<T> params(1,numSamples);
for (index_t p = 0; p < numSamples; ++p)
params.at(p) = 1.*p/(numSamples-1);
gsMatrix<T> curveValues;
curve.eval_into(params,curveValues);
gsMatrix<T> lens(numSamples,1);
lens.at(0) = 0.;
for (index_t p = 1; p < numSamples; ++p)
lens.at(p) = lens.at(p-1) + distance(curveValues,p,curveValues,p-1,true);
gsMatrix<T> lenParams(1,numSamples);
for (index_t p = 0; p < numSamples; ++p)
lenParams.at(p) = lens.at(p)/lens.at(numSamples-1);
typename gsGeometry<T>::uPtr simpleCurve = fittingDirichlet(lenParams,curveValues,basis);
simpleCurve->eval_into(params,curveValues);
for (index_t p = 1; p < numSamples; ++p)
lens.at(p) = lens.at(p-1) + distance(curveValues,p,curveValues,p-1,true);
for (index_t p = 0; p < numSamples; ++p)
lenParams.at(p) = lens.at(p)/lens.at(numSamples-1);
return fittingDirichlet(lenParams,curveValues,curve.basis());
}
template<class T>
T curveDistance(gsGeometry<T> const & curveA,
gsGeometry<T> const & curveB,
index_t numSamples)
{
gsMatrix<T> params(1,numSamples);
for (index_t p = 0; p < numSamples; ++p)
params.at(p) = 1.*p/(numSamples-1);
gsMatrix<T> pointsA, pointsB;
curveA.eval_into(params,pointsA);
curveB.eval_into(params,pointsB);
T dist = 0.;
for (int p = 0; p < numSamples; ++p)
dist += pow(distance(pointsA,p,pointsB,p,true),2);
return sqrt(dist/numSamples);
}
template <class T>
typename gsGeometry<T>::uPtr fittingDirichlet(gsMatrix<T> const & params,
gsMatrix<T> const & points,
gsBasis<T> const & basis)
{
index_t numSamples = params.cols();
index_t num = basis.size();
index_t dim = points.rows();
gsSparseMatrix<T> A(num,num);
gsMatrix<T> b(num,dim);
b.setZero();
gsMatrix<T> basisValues;
gsMatrix<index_t> activeBasis;
basis.eval_into(params,basisValues);
basis.active_into(params,activeBasis);
for (index_t p = 1; p < numSamples; ++p)
{
index_t numActive = activeBasis.rows();
for (index_t i = 0; i < numActive; ++i)
{
if (activeBasis(i,p) == 0)
{
for (index_t j = 0; j < numActive; ++j)
{
if (activeBasis(j,p) != 0 && activeBasis(j,p) != num-1 )
b.row(activeBasis(j,p)-1) -= basisValues(i,p) * basisValues(j,p) *
points.col(0).transpose() * (params.at(p)-params.at(p-1));
}
}
else if (activeBasis(i,p) == num-1)
{
for (index_t j = 0; j < numActive; ++j)
{
if (activeBasis(j,p) != 0 && activeBasis(j,p) != num-1 )
b.row(activeBasis(j,p)-1) -= basisValues(i,p) * basisValues(j,p) *
points.col(numSamples-1).transpose() * (params.at(p)-params.at(p-1));
}
}
else
{
b.row(activeBasis(i,p)-1) += basisValues(i,p) * points.col(p).transpose() * (params.at(p)-params.at(p-1));
for (index_t j = 0; j < numActive; ++j)
if (activeBasis(j,p) != 0 && activeBasis(j,p) != num-1 )
A(activeBasis(i,p)-1, activeBasis(j,p)-1) += basisValues(i,p) * basisValues(j,p) * (params.at(p)-params.at(p-1));
}
}
}
A.makeCompressed();
typename gsSparseSolver<T>::CGDiagonal solver(A);
gsMatrix<T> x = solver.solve(b);
gsMatrix<T> coefs(num,dim);
coefs.row(0) = points.col(0).transpose();
coefs.block(1,0,num-2,dim) = x.block(0,0,num-2,dim);
coefs.row(num-1) = points.col(numSamples-1).transpose();
return basis.makeGeometry(give(coefs));
}
template<class T>
typename gsGeometry<T>::uPtr genPatchInterpolation(gsGeometry<T> const & A, gsGeometry<T> const & B,
index_t deg, index_t num, bool xiDir)
{
GISMO_ENSURE(A.parDim() == B.parDim(), "Geometries are incompatible: different parametric dimensions: " +
util::to_string(A.parDim()) + " and " + util::to_string(B.parDim()) + "\n");
short_t pDim = A.parDim();
GISMO_ASSERT(pDim == 1 || pDim ==2, "Can only interpolate between curves or surfaces. Given geometries have parametric dimension " +
util::to_string(pDim) + "\n");
for (index_t d = 0; d < pDim; ++d)
GISMO_ENSURE(A.degree(d) == B.degree(d), "Geometries are incompatible: different splines degrees in dimension" +
util::to_string(d) + ": " + util::to_string(A.degree(d)) +
" and " + util::to_string(B.degree(d)) + "\n");
GISMO_ENSURE(A.targetDim() == B.targetDim(), "Geometries are incompatible: different physical dimensions: " +
util::to_string(A.targetDim()) + " and " + util::to_string(B.targetDim()) + "\n");
short_t tDim = A.targetDim();
GISMO_ASSERT(A.coefsSize() == B.coefsSize(), "Geometries are incompatible: different number of control points: " +
util::to_string(A.coefsSize()) + " and " + util::to_string(B.coefsSize()) + "\n");
index_t baseNum = A.coefsSize();
gsKnotVector<T> newKnots(0.0,1.0, num - deg - 1, deg + 1);
gsMultiPatch<> temp;
temp.addPatch(A.clone());
if (pDim == 1)
{
gsMatrix<T> coefs(baseNum*num,tDim);
T part = 1./(num-deg);
T pos = 0.;
for (index_t i = 0; i < num; ++i)
{
if (i < deg)
pos += part/deg*i;
else if (deg <= i && i < num-deg )
pos += part;
else
pos += part/deg*(num-i);
for (index_t j = 0; j < baseNum; ++j)
{
if (xiDir)
coefs.row(j*num+i) = combine(A.coefs(),B.coefs(),pos,j,j).row(0);
else
coefs.row(i*baseNum+j) = combine(A.coefs(),B.coefs(),pos,j,j).row(0);
}
}
if (xiDir)
{
gsTensorBSplineBasis<2,T> basis(newKnots,
(static_cast<gsBSpline<T> &>(temp.patch(0))).knots());
return basis.makeGeometry(give(coefs));
}
else
{
gsTensorBSplineBasis<2,T> basis((static_cast<gsBSpline<T> &>(temp.patch(0))).knots(),
newKnots);
return basis.makeGeometry(give(coefs));
}
}
else
{
gsTensorBSplineBasis<3,T> basis((static_cast<gsTensorBSpline<2,T> &>(temp.patch(0))).knots(0),
(static_cast<gsTensorBSpline<2,T> &>(temp.patch(0))).knots(1),
newKnots);
gsMatrix<T> coefs(baseNum*num,tDim);
T part = 1./(num-deg);
T pos = 0.;
for (index_t i = 0; i < num; ++i)
{
if (i < deg)
pos += part/deg*i;
else if (deg <= i && i < num-deg )
pos += part;
else
pos += part/deg*(num-i);
for (index_t j = 0; j < baseNum; ++j)
coefs.row(i*baseNum+j) = combine(A.coefs(),B.coefs(),pos,j,j).row(0);
}
return basis.makeGeometry(give(coefs));
}
}
template<class T>
typename gsGeometry<T>::uPtr genPatchScaling(gsGeometry<T> const & boundary,
index_t deg, index_t num,
T scaling, gsVector<T> const & center)
{
typename gsGeometry<T>::uPtr scaledBoundary = boundary.clone();
scaledBoundary->translate(-1*center);
scaledBoundary->scale(scaling);
scaledBoundary->translate(center);
return genPatchInterpolation(boundary,*scaledBoundary,deg,num);
}
template<class T>
typename gsGeometry<T>::uPtr genLine(index_t deg, index_t num,
gsMatrix<T> const & A, gsMatrix<T> const & B,
index_t iA, index_t iB)
{
GISMO_ENSURE(num - deg - 1 >= 0,"Too few DoFs\n");
GISMO_ENSURE(A.cols() == B.cols(),"Points have different dimensions\n");
gsKnotVector<T> knotsCoarse(0.0,1.0, 0, 2);
index_t dim = A.cols();
gsMatrix<T> coefs(2,dim);
coefs.row(0) = A.row(iA);
coefs.row(1) = B.row(iB);
// gen simplest possible Bspline line
typename gsBSpline<T>::uPtr line1 = typename gsBSpline<T>::uPtr(new gsBSpline<T>(knotsCoarse,coefs));
// refine it
for (index_t i = 0; i < deg - 1; ++i)
line1->degreeElevate();
gsKnotVector<T> knotsFine(0.0,1.0, num - deg - 1, deg + 1);
for (index_t i = 0; i < num - deg - 1; ++i)
line1->insertKnot(knotsFine.at(i+deg+1));
return line1;
}
template<class T>
typename gsGeometry<T>::uPtr genCircle(index_t deg, index_t num,
T radius, T x0, T y0,
T angle0, T arcAngle)
{
GISMO_ENSURE(num - deg - 1 >= 0,"Too few DoFs\n");
gsKnotVector<T> knots(0.0,1.0, num - deg - 1, deg + 1);
gsBSplineBasis<T> basis(knots);
return genCircle(basis,radius,x0,y0,angle0,arcAngle);
}
template<class T>
typename gsGeometry<T>::uPtr genCircle(gsBasis<T> & basis,
T radius,
T x0, T y0,
T angle0, T arcAngle)
{
index_t numPoints = 1000;
gsMatrix<> params(1,numPoints);
gsMatrix<> points(2,numPoints);
for (index_t i = 0; i < numPoints; ++i)
{
params(0,i) = 1.*i/(numPoints-1);
points(0,i) = x0 + radius*cos(angle0 + i*arcAngle/(numPoints-1));
points(1,i) = y0 + radius*sin(angle0 + i*arcAngle/(numPoints-1));
}
return fittingDirichlet(params,points,basis);
}
template<class T>
typename gsGeometry<T>::uPtr genQuad(index_t xiDeg, index_t xiNum, index_t etaDeg, index_t etaNum,
gsMatrix<T> const & A, gsMatrix<T> const & B,
gsMatrix<T> const & C, gsMatrix<T> const & D,
index_t iA, index_t iB, index_t iC, index_t iD)
{
typename gsGeometry<T>::uPtr sideAB = genLine(xiDeg,xiNum,A,B,iA,iB);
typename gsGeometry<T>::uPtr sideCD = genLine(xiDeg,xiNum,C,D,iC,iD);
return genPatchInterpolation(*sideAB,*sideCD,etaDeg,etaNum);
}
template<class T>
typename gsGeometry<T>::uPtr genSphere(index_t xiDeg, index_t xiNum, index_t etaDeg, index_t etaNum,
T xi0, T xi1, T eta0, T eta1)
{
GISMO_ENSURE(xiNum - xiDeg - 1 >= 0,"Too few DoFs\n");
GISMO_ENSURE(etaNum - etaDeg - 1 >= 0,"Too few DoFs\n");
gsKnotVector<T> xiKnots(0.,1.,xiNum - xiDeg - 1, xiDeg + 1);
gsKnotVector<T> etaKnots(0.,1.,etaNum - etaDeg - 1, etaDeg + 1);
return genSphere(xiKnots,etaKnots,xi0,xi1,eta0,eta1);
}
template<class T>
typename gsGeometry<T>::uPtr genSphere(gsKnotVector<T> & xiKnots, gsKnotVector<T> & etaKnots,
T xi0, T xi1, T eta0, T eta1)
{
gsBSplineBasis<T> xiBasis(xiKnots);
typename gsGeometry<T>::uPtr xiCircle = genCircle(xiBasis,(T)1.,(T)0.,(T)0.,xi0,xi1-xi0);
gsBSplineBasis<T> etaBasis(etaKnots);
typename gsGeometry<T>::uPtr etaCircle = genCircle(xiBasis,(T)1.,(T)0.,(T)0.,xi0,xi1-xi0);
gsTensorBSplineBasis<2,T> basis(xiKnots,etaKnots);
index_t xiNum = xiCircle->coefsSize();
index_t etaNum = etaCircle->coefsSize();
gsMatrix<T> coefs(xiNum*etaNum,3);
for (index_t i = 0; i < xiNum; ++i)
{
for (index_t j = 0; j < etaNum; ++j)
{
coefs(j*xiNum+i,0) = xiCircle->coef(i,0)*etaCircle->coef(j,1);
coefs(j*xiNum+i,1) = xiCircle->coef(i,1)*etaCircle->coef(j,1);
coefs(j*xiNum+i,2) = etaCircle->coef(j,0);
}
}
return basis.makeGeometry(give(coefs));
}
template<class T>
typename gsGeometry<T>::uPtr genCylinder(gsGeometry<T> const & base,
index_t deg, index_t num, T height)
{
GISMO_ENSURE(num - deg - 1 >= 0,"Too few DoFs\n");
typename gsGeometry<T>::uPtr botBoundary = base.clone();
typename gsGeometry<T>::uPtr topBoundary = base.clone();
if (base.targetDim() < 3)
{
botBoundary->embed3d();
topBoundary->embed3d();
}
topBoundary->translate(gsVector<T,3>::vec(0.,0.,height));
return genPatchInterpolation(*botBoundary,*topBoundary,deg,num);
}
template<class T>
typename gsGeometry<T>::uPtr genScrew(gsGeometry<T> const & base,
index_t deg, index_t num,
T height, T pitch, T x0, T y0)
{
GISMO_ENSURE(num - deg - 1 >= 0,"Too few DoFs\n");
short_t pDim = base.parDim();
GISMO_ASSERT(pDim == 1 || pDim ==2,"Wrong geometry type\n");
gsKnotVector<> zKnots(0.0,1.0, num - deg - 1, deg + 1);
gsBSplineBasis<> zBasis(zKnots);
index_t numBase = base.coefsSize();
index_t numPoints = 10000;
gsMatrix<> params(1,numPoints);
gsMatrix<> points(3,numPoints);
for (index_t i = 0; i < numPoints; ++i)
{
params(0,i) = 1.*i/(numPoints-1);
points(0,i) = cos(params(0,i)*2*EIGEN_PI*pitch/360);
points(1,i) = sin(params(0,i)*2*EIGEN_PI*pitch/360);
points(2,i) = height*params(0,i);
}
typename gsGeometry<T>::uPtr helix = fittingDirichlet(params,points,zBasis);
gsMatrix<T> coefs(numBase*num,3);
gsMultiPatch<T> temp;
temp.addPatch(base.clone());
T oldAngle = 0.;
T oldRadius = 1.;
for (index_t i = 0; i < num; ++i)
{
T x = helix->coef(i,0);
T y = helix->coef(i,1);
T radius = sqrt(x*x+y*y);
T angle = atan2(y,x);
temp.patch(0).translate(gsVector<T,2>::vec(-1*x0,-1*y0));
temp.patch(0).rotate(angle-oldAngle);
temp.patch(0).scale(radius/oldRadius);
temp.patch(0).translate(gsVector<T,2>::vec(x0,y0));
for (index_t j = 0; j < numBase; j++)
{
coefs(i*numBase + j,0) = temp.patch(0).coef(j,0);
coefs(i*numBase + j,1) = temp.patch(0).coef(j,1);
coefs(i*numBase + j,2) = helix->coef(i,2);
}
oldRadius = radius;
oldAngle = angle;
}
if (pDim == 1)
{
gsTensorBSplineBasis<2,T> basis(static_cast<gsBSpline<T> &>(temp.patch(0)).knots(0),
zKnots);
return basis.makeGeometry(give(coefs));
}
else
{
gsTensorBSplineBasis<3,T> basis(static_cast<gsTensorBSpline<2,T> &>(temp.patch(0)).knots(0),
static_cast<gsTensorBSpline<2,T> &>(temp.patch(0)).knots(1),
zKnots);
return basis.makeGeometry(give(coefs));
}
}
template<class T>
typename gsGeometry<T>::uPtr genSpring(gsGeometry<T> const & crossSection,
T R, T springPitch,
index_t N, bool nurbs)
{
GISMO_ENSURE(crossSection.parDim() == 2, "Wrong dimension of the cross-section: " + util::to_string(crossSection.parDim()));
// cross-section knot vectors
gsKnotVector<T> xKnots = nurbs ? static_cast<const gsTensorNurbsBasis<2,T> &>(crossSection.basis()).knots(0)
: static_cast<const gsTensorBSplineBasis<2,T> &>(crossSection.basis()).knots(0);
gsKnotVector<T> yKnots = nurbs ? static_cast<const gsTensorNurbsBasis<2,T> &>(crossSection.basis()).knots(1)
: static_cast<const gsTensorBSplineBasis<2,T> &>(crossSection.basis()).knots(1);
// knot vector for the helical guiding line
std::vector<T> knots;
for (index_t i = 0; i < 3; ++i)
knots.push_back(0.);
for (index_t i = 0; i < N-1; ++i)
for (index_t j = 0; j < 2; ++j)
knots.push_back(1./N*(i+1));