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TriangleSetGeometryAlgorithms.inl
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TriangleSetGeometryAlgorithms.inl
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/******************************************************************************
* SOFA, Simulation Open-Framework Architecture *
* (c) 2006 INRIA, USTL, UJF, CNRS, MGH *
* *
* This program is free software; you can redistribute it and/or modify it *
* under the terms of the GNU Lesser General Public License as published by *
* the Free Software Foundation; either version 2.1 of the License, or (at *
* your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but WITHOUT *
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or *
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
* for more details. *
* *
* You should have received a copy of the GNU Lesser General Public License *
* along with this program. If not, see <http://www.gnu.org/licenses/>. *
*******************************************************************************
* Authors: The SOFA Team and external contributors (see Authors.txt) *
* *
* Contact information: contact@sofa-framework.org *
******************************************************************************/
#pragma once
#include <sofa/component/topology/container/dynamic/TriangleSetGeometryAlgorithms.h>
#include <sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.h>
#include <sofa/component/topology/container/dynamic/TriangleSetTopologyModifier.h>
#include <sofa/core/visual/VisualParams.h>
#include <sofa/component/topology/container/dynamic/CommonAlgorithms.h>
#include <fstream>
#ifdef NDEBUG
#define DO_EXTRADEBUG_MESSAGES false
#else
#define DO_EXTRADEBUG_MESSAGES true
#endif //
namespace sofa::component::topology::container::dynamic
{
const size_t permutation3[6][3]={{0,1,2},{0,2,1},{1,0,2},{1,2,0},{2,0,1},{2,1,0}};
template< class DataTypes>
NumericalIntegrationDescriptor<typename TriangleSetGeometryAlgorithms< DataTypes >::Real,3> &TriangleSetGeometryAlgorithms< DataTypes >::getTriangleNumericalIntegrationDescriptor()
{
// initialize the cubature table only if needed.
if (initializedCubatureTables==false) {
initializedCubatureTables=true;
defineTetrahedronCubaturePoints();
}
return triangleNumericalIntegration;
}
template< class DataTypes>
void TriangleSetGeometryAlgorithms< DataTypes >::defineTetrahedronCubaturePoints() {
typedef typename NumericalIntegrationDescriptor<typename TriangleSetGeometryAlgorithms< DataTypes >::Real,3>::QuadraturePoint QuadraturePoint;
typedef typename NumericalIntegrationDescriptor<typename TriangleSetGeometryAlgorithms< DataTypes >::Real,3>::BarycentricCoordinatesType BarycentricCoordinatesType;
// Gauss method
typename NumericalIntegrationDescriptor<typename TriangleSetGeometryAlgorithms< DataTypes >::Real,3>::QuadratureMethod m=NumericalIntegrationDescriptor<typename TriangleSetGeometryAlgorithms< DataTypes >::Real,3>::GAUSS_SIMPLEX_METHOD;
typename NumericalIntegrationDescriptor<typename TriangleSetGeometryAlgorithms< DataTypes >::Real,3>::QuadraturePointArray qpa;
BarycentricCoordinatesType v;
/// integration with linear accuracy.
v=BarycentricCoordinatesType(1/(Real)3.0,1/(Real)3.0,1/(Real)3.0);
qpa.push_back(QuadraturePoint(v,1/(Real)2));
triangleNumericalIntegration.addQuadratureMethod(m,1,qpa);
/// integration with quadratic accuracy.
qpa.clear();
Real a=1/(Real)6;
Real b=(Real) (2.0/3.0);
sofa::Index i;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,1/(Real)6));
}
triangleNumericalIntegration.addQuadratureMethod(m,2,qpa);
/// integration with cubic accuracy.
qpa.clear();
v=BarycentricCoordinatesType(1/(Real)3.0,1/(Real)3.0,1/(Real)3.0);
qpa.push_back(QuadraturePoint(v,(Real) -9/32));
a=(Real)1/5;
b=(Real)3/5;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,(Real)25/(Real)96));
}
triangleNumericalIntegration.addQuadratureMethod(m,3,qpa);
/// integration with quadric accuracy with 6 points
qpa.clear();
a=(Real)0.445948490915965;
b=(Real)1-2*a;
Real c1= (Real)0.111690794839005;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
a=(Real)0.091576213509771;
b=(Real)1-2*a;
Real c2= (Real)0.054975871827661;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c2));
}
triangleNumericalIntegration.addQuadratureMethod(m,4,qpa);
/// integration with quintic accuracy and 7 points
qpa.clear();
v=BarycentricCoordinatesType(1/(Real)3.0,1/(Real)3.0,1/(Real)3.0);
qpa.push_back(QuadraturePoint(v,9/(Real)80));
a=(Real)(6+sqrt(15))/21;
b=(Real)1-2*a;
c1=(Real)(155+sqrt(15))/2400;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
a=(Real)4/7-a;
b=(Real)1-2*a;
c2=(Real)31/240 -c1;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c2));
}
triangleNumericalIntegration.addQuadratureMethod(m,5,qpa);
/// integration with order 6 accuracy and 12 points
qpa.clear();
a=(Real) 0.063089104491502;
b=(Real)1-2*a;
c1=(Real)0.025422453185103;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
a=(Real) 0.249286745170910;
b=(Real)1-2*a;
c1=(Real)0.058393137863189;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
Real aa[3];
aa[0]=(Real)0.310352451033785;
aa[1]=(Real)0.053145049844816;
aa[2]=(Real)(1.0-aa[0]-aa[1]);
c2=(Real)0.041425537809187;
for (i=0;i<6;++i) {
v=BarycentricCoordinatesType(aa[permutation3[i][0]],aa[permutation3[i][1]],aa[permutation3[i][2]]);
qpa.push_back(QuadraturePoint(v,c2));
}
triangleNumericalIntegration.addQuadratureMethod(m,6,qpa);
/// integration with order 7 accuracy and 13 points
qpa.clear();
v=BarycentricCoordinatesType(1/(Real)3.0,1/(Real)3.0,1/(Real)3.0);
qpa.push_back(QuadraturePoint(v,(Real)-0.0747850222338));
a=(Real)0.0651301029022;
b=(Real)1-2*a;
c1=(Real)0.0266736178044;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
a=(Real) 0.2603459660790;
b=(Real)1-2*a;
c1=(Real)0.0878076287166;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
aa[0]=(Real)0.3128654960049;
aa[1]=(Real)0.6384441885698;
aa[2]=(Real)(1.0-aa[0]-aa[1]);
c2=(Real)0.0385568804451;
for (i=0;i<6;++i) {
v=BarycentricCoordinatesType(aa[permutation3[i][0]],aa[permutation3[i][1]],aa[permutation3[i][2]]);
qpa.push_back(QuadraturePoint(v,c2));
}
triangleNumericalIntegration.addQuadratureMethod(m,7,qpa);
/// integration with order 8 accuracy and 16 points
qpa.clear();
v=BarycentricCoordinatesType(1/(Real)3.0,1/(Real)3.0,1/(Real)3.0);
c1=(Real)0.1443156076777871682510911104890646/2.0;
qpa.push_back(QuadraturePoint(v,(Real)c1));
a=(Real)0.1705693077517602066222935014914645;
b=(Real)1-2*a;
c1=(Real)0.1032173705347182502817915502921290/2.0;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
a=(Real)0.0505472283170309754584235505965989;
b=(Real)1-2*a;
c1=(Real)0.0324584976231980803109259283417806/2.0;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
a=(Real)0.4592925882927231560288155144941693;
b=(Real)1-2*a;
c1=(Real)0.0950916342672846247938961043885843/2.0;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
aa[0]=(Real)0.2631128296346381134217857862846436;
aa[1]=(Real)0.0083947774099576053372138345392944;
aa[2]=(Real)(1.0-aa[0]-aa[1]);
c2=(Real)0.0272303141744349942648446900739089/2.0;
for (i=0;i<6;++i) {
v=BarycentricCoordinatesType(aa[permutation3[i][0]],aa[permutation3[i][1]],aa[permutation3[i][2]]);
qpa.push_back(QuadraturePoint(v,c2));
}
triangleNumericalIntegration.addQuadratureMethod(m,8,qpa);
/// integration with order 10 accuracy and 25 points from https://github.com/libMesh/libmesh/blob/master/src/quadrature/quadrature_gauss_2D.C
qpa.clear();
v=BarycentricCoordinatesType(1/(Real)3.0,1/(Real)3.0,1/(Real)3.0);
c1=(Real)4.5408995191376790047643297550014267e-02L;
qpa.push_back(QuadraturePoint(v,(Real)c1));
a=(Real)4.8557763338365737736750753220812615e-01L;
b=(Real)1-2*a;
c1=(Real)1.8362978878233352358503035945683300e-02L;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
a=(Real)1.0948157548503705479545863134052284e-01L;
b=(Real)1-2*a;
c1=(Real)2.2660529717763967391302822369298659e-02L;
for (i=0;i<3;++i) {
v=BarycentricCoordinatesType(a,a,a);
v[i]=b;
qpa.push_back(QuadraturePoint(v,c1));
}
aa[0]=(Real)3.0793983876412095016515502293063162e-01L;
aa[1]=(Real)5.5035294182099909507816172659300821e-01L;
aa[2]=(Real)(1.0-aa[0]-aa[1]);
c2=(Real)3.6378958422710054302157588309680344e-02L;
for (i=0;i<6;++i) {
v=BarycentricCoordinatesType(aa[permutation3[i][0]],aa[permutation3[i][1]],aa[permutation3[i][2]]);
qpa.push_back(QuadraturePoint(v,c2));
}
aa[0]=(Real)2.4667256063990269391727646541117681e-01L;
aa[1]=(Real)7.2832390459741092000873505358107866e-01L;
aa[2]=(Real)(1.0-aa[0]-aa[1]);
c2=(Real)1.4163621265528742418368530791049552e-02L;
for (i=0;i<6;++i) {
v=BarycentricCoordinatesType(aa[permutation3[i][0]],aa[permutation3[i][1]],aa[permutation3[i][2]]);
qpa.push_back(QuadraturePoint(v,c2));
}
aa[0]=(Real)6.6803251012200265773540212762024737e-02L;
aa[1]=(Real)9.2365593358750027664630697761508843e-01L;
aa[2]=(Real)(1.0-aa[0]-aa[1]);
c2=(Real)4.7108334818664117299637354834434138e-03L;
for (i=0;i<6;++i) {
v=BarycentricCoordinatesType(aa[permutation3[i][0]],aa[permutation3[i][1]],aa[permutation3[i][2]]);
qpa.push_back(QuadraturePoint(v,c2));
}
triangleNumericalIntegration.addQuadratureMethod(m,10,qpa);
}
template<class DataTypes>
void TriangleSetGeometryAlgorithms< DataTypes >::init()
{
EdgeSetGeometryAlgorithms<DataTypes>::init();
this->getContext()->get(m_container);
this->getContext()->get(m_modifier);
TriangleSetGeometryAlgorithms< DataTypes >::reinit();
}
template<class DataTypes>
void TriangleSetGeometryAlgorithms< DataTypes >::reinit()
{
EdgeSetGeometryAlgorithms<DataTypes>::reinit();
if (p_recomputeTrianglesOrientation.getValue())
this->reorderTrianglesOrientationFromNormals();
}
template< class DataTypes>
void TriangleSetGeometryAlgorithms< DataTypes >::computeTriangleAABB(const TriangleID i, Coord& minCoord, Coord& maxCoord) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p =(this->object->read(core::ConstVecCoordId::position())->getValue());
for(PointID i=0; i<3; ++i)
{
minCoord[i] = std::min(p[t[0]][i], std::min(p[t[1]][i], p[t[2]][i]));
maxCoord[i] = std::max(p[t[0]][i], std::max(p[t[1]][i], p[t[2]][i]));
}
}
template<class DataTypes>
typename DataTypes::Coord TriangleSetGeometryAlgorithms<DataTypes>::computeTriangleCenter(const TriangleID i) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p =(this->object->read(core::ConstVecCoordId::position())->getValue());
return (p[t[0]] + p[t[1]] + p[t[2]]) / (Real) 3.0;
}
template<class DataTypes>
typename DataTypes::Coord TriangleSetGeometryAlgorithms<DataTypes>::computeRestTriangleCenter(const TriangleID i) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p = (this->object->read(core::ConstVecCoordId::restPosition())->getValue());
return (p[t[0]] + p[t[1]] + p[t[2]]) / (Real) 3.0;
}
template<class DataTypes>
void TriangleSetGeometryAlgorithms<DataTypes>::computeTriangleCircumcenterBaryCoefs(sofa::type::Vec<3,Real> &baryCoord,
const TriangleID i) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p =(this->object->read(core::ConstVecCoordId::position())->getValue());
Real a2, b2, c2; // square lengths of the 3 edges
a2 = (p[t[1]]-p[t[0]]).norm2();
b2 = (p[t[2]]-p[t[1]]).norm2();
c2 = (p[t[0]]-p[t[2]]).norm2();
Real n = a2*(-a2+b2+c2) + b2*(a2-b2+c2) + c2*(a2+b2-c2);
baryCoord[2] = a2*(-a2+b2+c2) / n;
baryCoord[0] = b2*(a2-b2+c2) / n;
baryCoord[1] = c2*(a2+b2-c2) / n;
// barycentric coordinates are defined as
//baryCoord = sofa::type::Vec<3,Real>(a2*(-a2+b2+c2) / n, b2*(a2-b2+c2) / n, c2*(a2+b2-c2) / n);
}
template<class DataTypes>
typename DataTypes::Coord TriangleSetGeometryAlgorithms<DataTypes>::computeTriangleCircumcenter(const TriangleID i) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p =(this->object->read(core::ConstVecCoordId::position())->getValue());
sofa::type::Vec<3,Real> barycentricCoords;
computeTriangleCircumcenterBaryCoefs(barycentricCoords, i);
return (p[t[0]]*barycentricCoords[0] + p[t[1]]*barycentricCoords[1] + p[t[2]]*barycentricCoords[2]);
}
template< class DataTypes>
void TriangleSetGeometryAlgorithms< DataTypes >::getTriangleVertexCoordinates(const TriangleID i, Coord pnt[3]) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p =(this->object->read(core::ConstVecCoordId::position())->getValue());
for(PointID i=0; i<3; ++i)
{
pnt[i] = p[t[i]];
}
}
template< class DataTypes>
void TriangleSetGeometryAlgorithms< DataTypes >::getRestTriangleVertexCoordinates(const TriangleID i, Coord pnt[3]) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p = (this->object->read(core::ConstVecCoordId::restPosition())->getValue());
for(PointID i=0; i<3; ++i)
{
pnt[i] = p[t[i]];
}
}
template< class DataTypes>
typename DataTypes::Real TriangleSetGeometryAlgorithms< DataTypes >::computeTriangleArea( const TriangleID i) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p =(this->object->read(core::ConstVecCoordId::position())->getValue());
Real area = (Real)(areaProduct(p[t[1]]-p[t[0]], p[t[2]]-p[t[0]]) * 0.5);
return area;
}
template< class DataTypes>
typename DataTypes::Real TriangleSetGeometryAlgorithms< DataTypes >::computeRestTriangleArea( const TriangleID i) const
{
const Triangle &t = this->m_topology->getTriangle(i);
const typename DataTypes::VecCoord& p = (this->object->read(core::ConstVecCoordId::restPosition())->getValue());
Real area = (Real) (areaProduct(p[t[1]]-p[t[0]],p[t[2]]-p[t[0]]) * 0.5);
return area;
}
/// computes the edge length of all edges are store in the array interface
template<class DataTypes>
void TriangleSetGeometryAlgorithms<DataTypes>::computeTriangleArea( BasicArrayInterface<Real> &ai) const
{
const sofa::type::vector<Triangle> &ta = this->m_topology->getTriangles();
const typename DataTypes::VecCoord& p =(this->object->read(core::ConstVecCoordId::position())->getValue());
for (size_t i=0; i<ta.size(); ++i)
{
const Triangle &t=ta[i];
Coord vec1 = p[t[1]] - p[t[0]];
Coord vec2 = p[t[2]] - p[t[0]];
ai[(int)i]=(Real)(areaProduct(vec1, vec2) * 0.5);
}
}
// Computes the point defined by 2 indices of vertex and 1 barycentric coordinate
template<class DataTypes>
auto TriangleSetGeometryAlgorithms< DataTypes >::computeBaryEdgePoint(PointID p0, PointID p1, Real coord_p) const -> sofa::type::Vec<3, Real>
{
const typename DataTypes::VecCoord& vect_c =(this->object->read(core::ConstVecCoordId::position())->getValue());
sofa::type::Vec<3,Real> c0; c0 = vect_c[p0];
sofa::type::Vec<3,Real> c1; c1 = vect_c[p1];
return c0*(1-coord_p) + c1*coord_p;
}
template<class DataTypes>
auto TriangleSetGeometryAlgorithms< DataTypes >::computeBaryTrianglePoint(PointID p0, PointID p1, PointID p2, sofa::type::Vec<3,Real>& coord_p) const -> sofa::type::Vec<3, Real>
{
const typename DataTypes::VecCoord& vect_c =(this->object->read(core::ConstVecCoordId::position())->getValue());
sofa::type::Vec<3,Real> c0; c0 = vect_c[p0];
sofa::type::Vec<3,Real> c1; c1 = vect_c[p1];
sofa::type::Vec<3,Real> c2; c2 = vect_c[p2];
return c0*coord_p[0] + c1*coord_p[1] + c2*coord_p[2];
}
// Computes the opposite point to ind_p
template<class DataTypes>
auto TriangleSetGeometryAlgorithms< DataTypes >::getOppositePoint(PointID ind_p,
const Edge& indices,
Real coord_p) const -> sofa::type::Vec<3, Real>
{
const typename DataTypes::VecCoord& vect_c =(this->object->read(core::ConstVecCoordId::position())->getValue());
const typename DataTypes::Coord& c1 = vect_c[indices[0]];
const typename DataTypes::Coord& c2 = vect_c[indices[1]];
sofa::type::Vec<3,Real> p;
if(ind_p == indices[0])
{
p[0]= (Real) c2[0];
p[1]= (Real) c2[1];
p[2]= (Real) c2[2];
}
else
{
if(ind_p == indices[1])
{
p[0]= (Real) c1[0];
p[1]= (Real) c1[1];
p[2]= (Real) c1[2];
}
else
{
p[0]= (Real) ((1.0-coord_p)*c1[0] + coord_p*c2[0]);
p[1]= (Real) ((1.0-coord_p)*c1[1] + coord_p*c2[1]);
p[2]= (Real) ((1.0-coord_p)*c1[2] + coord_p*c2[2]);
}
}
return p;
}
// Computes the normal vector of a triangle indexed by ind_t (not normed)
template<class DataTypes>
auto TriangleSetGeometryAlgorithms< DataTypes >::computeTriangleNormal(const TriangleID ind_t) const -> sofa::type::Vec<3, Real>
{
const Triangle &t = this->m_topology->getTriangle(ind_t);
const typename DataTypes::VecCoord& vect_c =(this->object->read(core::ConstVecCoordId::position())->getValue());
const typename DataTypes::Coord& c0 = vect_c[t[0]];
const typename DataTypes::Coord& c1 = vect_c[t[1]];
const typename DataTypes::Coord& c2 = vect_c[t[2]];
sofa::type::Vec<3,Real> p0;
p0[0] = (Real) (c0[0]);
p0[1] = (Real) (c0[1]);
p0[2] = (Real) (c0[2]);
sofa::type::Vec<3,Real> p1;
p1[0] = (Real) (c1[0]);
p1[1] = (Real) (c1[1]);
p1[2] = (Real) (c1[2]);
sofa::type::Vec<3,Real> p2;
p2[0] = (Real) (c2[0]);
p2[1] = (Real) (c2[1]);
p2[2] = (Real) (c2[2]);
sofa::type::Vec<3,Real> normal_t=(p1-p0).cross( p2-p0);
return normal_t;
}
// barycentric coefficients of point p in triangle (a,b,c) indexed by ind_t
template<class DataTypes>
auto TriangleSetGeometryAlgorithms< DataTypes >::computeTriangleBarycoefs(
const TriangleID ind_t,
const sofa::type::Vec<3,Real> &p) const -> sofa::type::vector<SReal>
{
const Triangle &t=this->m_topology->getTriangle(ind_t);
return compute3PointsBarycoefs(p, t[0], t[1], t[2],false);
}
// barycentric coefficients of point p in initial triangle (a,b,c) indexed by ind_t
template<class DataTypes>
auto TriangleSetGeometryAlgorithms< DataTypes >::computeRestTriangleBarycoefs(
const TriangleID ind_t,
const sofa::type::Vec<3, Real>& p) const -> sofa::type::vector<SReal>
{
const Triangle& t = this->m_topology->getTriangle(ind_t);
return compute3PointsBarycoefs(p, t[0], t[1], t[2], true);
}
// barycentric coefficients of point p in triangle whose vertices are indexed by (ind_p1,ind_p2,ind_p3)
template<class DataTypes>
auto TriangleSetGeometryAlgorithms< DataTypes >::compute3PointsBarycoefs(
const sofa::type::Vec<3, Real> &p,
PointID ind_p1,
PointID ind_p2,
PointID ind_p3,
bool bRest) const -> sofa::type::vector<SReal>
{
const Real ZERO = 1e-12;
sofa::type::vector< SReal > baryCoefs;
const typename DataTypes::VecCoord& vect_c = (bRest ? (this->object->read(core::ConstVecCoordId::restPosition())->getValue()) : (this->object->read(core::ConstVecCoordId::position())->getValue()));
const typename DataTypes::Coord& c0 = vect_c[ind_p1];
const typename DataTypes::Coord& c1 = vect_c[ind_p2];
const typename DataTypes::Coord& c2 = vect_c[ind_p3];
sofa::type::Vec<3,Real> a;
a[0] = (Real) (c0[0]);
a[1] = (Real) (c0[1]);
a[2] = (Real) (c0[2]);
sofa::type::Vec<3,Real> b;
b[0] = (Real) (c1[0]);
b[1] = (Real) (c1[1]);
b[2] = (Real) (c1[2]);
sofa::type::Vec<3,Real> c;
c[0] = (Real) (c2[0]);
c[1] = (Real) (c2[1]);
c[2] = (Real) (c2[2]);
sofa::type::Vec<3,Real> M = (sofa::type::Vec<3,Real>) (b-a).cross(c-a);
Real norm2_M = M*(M);
Real coef_a, coef_b, coef_c;
//if(norm2_M==0.0) // triangle (a,b,c) is flat
if(norm2_M < ZERO) // triangle (a,b,c) is flat
{
coef_a = (Real) (1.0/3.0);
coef_b = (Real) (1.0/3.0);
coef_c = (Real) (1.0 - (coef_a + coef_b));
}
else
{
sofa::type::Vec<3,Real> N = M/norm2_M;
coef_a = N*((b-p).cross(c-p));
coef_b = N*((c-p).cross(a-p));
coef_c = (Real) (1.0 - (coef_a + coef_b)); //N*((a-p).cross(b-p));
}
baryCoefs.push_back(coef_a);
baryCoefs.push_back(coef_b);
baryCoefs.push_back(coef_c);
return baryCoefs;
}
// Find the two closest points from two triangles (each of the point belonging to one triangle)
template<class DataTypes>
void TriangleSetGeometryAlgorithms< DataTypes >::computeClosestIndexPair(const TriangleID ind_ta, const TriangleID ind_tb,
PointID &ind1, PointID &ind2) const
{
const typename DataTypes::VecCoord& vect_c =(this->object->read(core::ConstVecCoordId::position())->getValue());
const Triangle &ta=this->m_topology->getTriangle(ind_ta);
const Triangle &tb=this->m_topology->getTriangle(ind_tb);
Real min_value=(Real) 0.0;
bool is_init = false;
for(unsigned int i=0; i<3; i++)
{
const typename DataTypes::Coord& ca=vect_c[ta[i]];
sofa::type::Vec<3,Real> pa;
pa[0] = (Real) (ca[0]);
pa[1] = (Real) (ca[1]);
pa[2] = (Real) (ca[2]);
for(unsigned int j=0; j!=i && j<3; j++)
{
const typename DataTypes::Coord& cb=vect_c[tb[i]];
sofa::type::Vec<3,Real> pb;
pb[0] = (Real) (cb[0]);
pb[1] = (Real) (cb[1]);
pb[2] = (Real) (cb[2]);
Real norm_v_normal = (pa-pb)*(pa-pb);
if(!is_init)
{
min_value = norm_v_normal;
ind1 = ta[i];
ind2 = tb[j];
is_init = true;
}
else
{
if(norm_v_normal<min_value)
{
min_value = norm_v_normal;
ind1 = ta[i];
ind2 = tb[j];
}
}
}
}
return;
}
// test if a point is inside the triangle indexed by ind_t
template<class DataTypes>
bool TriangleSetGeometryAlgorithms< DataTypes >::isPointInsideTriangle(const TriangleID ind_t,
bool is_tested,
const sofa::type::Vec<3,Real>& p,
TriangleID &ind_t_test,
bool bRest) const
{
const Real ZERO = -1e-12;
const typename DataTypes::VecCoord& vect_c = bRest
? (this->object->read(core::ConstVecCoordId::restPosition())->getValue())
:(this->object->read(core::ConstVecCoordId::position())->getValue());
const Triangle &t=this->m_topology->getTriangle(ind_t);
const typename DataTypes::Coord& c0=vect_c[t[0]];
const typename DataTypes::Coord& c1=vect_c[t[1]];
const typename DataTypes::Coord& c2=vect_c[t[2]];
sofa::type::Vec<3,Real> ptest = p;
sofa::type::Vec<3,Real> p0;
p0[0] = (Real) (c0[0]);
p0[1] = (Real) (c0[1]);
p0[2] = (Real) (c0[2]);
sofa::type::Vec<3,Real> p1;
p1[0] = (Real) (c1[0]);
p1[1] = (Real) (c1[1]);
p1[2] = (Real) (c1[2]);
sofa::type::Vec<3,Real> p2;
p2[0] = (Real) (c2[0]);
p2[1] = (Real) (c2[1]);
p2[2] = (Real) (c2[2]);
sofa::type::Vec<3,Real> v_normal = (p2-p0).cross(p1-p0);
Real norm_v_normal = v_normal*(v_normal);
if(norm_v_normal != 0.0)
{
sofa::type::Vec<3,Real> n_01 = (p1-p0).cross(v_normal);
sofa::type::Vec<3,Real> n_12 = (p2-p1).cross(v_normal);
sofa::type::Vec<3,Real> n_20 = (p0-p2).cross(v_normal);
Real v_01 = (Real) ((ptest-p0)*(n_01));
Real v_12 = (Real) ((ptest-p1)*(n_12));
Real v_20 = (Real) ((ptest-p2)*(n_20));
const bool is_inside = (v_01 > ZERO) && (v_12 > ZERO) && (v_20 > ZERO);
if(is_tested && (!is_inside))
{
sofa::type::vector< TriangleID > shell;
EdgeID ind_edge = 0;
if(v_01 < 0.0)
{
if(v_12 < 0.0) /// vertex 1
{
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundVertex(t[1]));
}
else
{
if(v_20 < 0.0) /// vertex 0
{
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundVertex(t[0]));
}
else // v_01 < 0.0
{
ind_edge=this->m_topology->getEdgeIndex(t[0],t[1]);
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundEdge(ind_edge));
}
}
}
else
{
if(v_12 < 0.0)
{
if(v_20 < 0.0) /// vertex 2
{
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundVertex(t[2]));
}
else // v_12 < 0.0
{
ind_edge=this->m_topology->getEdgeIndex(t[1],t[2]);
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundEdge(ind_edge));
}
}
else // v_20 < 0.0
{
ind_edge=this->m_topology->getEdgeIndex(t[2],t[0]);
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundEdge(ind_edge));
}
}
size_t i =0;
bool is_in_next_triangle=false;
TriangleID ind_triangle=0;
TriangleID ind_t_false_init;
TriangleID &ind_t_false = ind_t_false_init;
if(shell.size()>1)
{
while(i < shell.size() && !is_in_next_triangle)
{
ind_triangle=shell[i];
if(ind_triangle != ind_t)
{
is_in_next_triangle = isPointInTriangle(ind_triangle, false, p, ind_t_false);
}
i++;
}
if(is_in_next_triangle)
{
ind_t_test=ind_triangle;
//msg_info() << "correct to triangle indexed by " << ind_t_test;
}
else // not found
{
//msg_info() << "not found !!! ";
ind_t_test=ind_t;
}
}
else
{
ind_t_test=ind_t;
}
}
return is_inside;
}
else // triangle is flat
{
//msg_info() << "INFO_print : triangle is flat";
return false;
}
}
// test if a point is in the triangle indexed by ind_t
template<class DataTypes>
bool TriangleSetGeometryAlgorithms< DataTypes >::isPointInTriangle(const TriangleID ind_t,
bool is_tested,
const sofa::type::Vec<3,Real>& p,
TriangleID &ind_t_test) const
{
const Real ZERO = 1e-12;
const typename DataTypes::VecCoord& vect_c =(this->object->read(core::ConstVecCoordId::position())->getValue());
const Triangle &t=this->m_topology->getTriangle(ind_t);
const typename DataTypes::Coord& c0=vect_c[t[0]];
const typename DataTypes::Coord& c1=vect_c[t[1]];
const typename DataTypes::Coord& c2=vect_c[t[2]];
sofa::type::Vec<3,Real> ptest = p;
sofa::type::Vec<3,Real> p0;
p0[0] = (Real) (c0[0]);
p0[1] = (Real) (c0[1]);
p0[2] = (Real) (c0[2]);
sofa::type::Vec<3,Real> p1;
p1[0] = (Real) (c1[0]);
p1[1] = (Real) (c1[1]);
p1[2] = (Real) (c1[2]);
sofa::type::Vec<3,Real> p2;
p2[0] = (Real) (c2[0]);
p2[1] = (Real) (c2[1]);
p2[2] = (Real) (c2[2]);
sofa::type::Vec<3,Real> v_normal = (p2-p0).cross(p1-p0);
Real norm_v_normal = v_normal*(v_normal);
//if(norm_v_normal != 0.0)
if(norm_v_normal > ZERO)
{
sofa::type::Vec<3,Real> n_01 = (p1-p0).cross(v_normal);
sofa::type::Vec<3,Real> n_12 = (p2-p1).cross(v_normal);
sofa::type::Vec<3,Real> n_20 = (p0-p2).cross(v_normal);
Real v_01 = (Real) ((ptest-p0)*(n_01));
Real v_12 = (Real) ((ptest-p1)*(n_12));
Real v_20 = (Real) ((ptest-p2)*(n_20));
//bool is_inside = (v_01 > 0.0) && (v_12 > 0.0) && (v_20 > 0.0);
const bool is_inside = (v_01 > -ZERO) && (v_12 > -ZERO) && (v_20 >= -ZERO);
if(is_tested && (!is_inside))
{
sofa::type::vector< TriangleID > shell;
EdgeID ind_edge = 0;
//if(v_01 < 0.0)
if(v_01 < -ZERO)
{
//if(v_12 < 0.0) /// vertex 1
if(v_12 < -ZERO) /// vertex 1
{
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundVertex(t[1]));
}
else
{
//if(v_20 < 0.0) /// vertex 0
if(v_20 < -ZERO) /// vertex 0
{
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundVertex(t[0]));
}
else // v_01 < 0.0
{
ind_edge=this->m_topology->getEdgeIndex(t[0],t[1]);
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundEdge(ind_edge));
}
}
}
else
{
//if(v_12 < 0.0)
if(v_12 < -ZERO)
{
//if(v_20 < 0.0) /// vertex 2
if(v_20 < -ZERO) /// vertex 2
{
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundVertex(t[2]));
}
else // v_12 < 0.0
{
ind_edge=this->m_topology->getEdgeIndex(t[1],t[2]);
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundEdge(ind_edge));
}
}
else // v_20 < 0.0
{
ind_edge=this->m_topology->getEdgeIndex(t[2],t[0]);
shell =(sofa::type::vector< TriangleID >) (this->m_topology->getTrianglesAroundEdge(ind_edge));
}
}
size_t i =0;
bool is_in_next_triangle=false;
TriangleID ind_triangle=0;
TriangleID ind_t_false_init;
TriangleID &ind_t_false = ind_t_false_init;
if(shell.size()>1)
{
while(i < shell.size() && !is_in_next_triangle)
{
ind_triangle=shell[i];
if(ind_triangle != ind_t)
{
is_in_next_triangle = isPointInTriangle(ind_triangle, false, p, ind_t_false);
}
i++;
}
if(is_in_next_triangle)
{
ind_t_test=ind_triangle;
//msg_info() << "correct to triangle indexed by " << ind_t_test;
}
else // not found
{
//msg_info() << "not found !!! ";
ind_t_test=ind_t;
}
}
else
{
ind_t_test=ind_t;
}
}
return is_inside;
}
else // triangle is flat
{
//msg_info() << "INFO_print : triangle is flat";
return false;
}
}
// Tests how to triangularize a quad whose vertices are defined by (p_q1, p_q2, ind_q3, ind_q4) according to the Delaunay criterion
template<class DataTypes>
bool TriangleSetGeometryAlgorithms< DataTypes >::isQuadDeulaunayOriented(const typename DataTypes::Coord& p_q1,
const typename DataTypes::Coord& p_q2,
QuadID ind_q3,
QuadID ind_q4)
{
sofa::type::vector< Real > baryCoefs;
const typename DataTypes::VecCoord& vect_c =(this->object->read(core::ConstVecCoordId::position())->getValue());
const typename DataTypes::Coord& c3 = vect_c[ind_q3];
const typename DataTypes::Coord& c4 = vect_c[ind_q4];
return isQuadDeulaunayOriented(p_q1, p_q2, c3, c4);
}
/** \brief Tests how to triangularize a quad whose vertices are defined by (p1, p2, p3, p4) according to the Delaunay criterion
*
*/
template<class DataTypes>
bool TriangleSetGeometryAlgorithms< DataTypes >::isQuadDeulaunayOriented(const typename DataTypes::Coord& p1,
const typename DataTypes::Coord& p2,
const typename DataTypes::Coord& p3,
const typename DataTypes::Coord& p4)
{
// use formula with angles
// A----B p1----p2
// \ \ \ \
// D----C p4----p3
// if the sum of opposites angles (not on the common edge) is < 180deg, the triangles meet the Delaunay condition
sofa::type::Vec<3, Real> AB = { p2[0] - p1[0], p2[1] - p1[1], p2[2] - p1[2] };
sofa::type::Vec<3, Real> AD = { p4[0] - p1[0], p4[1] - p1[1], p4[2] - p1[2] };
sofa::type::Vec<3, Real> CB = { p2[0] - p3[0], p2[1] - p3[1], p2[2] - p3[2] };
sofa::type::Vec<3, Real> CD = { p4[0] - p3[0], p4[1] - p3[1], p4[2] - p3[2] };
AB.normalize();
AD.normalize();
Real alpha = acos(dot(AB, AD));
CB.normalize();
CD.normalize();
Real beta = acos(CB * CD);
const bool isDelau = (alpha + beta <= M_PI);
return isDelau;
}
template<class DataTypes>
bool TriangleSetGeometryAlgorithms< DataTypes >::isDiagonalsIntersectionInQuad (const typename DataTypes::Coord triangle1[3],const typename DataTypes::Coord triangle2[3])
{
Coord CommonEdge[2], oppositeVertices[2];
unsigned int cpt = 0;
bool test = false;
for (unsigned int i = 0; i<3; i++)
{
test = false;
for (unsigned int j = 0; j<3; j++)
if(triangle1[i] == triangle2[j])
{
test = true;
break;
}
if(test)
{
CommonEdge[cpt] = triangle1[i];
cpt++;
}
else
oppositeVertices[0] = triangle1[i];
}
for (unsigned int i = 0; i<3; i++)
{