RMesh::MeshPCA RMesh::mesh::buildPCA( vector<Primitives::Point3d> &points )
{
vector<CGAL_Point> cgal_points;
CGAL_Line line;
CGAL_Plane plane;
MeshPCA pca;
Primitives::BBoxD bbox;
bbox.Set(points);
for( int i = 0; i < points.size(); ++i )
{
cgal_points.push_back( build_CGAL_Point( points[i] ));
}
linear_least_squares_fitting_3( cgal_points.begin(), cgal_points.end(), plane,CGAL::Dimension_tag<0>());
// fit line to triangle vertices
linear_least_squares_fitting_3( cgal_points.begin(), cgal_points.end(), line, CGAL::Dimension_tag<0>());
pca.up = build_Vector3d( line.direction().vector() );
pca.down = pca.up * (-1.0);
pca.front = build_Vector3d( plane.orthogonal_direction().vector() );
pca.back = pca.front * (-1.0);
pca.right = pca.up.Cross( pca.front );
pca.left = pca.right * (-1.0);
pca.center = bbox.Center();
pca.is_valid = true;
return pca;
}
void RMesh::mesh::buildPCA(RMesh::mesh &m)
{
vector<CGAL_Triangle> triangles;
getCGALTriangles(m, triangles);
CGAL_Line line;
CGAL_Plane plane;
// fit plane to whole triangles
linear_least_squares_fitting_3( triangles.begin(), triangles.end(), plane,CGAL::Dimension_tag<2>());
// fit line to triangle vertices
linear_least_squares_fitting_3( triangles.begin(), triangles.end(), line, CGAL::Dimension_tag<0>());
m.axes.up = build_Vector3d( line.direction().vector() );
m.axes.down = m.axes.up * (-1.0);
m.axes.front = build_Vector3d( plane.orthogonal_direction().vector() );
m.axes.back = m.axes.front * (-1.0);
m.axes.right = m.axes.up.Cross( m.axes.front );
m.axes.left = m.axes.right * (-1.0);
m.axes.is_valid = true;
}
void fit_point_set(std::list<Point>& points,
Plane& plane,
Line& line)
{
// fit a plane
// call all versions of the function
Kernel kernel;
FT quality;
Point centroid;
std::cout << "fit 3D line...";
quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,CGAL::Dimension_tag<0>());
quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>());
quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),kernel,
CGAL::Default_diagonalize_traits<FT,3>());
std::cout << "done (quality: " << quality << ")" << std::endl;
std::cout << "fit 3D plane...";
quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,CGAL::Dimension_tag<0>());
quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,centroid,CGAL::Dimension_tag<0>());
quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,centroid,CGAL::Dimension_tag<0>(),kernel,
CGAL::Default_diagonalize_traits<FT,3>());
std::cout << "done (quality: " << quality << ")" << std::endl;
}
int main(void)
{
std::cout << "Test linear least squares fitting of 3D spheres" << std::endl;
// centers
Point c1(0.0,0.0,0.0);
Point c2(1.0,1.0,1.0);
// radii
FT sqr1 = 0.1;
FT sqr2 = 0.5;
// add two spheres
std::list<Sphere> spheres;
spheres.push_back(Sphere(c1,sqr1));
spheres.push_back(Sphere(c2,sqr2));
Line line;
Plane plane;
Kernel kernel;
Point centroid;
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<3>(),kernel);
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<2>(),kernel);
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<3>(),kernel);
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<2>(),kernel);
return 0;
}
int main()
{
std::cout << "Test 3D linear least squares fitting of tetrahedra" << std::endl;
// generate two tetrahedra
std::list<Tetrahedron> tetrahedra;
Point a(0.0,0.0,0.0);
Point b(1.0,0.0,0.0);
Point c(0.0,1.0,0.0);
Point d(0.0,0.0,1.0);
Point e(0.0,1.0,1.0);
tetrahedra.push_back(Tetrahedron(a,b,c,d));
tetrahedra.push_back(Tetrahedron(a,b,c,e));
Line line;
Plane plane;
Point centroid;
// fit line, no centroid
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,CGAL::Dimension_tag<1>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,CGAL::Dimension_tag<0>());
// fit line, centroid
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<1>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<0>());
// fit plane, no centroid
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,CGAL::Dimension_tag<1>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,CGAL::Dimension_tag<0>());
// fit plane, centroid
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<2>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<1>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<0>());
// If Eigen is available, it's used by default everywhere.
// These additional lines test the fallback version
#ifdef CGAL_EIGEN3_ENABLED
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<3>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<2>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<1>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,centroid,CGAL::Dimension_tag<0>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<3>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<2>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<1>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,centroid,CGAL::Dimension_tag<0>(),
Kernel(), CGAL::Diagonalize_traits<FT, 3>());
#endif
return 0;
}
