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119 lines
5.8 KiB
119 lines
5.8 KiB
#include "half_space_box.h"
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#include "assign_scalar.h"
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#include <CGAL/Point_3.h>
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#include <CGAL/Vector_3.h>
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template <typename DerivedV>
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IGL_INLINE void igl::copyleft::cgal::half_space_box(
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const CGAL::Plane_3<CGAL::Epeck> & P,
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const Eigen::MatrixBase<DerivedV> & V,
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Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
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Eigen::Matrix<int,12,3> & BF)
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{
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typedef CGAL::Point_3<CGAL::Epeck> Point;
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typedef CGAL::Vector_3<CGAL::Epeck> Vector;
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typedef CGAL::Epeck::FT EScalar;
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Point o3(V(0,0),V(0,1),V(0,2));
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Point o2 = P.projection(o3);
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//https://math.stackexchange.com/a/4112622/35376
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const auto copysign = [](const EScalar & a, const EScalar & b)->EScalar
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{
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return (b>=0 ? abs(a) : -abs(a));
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};
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Vector n = P.orthogonal_vector();
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Vector u(
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copysign(n.z(),n.x()),
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copysign(n.z(),n.y()),
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-copysign(n.x(),n.z()) - copysign(n.y(),n.z()));
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// L1 of bounding box diagonal. ‖x‖₂ ≤ ‖x‖₁
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const EScalar bbd =
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(EScalar(V.col(0).maxCoeff())- EScalar(V.col(0).minCoeff())) +
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(EScalar(V.col(1).maxCoeff())- EScalar(V.col(1).minCoeff())) +
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(EScalar(V.col(2).maxCoeff())- EScalar(V.col(2).minCoeff()));
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const EScalar bbd_sqr = bbd*bbd;
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// now we have a center o2 and a vector u to the farthest point on the plane
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std::vector<Point> vBV;vBV.reserve(8);
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Vector v = CGAL::cross_product(u,n);
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// Scale u,v,n to be longer than bbd
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const auto & longer_than = [](const EScalar min_sqr, Vector & x)
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{
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assert(x.squared_length() > 0);
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while(x.squared_length() < min_sqr)
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{
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x = 2.*x;
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}
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};
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longer_than(bbd_sqr,u);
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longer_than(bbd_sqr,v);
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longer_than(bbd_sqr,n);
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vBV.emplace_back( o2 + u + v);
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vBV.emplace_back( o2 - u + v);
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vBV.emplace_back( o2 - u - v);
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vBV.emplace_back( o2 + u - v);
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vBV.emplace_back( o2 + u + v - n);
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vBV.emplace_back( o2 - u + v - n);
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vBV.emplace_back( o2 - u - v - n);
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vBV.emplace_back( o2 + u - v - n);
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BV.resize(8,3);
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for(int b = 0;b<8;b++)
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{
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igl::copyleft::cgal::assign_scalar(vBV[b].x(),BV(b,0));
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igl::copyleft::cgal::assign_scalar(vBV[b].y(),BV(b,1));
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igl::copyleft::cgal::assign_scalar(vBV[b].z(),BV(b,2));
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}
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BF.resize(12,3);
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BF<<
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1,0,2,
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2,0,3,
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4,5,6,
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4,6,7,
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0,1,4,
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4,1,5,
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1,2,5,
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5,2,6,
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2,3,6,
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6,3,7,
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3,0,7,
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7,0,4;
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}
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template <typename Derivedp, typename Derivedn, typename DerivedV>
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IGL_INLINE void igl::copyleft::cgal::half_space_box(
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const Eigen::MatrixBase<Derivedp> & p,
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const Eigen::MatrixBase<Derivedn> & n,
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const Eigen::MatrixBase<DerivedV> & V,
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Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
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Eigen::Matrix<int,12,3> & BF)
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{
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typedef CGAL::Plane_3<CGAL::Epeck> Plane;
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typedef CGAL::Point_3<CGAL::Epeck> Point;
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typedef CGAL::Vector_3<CGAL::Epeck> Vector;
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Plane P(Point(p(0),p(1),p(2)),Vector(n(0),n(1),n(2)));
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return half_space_box(P,V,BV,BF);
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}
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template <typename Derivedequ, typename DerivedV>
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IGL_INLINE void igl::copyleft::cgal::half_space_box(
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const Eigen::MatrixBase<Derivedequ> & equ,
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const Eigen::MatrixBase<DerivedV> & V,
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Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
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Eigen::Matrix<int,12,3> & BF)
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{
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typedef CGAL::Plane_3<CGAL::Epeck> Plane;
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Plane P(equ(0),equ(1),equ(2),equ(3));
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return half_space_box(P,V,BV,BF);
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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// generated by autoexplicit.sh
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template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<double, 1, 4, 1, 1, 4>, Eigen::Matrix<double, -1, -1, 0, -1, -1>>(Eigen::MatrixBase<Eigen::Matrix<double, 1, 4, 1, 1, 4>> const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1>> const&, Eigen::Matrix<CGAL::Epeck::FT, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
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template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<double, -1, 3, 1, -1, 3> >(CGAL::Plane_3<CGAL::Epeck> const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::Matrix<CGAL::Epeck::FT, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
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// generated by autoexplicit.sh
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template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<float, -1, 3, 1, -1, 3> >(CGAL::Plane_3<CGAL::Epeck> const&, Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::Matrix<CGAL::Epeck::FT, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
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template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<CGAL::Epeck::FT, 1, 4, 1, 1, 4>, Eigen::Matrix<CGAL::Epeck::FT, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Epeck::FT, 1, 4, 1, 1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Epeck::FT, -1, 3, 0, -1, 3> > const&, Eigen::Matrix<CGAL::Epeck::FT, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
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template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<CGAL::Epeck::FT, 1, 4, 1, 1, 4>, Eigen::Matrix<CGAL::Epeck::FT, -1, 4, 0, -1, 4> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Epeck::FT, 1, 4, 1, 1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Epeck::FT, -1, 4, 0, -1, 4> > const&, Eigen::Matrix<CGAL::Epeck::FT, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
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template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<CGAL::Epeck::FT, 1, 4, 1, 1, 4>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Epeck::FT, 1, 4, 1, 1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::Matrix<CGAL::Epeck::FT, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
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template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::Matrix<CGAL::Epeck::FT, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
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#endif
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