convex.hxx

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#ifndef COAL_SHAPE_CONVEX_HXX
#define COAL_SHAPE_CONVEX_HXX
 
#include <set>
#include <vector>
#include <iostream>
 
namespace coal {
 
template <typename PolygonT>
Convex<PolygonT>::Convex(std::shared_ptr<std::vector<Vec3s>> points_,
                         unsigned int num_points_,
                         std::shared_ptr<std::vector<PolygonT>> polygons_,
                         unsigned int num_polygons_)
    : ConvexBase(), polygons(polygons_), num_polygons(num_polygons_) {
  this->initialize(points_, num_points_);
  this->fillNeighbors();
  this->buildSupportWarmStart();
}
 
template <typename PolygonT>
Convex<PolygonT>::Convex(const Convex<PolygonT>& other)
    : ConvexBase(other), num_polygons(other.num_polygons) {
  if (other.polygons.get()) {
    polygons.reset(new std::vector<PolygonT>(*(other.polygons)));
  } else
    polygons.reset();
}
 
template <typename PolygonT>
Convex<PolygonT>::~Convex() {}
 
template <typename PolygonT>
void Convex<PolygonT>::set(std::shared_ptr<std::vector<Vec3s>> points_,
                           unsigned int num_points_,
                           std::shared_ptr<std::vector<PolygonT>> polygons_,
                           unsigned int num_polygons_) {
  ConvexBase::set(points_, num_points_);
 
  this->num_polygons = num_polygons_;
  this->polygons = polygons_;
 
  this->fillNeighbors();
  this->buildSupportWarmStart();
}
 
template <typename PolygonT>
Convex<PolygonT>* Convex<PolygonT>::clone() const {
  return new Convex(*this);
}
 
template <typename PolygonT>
Matrix3s Convex<PolygonT>::computeMomentofInertia() const {
  typedef typename PolygonT::size_type size_type;
  typedef typename PolygonT::index_type index_type;
 
  Matrix3s C = Matrix3s::Zero();
 
  Matrix3s C_canonical;
  C_canonical << Scalar(1 / 60),  //
      Scalar(1 / 120),            //
      Scalar(1 / 120),            //
      Scalar(1 / 120),            //
      Scalar(1 / 60),             //
      Scalar(1 / 120),            //
      Scalar(1 / 120),            //
      Scalar(1 / 120),            //
      Scalar(1 / 60);
 
  if (!(points.get())) {
    std::cerr
        << "Error in `Convex::computeMomentofInertia`! Convex has no vertices."
        << std::endl;
    return C;
  }
  const std::vector<Vec3s>& points_ = *points;
  if (!(polygons.get())) {
    std::cerr
        << "Error in `Convex::computeMomentofInertia`! Convex has no polygons."
        << std::endl;
    return C;
  }
  const std::vector<PolygonT>& polygons_ = *polygons;
  for (unsigned int i = 0; i < num_polygons; ++i) {
    const PolygonT& polygon = polygons_[i];
 
    // compute the center of the polygon
    Vec3s plane_center(0, 0, 0);
    for (size_type j = 0; j < polygon.size(); ++j)
      plane_center += points_[polygon[(index_type)j]];
    plane_center /= Scalar(polygon.size());
 
    // compute the volume of tetrahedron making by neighboring two points, the
    // plane center and the reference point (zero) of the convex shape
    const Vec3s& v3 = plane_center;
    for (size_type j = 0; j < polygon.size(); ++j) {
      index_type e_first = polygon[static_cast<index_type>(j)];
      index_type e_second =
          polygon[static_cast<index_type>((j + 1) % polygon.size())];
      const Vec3s& v1 = points_[e_first];
      const Vec3s& v2 = points_[e_second];
      Matrix3s A;
      A << v1.transpose(), v2.transpose(),
          v3.transpose();  // this is A' in the original document
      C += A.transpose() * C_canonical * A * (v1.cross(v2)).dot(v3);
    }
  }
 
  return C.trace() * Matrix3s::Identity() - C;
}
 
template <typename PolygonT>
Vec3s Convex<PolygonT>::computeCOM() const {
  typedef typename PolygonT::size_type size_type;
  typedef typename PolygonT::index_type index_type;
 
  Vec3s com(0, 0, 0);
  Scalar vol = 0;
  if (!(points.get())) {
    std::cerr << "Error in `Convex::computeCOM`! Convex has no vertices."
              << std::endl;
    return com;
  }
  const std::vector<Vec3s>& points_ = *points;
  if (!(polygons.get())) {
    std::cerr << "Error in `Convex::computeCOM`! Convex has no polygons."
              << std::endl;
    return com;
  }
  const std::vector<PolygonT>& polygons_ = *polygons;
  for (unsigned int i = 0; i < num_polygons; ++i) {
    const PolygonT& polygon = polygons_[i];
    // compute the center of the polygon
    Vec3s plane_center(0, 0, 0);
    for (size_type j = 0; j < polygon.size(); ++j)
      plane_center += points_[polygon[(index_type)j]];
    plane_center /= Scalar(polygon.size());
 
    // compute the volume of tetrahedron making by neighboring two points, the
    // plane center and the reference point (zero) of the convex shape
    const Vec3s& v3 = plane_center;
    for (size_type j = 0; j < polygon.size(); ++j) {
      index_type e_first = polygon[static_cast<index_type>(j)];
      index_type e_second =
          polygon[static_cast<index_type>((j + 1) % polygon.size())];
      const Vec3s& v1 = points_[e_first];
      const Vec3s& v2 = points_[e_second];
      Scalar d_six_vol = (v1.cross(v2)).dot(v3);
      vol += d_six_vol;
      com += (points_[e_first] + points_[e_second] + plane_center) * d_six_vol;
    }
  }
 
  return com / (vol * 4);  // here we choose zero as the reference
}
 
template <typename PolygonT>
Scalar Convex<PolygonT>::computeVolume() const {
  typedef typename PolygonT::size_type size_type;
  typedef typename PolygonT::index_type index_type;
 
  Scalar vol = 0;
  if (!(points.get())) {
    std::cerr << "Error in `Convex::computeVolume`! Convex has no vertices."
              << std::endl;
    return vol;
  }
  const std::vector<Vec3s>& points_ = *points;
  if (!(polygons.get())) {
    std::cerr << "Error in `Convex::computeVolume`! Convex has no polygons."
              << std::endl;
    return vol;
  }
  const std::vector<PolygonT>& polygons_ = *polygons;
  for (unsigned int i = 0; i < num_polygons; ++i) {
    const PolygonT& polygon = polygons_[i];
 
    // compute the center of the polygon
    Vec3s plane_center(0, 0, 0);
    for (size_type j = 0; j < polygon.size(); ++j)
      plane_center += points_[polygon[(index_type)j]];
    plane_center /= Scalar(polygon.size());
 
    // compute the volume of tetrahedron making by neighboring two points, the
    // plane center and the reference point (zero point) of the convex shape
    const Vec3s& v3 = plane_center;
    for (size_type j = 0; j < polygon.size(); ++j) {
      index_type e_first = polygon[static_cast<index_type>(j)];
      index_type e_second =
          polygon[static_cast<index_type>((j + 1) % polygon.size())];
      const Vec3s& v1 = points_[e_first];
      const Vec3s& v2 = points_[e_second];
      Scalar d_six_vol = (v1.cross(v2)).dot(v3);
      vol += d_six_vol;
    }
  }
 
  return vol / 6;
}
 
template <typename PolygonT>
void Convex<PolygonT>::fillNeighbors() {
  neighbors.reset(new std::vector<Neighbors>(num_points));
 
  typedef typename PolygonT::size_type size_type;
  typedef typename PolygonT::index_type index_type;
  std::vector<std::set<index_type>> nneighbors(num_points);
  unsigned int c_nneighbors = 0;
 
  if (!(polygons.get())) {
    std::cerr << "Error in `Convex::fillNeighbors`! Convex has no polygons."
              << std::endl;
  }
  const std::vector<PolygonT>& polygons_ = *polygons;
  for (unsigned int l = 0; l < num_polygons; ++l) {
    const PolygonT& polygon = polygons_[l];
    const size_type n = polygon.size();
 
    for (size_type j = 0; j < polygon.size(); ++j) {
      size_type i = (j == 0) ? n - 1 : j - 1;
      size_type k = (j == n - 1) ? 0 : j + 1;
      index_type pi = polygon[(index_type)i], pj = polygon[(index_type)j],
                 pk = polygon[(index_type)k];
      // Update neighbors of pj;
      if (nneighbors[pj].count(pi) == 0) {
        c_nneighbors++;
        nneighbors[pj].insert(pi);
      }
      if (nneighbors[pj].count(pk) == 0) {
        c_nneighbors++;
        nneighbors[pj].insert(pk);
      }
    }
  }
 
  nneighbors_.reset(new std::vector<unsigned int>(c_nneighbors));
 
  unsigned int* p_nneighbors = nneighbors_->data();
  std::vector<Neighbors>& neighbors_ = *neighbors;
  for (unsigned int i = 0; i < num_points; ++i) {
    Neighbors& n = neighbors_[i];
    if (nneighbors[i].size() >= (std::numeric_limits<unsigned char>::max)())
      COAL_THROW_PRETTY("Too many neighbors.", std::logic_error);
    n.count_ = (unsigned char)nneighbors[i].size();
    n.n_ = p_nneighbors;
    p_nneighbors =
        std::copy(nneighbors[i].begin(), nneighbors[i].end(), p_nneighbors);
  }
  assert(p_nneighbors == nneighbors_->data() + c_nneighbors);
}
 
}  // namespace coal
 
#endif