capsule-inl.h

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#ifndef FCL_SHAPE_CAPSULE_INL_H
#define FCL_SHAPE_CAPSULE_INL_H
 
#include <iomanip>
#include <sstream>
 
#include "fcl/geometry/shape/capsule.h"
#include "fcl/geometry/shape/representation.h"
 
namespace fcl
{
 
//==============================================================================
extern template
class FCL_EXPORT Capsule<double>;
 
//==============================================================================
template <typename S>
Capsule<S>::Capsule(S radius, S lz)
  : ShapeBase<S>(), radius(radius), lz(lz)
{
  // Do nothing
}
 
//==============================================================================
template <typename S>
void Capsule<S>::computeLocalAABB()
{
  const Vector3<S> v_delta(radius, radius, 0.5 * lz + radius);
  this->aabb_local.max_ = v_delta;
  this->aabb_local.min_ = -v_delta;
 
  this->aabb_center = this->aabb_local.center();
  this->aabb_radius = (this->aabb_local.min_ - this->aabb_center).norm();
}
 
//==============================================================================
template <typename S>
NODE_TYPE Capsule<S>::getNodeType() const
{
  return GEOM_CAPSULE;
}
 
//==============================================================================
template <typename S>
S Capsule<S>::computeVolume() const
{
  return constants<S>::pi() * radius * radius *(lz + radius * 4/3.0);
}
 
//==============================================================================
// Compare https://www.gamedev.net/articles/programming/math-and-physics/capsule-inertia-tensor-r3856/
template <typename S>
Matrix3<S> Capsule<S>::computeMomentofInertia() const
{
  S l2 = lz * lz;
  S r2 = radius * radius;
 
  S v_cyl = r2 * lz * constants<S>::pi();
  S v_sph = r2 * radius * constants<S>::pi() * 4 / 3.0;
 
  S ix = v_cyl * (l2 / 12. + r2 / 4.) + v_sph * (0.4 * r2 + 0.25 * l2 + 3. * radius * lz / 8.);
  S iz = (0.5 * v_cyl + 0.4 * v_sph) * r2;
 
  return Vector3<S>(ix, ix, iz).asDiagonal();
}
 
//==============================================================================
template <typename S>
std::vector<Vector3<S>> Capsule<S>::getBoundVertices(
    const Transform3<S>& tf) const
{
  std::vector<Vector3<S>> result(36);
  const auto m = (1 + std::sqrt(5.0)) / 2.0;
 
  auto hl = lz * 0.5;
  auto edge_size = radius * 6 / (std::sqrt(27.0) + std::sqrt(15.0));
  auto a = edge_size;
  auto b = m * edge_size;
  auto r2 = radius * 2 / std::sqrt(3.0);
 
  result[0] = tf * Vector3<S>(0, a, b + hl);
  result[1] = tf * Vector3<S>(0, -a, b + hl);
  result[2] = tf * Vector3<S>(0, a, -b + hl);
  result[3] = tf * Vector3<S>(0, -a, -b + hl);
  result[4] = tf * Vector3<S>(a, b, hl);
  result[5] = tf * Vector3<S>(-a, b, hl);
  result[6] = tf * Vector3<S>(a, -b, hl);
  result[7] = tf * Vector3<S>(-a, -b, hl);
  result[8] = tf * Vector3<S>(b, 0, a + hl);
  result[9] = tf * Vector3<S>(b, 0, -a + hl);
  result[10] = tf * Vector3<S>(-b, 0, a + hl);
  result[11] = tf * Vector3<S>(-b, 0, -a + hl);
 
  result[12] = tf * Vector3<S>(0, a, b - hl);
  result[13] = tf * Vector3<S>(0, -a, b - hl);
  result[14] = tf * Vector3<S>(0, a, -b - hl);
  result[15] = tf * Vector3<S>(0, -a, -b - hl);
  result[16] = tf * Vector3<S>(a, b, -hl);
  result[17] = tf * Vector3<S>(-a, b, -hl);
  result[18] = tf * Vector3<S>(a, -b, -hl);
  result[19] = tf * Vector3<S>(-a, -b, -hl);
  result[20] = tf * Vector3<S>(b, 0, a - hl);
  result[21] = tf * Vector3<S>(b, 0, -a - hl);
  result[22] = tf * Vector3<S>(-b, 0, a - hl);
  result[23] = tf * Vector3<S>(-b, 0, -a - hl);
 
  auto c = 0.5 * r2;
  auto d = radius;
  result[24] = tf * Vector3<S>(r2, 0, hl);
  result[25] = tf * Vector3<S>(c, d, hl);
  result[26] = tf * Vector3<S>(-c, d, hl);
  result[27] = tf * Vector3<S>(-r2, 0, hl);
  result[28] = tf * Vector3<S>(-c, -d, hl);
  result[29] = tf * Vector3<S>(c, -d, hl);
 
  result[30] = tf * Vector3<S>(r2, 0, -hl);
  result[31] = tf * Vector3<S>(c, d, -hl);
  result[32] = tf * Vector3<S>(-c, d, -hl);
  result[33] = tf * Vector3<S>(-r2, 0, -hl);
  result[34] = tf * Vector3<S>(-c, -d, -hl);
  result[35] = tf * Vector3<S>(c, -d, -hl);
 
  return result;
}
 
//==============================================================================
template <typename S>
std::string Capsule<S>::representation(int precision) const {
  const char* S_str = detail::ScalarRepr<S>::value();
  std::stringstream ss;
  ss << std::setprecision(precision);
  ss << "Capsule<" << S_str << ">(" << radius << ", " << lz << ");";
  return ss.str();
}
 
} // namespace fcl
 
#endif