geometric_shapes.h

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/** \author Jia Pan */


#ifndef HPP_FCL_GEOMETRIC_SHAPES_H
#define HPP_FCL_GEOMETRIC_SHAPES_H

#include <boost/math/constants/constants.hpp>

#include <hpp/fcl/collision_object.h>
#include <hpp/fcl/data_types.h>
#include <string.h>

namespace hpp
{
namespace fcl
{

/// @brief Base class for all basic geometric shapes
class ShapeBase : public CollisionGeometry
{
public:
  ShapeBase() {}

  virtual ~ShapeBase () {};

  /// @brief Get object type: a geometric shape
  OBJECT_TYPE getObjectType() const { return OT_GEOM; }
};

/// @brief Triangle stores the points instead of only indices of points
class TriangleP : public ShapeBase
{
public:
  TriangleP(const Vec3f& a_, const Vec3f& b_, const Vec3f& c_) : ShapeBase(), a(a_), b(b_), c(c_)
  {
  }

  /// @brief virtual function of compute AABB in local coordinate
  void computeLocalAABB();
  
  NODE_TYPE getNodeType() const { return GEOM_TRIANGLE; }

  Vec3f a, b, c;
};

/// @brief Center at zero point, axis aligned box
class Box : public ShapeBase
{
public:
  Box(FCL_REAL x, FCL_REAL y, FCL_REAL z) : ShapeBase(), halfSide(x/2, y/2, z/2)
  {
  }

  Box(const Vec3f& side_) : ShapeBase(), halfSide(side_/2) 
  {
  }

  Box() {}

  /// @brief box side half-length
  Vec3f halfSide;

  /// @brief Compute AABB
  void computeLocalAABB();

  /// @brief Get node type: a box
  NODE_TYPE getNodeType() const { return GEOM_BOX; }

  FCL_REAL computeVolume() const
  {
    return 8*halfSide.prod();
  }

  Matrix3f computeMomentofInertia() const
  {
    FCL_REAL V = computeVolume();
    Vec3f s (halfSide.cwiseAbs2() * V);
    return (Vec3f (s[1] + s[2], s[0] + s[2], s[0] + s[1]) / 3).asDiagonal();
  }
};

/// @brief Center at zero point sphere
class Sphere : public ShapeBase
{
public:
  Sphere(FCL_REAL radius_) : ShapeBase(), radius(radius_)
  {
  }
  
  /// @brief Radius of the sphere 
  FCL_REAL radius;

  /// @brief Compute AABB 
  void computeLocalAABB();

  /// @brief Get node type: a sphere 
  NODE_TYPE getNodeType() const { return GEOM_SPHERE; }

  Matrix3f computeMomentofInertia() const
  {
    FCL_REAL I = 0.4 * radius * radius * computeVolume();
    return I * Matrix3f::Identity();
  }

  FCL_REAL computeVolume() const
  {
    return 4 * boost::math::constants::pi<FCL_REAL>() * radius * radius / 3;
  }
};

/// @brief Center at zero point capsule 
class Capsule : public ShapeBase
{
public:
  Capsule(FCL_REAL radius_, FCL_REAL lz_) : ShapeBase(), radius(radius_), lz(lz_)
  {
    lz = 0;
    HalfLength = lz/2;
  }

 // Capsule::Capsule() : HalfLength(lz/2), lz(0){} 

  /// @brief Radius of capsule 
  FCL_REAL radius;

  /// @brief Length along z axis 
  FCL_REAL lz;

  /// @brief Half Length along z axis 
  FCL_REAL HalfLength;

  /// @brief Compute AABB 
  void computeLocalAABB();

  /// @brief Get node type: a capsule 
  NODE_TYPE getNodeType() const { return GEOM_CAPSULE; }

  FCL_REAL computeVolume() const
  {
    return boost::math::constants::pi<FCL_REAL>() * radius * radius *(lz + radius * 4/3.0);
  }

  Matrix3f computeMomentofInertia() const
  {
    FCL_REAL v_cyl = radius * radius * lz * boost::math::constants::pi<FCL_REAL>();
    FCL_REAL v_sph = radius * radius * radius * boost::math::constants::pi<FCL_REAL>() * 4 / 3.0;
    
    FCL_REAL ix = v_cyl * lz * lz / 12.0 + 0.25 * v_cyl * radius + 0.4 * v_sph * radius * radius + 0.25 * v_sph * lz * lz;
    FCL_REAL iz = (0.5 * v_cyl + 0.4 * v_sph) * radius * radius;

    return (Matrix3f() << ix, 0, 0,
                          0, ix, 0,
                          0, 0, iz).finished();
  }
  
};

/// @brief Center at zero cone 
class Cone : public ShapeBase
{
public:
  Cone(FCL_REAL radius_, FCL_REAL lz_) : ShapeBase(), radius(radius_), lz(lz_)
  {
    lz = 0;
    HalfLength = lz/2;
  }

  //Cone::Cone() : HalfLength(lz/2), lz(0){} 

  /// @brief Radius of the cone 
  FCL_REAL radius;

  /// @brief Length along z axis 
  FCL_REAL lz;

  /// @brief Half Length along z axis 
  FCL_REAL HalfLength;

  /// @brief Compute AABB 
  void computeLocalAABB();

  /// @brief Get node type: a cone 
  NODE_TYPE getNodeType() const { return GEOM_CONE; }

  FCL_REAL computeVolume() const
  {
    return boost::math::constants::pi<FCL_REAL>() * radius * radius * lz / 3;
  }

  Matrix3f computeMomentofInertia() const
  {
    FCL_REAL V = computeVolume();
    FCL_REAL ix = V * (0.1 * lz * lz + 3 * radius * radius / 20);
    FCL_REAL iz = 0.3 * V * radius * radius;

    return (Matrix3f() << ix, 0, 0,
                          0, ix, 0,
                          0, 0, iz).finished();
  }

  Vec3f computeCOM() const
  {
    return Vec3f(0, 0, -0.25 * lz);
  }
};

/// @brief Center at zero cylinder 
class Cylinder : public ShapeBase
{
public:
  Cylinder(FCL_REAL radius_, FCL_REAL lz_) : ShapeBase(), radius(radius_), lz(lz_)
  {
    lz = 0;
    HalfLength = lz/2;
  }

 // Cylinder::Cylinder() : HalfLength(lz/2), lz(0){} 
  
  /// @brief Radius of the cylinder 
  FCL_REAL radius;

  /// @brief Length along z axis 
  FCL_REAL lz;

  /// @brief Half Length along z axis 
  FCL_REAL HalfLength;

  /// @brief Compute AABB 
  void computeLocalAABB();

  /// @brief Get node type: a cylinder 
  NODE_TYPE getNodeType() const { return GEOM_CYLINDER; }

  FCL_REAL computeVolume() const
  {
    return boost::math::constants::pi<FCL_REAL>() * radius * radius * lz;
  }

  Matrix3f computeMomentofInertia() const
  {
    FCL_REAL V = computeVolume();
    FCL_REAL ix = V * (3 * radius * radius + lz * lz) / 12;
    FCL_REAL iz = V * radius * radius / 2;
    return (Matrix3f() << ix, 0, 0,
                          0, ix, 0,
                          0, 0, iz).finished();
  }
};

/// @brief Convex polytope 
class Convex : public ShapeBase
{
public:
  /// @brief Constructing a convex, providing normal and offset of each polytype surface, and the points and shape topology information 
  /// \param points_ list of 3D points
  /// \param num_points_ number of 3D points
  /// \param polygons_ \copydoc Convex::polygons
  /// \param num_polygons_ the number of polygons.
  /// \note num_polygons_ is not the allocated size of polygons_.
  Convex(Vec3f* points_,
         int num_points_,
         int* polygons_,
         int num_polygons_) : ShapeBase()
  {
    num_polygons = num_polygons_;
    points = points_;
    num_points = num_points_;
    polygons = polygons_;
    edges = NULL;

    Vec3f sum (0,0,0);
    for(int i = 0; i < num_points; ++i)
    {
      sum += points[i];
    }

    center = sum * (FCL_REAL)(1.0 / num_points);

    fillEdges();
  }

  /// @brief Copy constructor 
  Convex(const Convex& other) : ShapeBase(other)
  {
    num_polygons = other.num_polygons;
    points = other.points;
    num_points = other.num_points;
    polygons = other.polygons;
    num_edges = other.num_edges;
    edges = new Edge[num_edges];
    memcpy(edges, other.edges, sizeof(Edge) * num_edges);
  }

  ~Convex()
  {
    delete [] edges;
  }

  /// @brief Compute AABB 
  void computeLocalAABB();

  /// @brief Get node type: a conex polytope 
  NODE_TYPE getNodeType() const { return GEOM_CONVEX; }

  /// @brief An array of indices to the points of each polygon, it should be the number of vertices
  /// followed by that amount of indices to "points" in counter clockwise order
  int* polygons;

  Vec3f* points;
  int num_points;
  int num_edges;
  int num_polygons;

  struct Edge
  {
    int first, second;
  };

  Edge* edges;

  /// @brief center of the convex polytope, this is used for collision: center is guaranteed in the internal of the polytope (as it is convex) 
  Vec3f center;

  /// based on http://number-none.com/blow/inertia/bb_inertia.doc
  Matrix3f computeMomentofInertia() const
  {
    
    Matrix3f C = Matrix3f::Zero();

    Matrix3f C_canonical;
    C_canonical << 1/60.0, 1/120.0, 1/120.0,
                   1/120.0, 1/60.0, 1/120.0,
                   1/120.0, 1/120.0, 1/60.0;

    int* points_in_poly = polygons;
    int* index = polygons + 1;
    for(int i = 0; i < num_polygons; ++i)
    {
      Vec3f plane_center(0,0,0);

      // compute the center of the polygon
      for(int j = 0; j < *points_in_poly; ++j)
        plane_center += points[index[j]];
      plane_center = plane_center * (1.0 / *points_in_poly);

      // compute the volume of tetrahedron making by neighboring two points, the plane center and the reference point (zero) of the convex shape
      const Vec3f& v3 = plane_center;
      for(int j = 0; j < *points_in_poly; ++j)
      {
        int e_first = index[j];
        int e_second = index[(j+1)%*points_in_poly];
        const Vec3f& v1 = points[e_first];
        const Vec3f& v2 = points[e_second];
        Matrix3f A; A << v1.transpose(), v2.transpose(), v3.transpose(); // this is A' in the original document
        C += A.derived().transpose() * C_canonical * A * (v1.cross(v2)).dot(v3);
      }
      
      points_in_poly += (*points_in_poly + 1);
      index = points_in_poly + 1;
    }

    return C.trace() * Matrix3f::Identity() - C;
  }

  Vec3f computeCOM() const
  {
    Vec3f com(0,0,0);
    FCL_REAL vol = 0;
    int* points_in_poly = polygons;
    int* index = polygons + 1;
    for(int i = 0; i < num_polygons; ++i)
    {
      Vec3f plane_center(0,0,0);

      // compute the center of the polygon
      for(int j = 0; j < *points_in_poly; ++j)
        plane_center += points[index[j]];
      plane_center = plane_center * (1.0 / *points_in_poly);

      // compute the volume of tetrahedron making by neighboring two points, the plane center and the reference point (zero) of the convex shape
      const Vec3f& v3 = plane_center;
      for(int j = 0; j < *points_in_poly; ++j)
      {
        int e_first = index[j];
        int e_second = index[(j+1)%*points_in_poly];
        const Vec3f& v1 = points[e_first];
        const Vec3f& v2 = points[e_second];
        FCL_REAL d_six_vol = (v1.cross(v2)).dot(v3);
        vol += d_six_vol;
        com += (points[e_first] + points[e_second] + plane_center) * d_six_vol;
      }
      
      points_in_poly += (*points_in_poly + 1);
      index = points_in_poly + 1;
    }

    return com / (vol * 4); // here we choose zero as the reference
  }

  FCL_REAL computeVolume() const
  {
    FCL_REAL vol = 0;
    int* points_in_poly = polygons;
    int* index = polygons + 1;
    for(int i = 0; i < num_polygons; ++i)
    {
      Vec3f plane_center(0,0,0);

      // compute the center of the polygon
      for(int j = 0; j < *points_in_poly; ++j)
        plane_center += points[index[j]];
      plane_center = plane_center * (1.0 / *points_in_poly);

      // compute the volume of tetrahedron making by neighboring two points, the plane center and the reference point (zero point) of the convex shape
      const Vec3f& v3 = plane_center;
      for(int j = 0; j < *points_in_poly; ++j)
      {
        int e_first = index[j];
        int e_second = index[(j+1)%*points_in_poly];
        const Vec3f& v1 = points[e_first];
        const Vec3f& v2 = points[e_second];
        FCL_REAL d_six_vol = (v1.cross(v2)).dot(v3);
        vol += d_six_vol;
      }
      
      points_in_poly += (*points_in_poly + 1);
      index = points_in_poly + 1;
    }

    return vol / 6;
  }

  

protected:
  /// @brief Get edge information 
  void fillEdges();
};


/// @brief Half Space: this is equivalent to the Plane in ODE. The separation plane is defined as n * x = d;
/// Points in the negative side of the separation plane (i.e. {x | n * x < d}) are inside the half space and points
/// in the positive side of the separation plane (i.e. {x | n * x > d}) are outside the half space
class Halfspace : public ShapeBase
{
public:
  /// @brief Construct a half space with normal direction and offset
  Halfspace(const Vec3f& n_, FCL_REAL d_) : ShapeBase(), n(n_), d(d_)
  {
    unitNormalTest();
  }

  /// @brief Construct a plane with normal direction and offset
  Halfspace(FCL_REAL a, FCL_REAL b, FCL_REAL c, FCL_REAL d_) : ShapeBase(), n(a, b, c), d(d_)
  {
    unitNormalTest();
  }

  Halfspace() : ShapeBase(), n(1, 0, 0), d(0)
  {
  }

  FCL_REAL signedDistance(const Vec3f& p) const
  {
    return n.dot(p) - d;
  }

  FCL_REAL distance(const Vec3f& p) const
  {
    return std::abs(n.dot(p) - d);
  }

  /// @brief Compute AABB
  void computeLocalAABB();

  /// @brief Get node type: a half space
  NODE_TYPE getNodeType() const { return GEOM_HALFSPACE; }
  
  /// @brief Plane normal
  Vec3f n;
  
  /// @brief Plane offset
  FCL_REAL d;

protected:

  /// @brief Turn non-unit normal into unit
  void unitNormalTest();
};

/// @brief Infinite plane 
class Plane : public ShapeBase
{
public:
  /// @brief Construct a plane with normal direction and offset 
  Plane(const Vec3f& n_, FCL_REAL d_) : ShapeBase(), n(n_), d(d_) 
  { 
    unitNormalTest(); 
  }
  
  /// @brief Construct a plane with normal direction and offset 
  Plane(FCL_REAL a, FCL_REAL b, FCL_REAL c, FCL_REAL d_) : ShapeBase(), n(a, b, c), d(d_)
  {
    unitNormalTest();
  }

  Plane() : ShapeBase(), n(1, 0, 0), d(0)
  {}

  FCL_REAL signedDistance(const Vec3f& p) const
  {
    return n.dot(p) - d;
  }

  FCL_REAL distance(const Vec3f& p) const
  {
    return std::abs(n.dot(p) - d);
  }

  /// @brief Compute AABB 
  void computeLocalAABB();

  /// @brief Get node type: a plane 
  NODE_TYPE getNodeType() const { return GEOM_PLANE; }

  /// @brief Plane normal 
  Vec3f n;

  /// @brief Plane offset 
  FCL_REAL d;

protected:
  
  /// @brief Turn non-unit normal into unit 
  void unitNormalTest();
};


}

} // namespace hpp

#endif