core/vgl/vgl_triangle_3d.h

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#ifndef VGL_TRIANGLE_3D_H_
#define VGL_TRIANGLE_3D_H_
//:
// \file
// \brief Some helpful functions when working with triangles
// \author Kieran O'Mahony
// \date 21 June 2007

#include <vcl_algorithm.h>
#include <vcl_utility.h>
#include <vcl_cmath.h>

#include <vgl/vgl_line_segment_3d.h>
#include <vgl/vgl_point_3d.h>

enum vgl_triangle_3d_intersection_t
{
  None=0,
  Skew,
  Coplanar
};

//: Check for coincident edges of triangles a and b
//  \return a vector of the coincident edges
vcl_vector<vcl_pair<unsigned,unsigned> > vgl_triangle_3d_coincident_edges(
  const vgl_point_3d<double>& a_p1,
  const vgl_point_3d<double>& a_p2,
  const vgl_point_3d<double>& a_p3,
  const vgl_point_3d<double>& b_p1,
  const vgl_point_3d<double>& b_p2,
  const vgl_point_3d<double>& b_p3);

//: Check if the given point is inside the triangle
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
//  \return true if point is inside
bool vgl_triangle_3d_test_inside(
  const vgl_point_3d<double>& i_pnt,
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3);

//: Check if point \a i_pnt is inside the triangle
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
//  \return true if point is inside
//  \note this method uses the less efficient 'angles' method which requires 3 calls to acos()
bool vgl_triangle_3d_test_inside_simple(
  const vgl_point_3d<double>& i_pnt,
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3 );


//: Compute the intersection point between the line segment and triangle
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
//  \return true if line intersects triangle
vgl_triangle_3d_intersection_t vgl_triangle_3d_line_intersection(
  const vgl_line_segment_3d<double>& line,
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3,
  vgl_point_3d<double>& i_pnt,
  bool ignore_coplanar = false);

//: Compute if the given triangles a and b intersect
//  The triangles are represented by their respective vertices \a a_p1, \a a_p2, \a a_p3
//  and \a b_p1, \a b_p2, \a b_p3
//  \return intersection type
vgl_triangle_3d_intersection_t vgl_triangle_3d_triangle_intersection(
  const vgl_point_3d<double>& a_p1,
  const vgl_point_3d<double>& a_p2,
  const vgl_point_3d<double>& a_p3,
  const vgl_point_3d<double>& b_p1,
  const vgl_point_3d<double>& b_p2,
  const vgl_point_3d<double>& b_p3);

//: Compute the intersection line of the given triangles
//  \see vgl_triangle_3d_triangle_intersection()
//  \note an intesection line is not computed for a coplanar intersection
vgl_triangle_3d_intersection_t vgl_triangle_3d_triangle_intersection(
  const vgl_point_3d<double>& a_p1,
  const vgl_point_3d<double>& a_p2,
  const vgl_point_3d<double>& a_p3,
  const vgl_point_3d<double>& b_p1,
  const vgl_point_3d<double>& b_p2,
  const vgl_point_3d<double>& b_p3,
  vgl_line_segment_3d<double>& i_line);

//: Compute the line of intersection of the given triangle and plane
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
//  \return intersection type
//  \note an intersection line is not defined (NaN) for a coplanar intersection
vgl_triangle_3d_intersection_t vgl_triangle_3d_plane_intersection(
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3,
  const vgl_plane_3d<double>& i_plane,
  vgl_line_segment_3d<double>& i_line);

//: Compute the longest side of the given triangle
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
//  \return length of the longest side
inline double vgl_triangle_3d_longest_side(
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3)
{
  double side_length_max = vcl_max( (p2 - p1).sqr_length(), (p3 - p2).sqr_length());
  side_length_max = vcl_max( side_length_max, (p1 - p3).sqr_length());
  return vcl_sqrt(side_length_max);
}

//: Compute the shortest side of the given triangle
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
//  \return length of the longest side
inline double vgl_triangle_3d_shortest_side(
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3)
{
  double side_length_min = vcl_min( (p2 - p1).sqr_length(), (p3 - p2).sqr_length());
  side_length_min = vcl_min( side_length_min, (p1 - p3).sqr_length());
  return vcl_sqrt(side_length_min);
}

//: Compute the closest point on a triangle to a reference point
//  The triangle is represented by its vertices \a p1, \a p2, \a p3.
//  \param q The reference point.
//  \return The closest point on the triangle. This may be inside the triangle, or it may be a point on one of the triangle edges.
vgl_point_3d<double> vgl_triangle_3d_closest_point(
  const vgl_point_3d<double>& q,
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3);

//: Compute the distance to the closest point on a triangle from a reference point.
//  The triangle is represented by its vertices \a p1, \a p2, \a p3.
//  \param q The reference point.
//  \return The distance to the closest point on the triangle. (The closest point may be inside the triangle, or it may be a point on one of the triangle edges.)
double vgl_triangle_3d_distance(
  const vgl_point_3d<double>& q,
  const vgl_point_3d<double>& p1,
  const vgl_point_3d<double>& p2,
  const vgl_point_3d<double>& p3);

//: Check if the two triangles are coplanar
//  The triangles are represented by their respective vertices \a a_p1, \a a_p2, \a a_p3
//  and \a b_p1, \a b_p2, \a b_p3
bool vgl_triangle_3d_triangle_coplanar(
  const vgl_point_3d<double>& a_p1,
  const vgl_point_3d<double>& a_p2,
  const vgl_point_3d<double>& a_p3,
  const vgl_point_3d<double>& b_p1,
  const vgl_point_3d<double>& b_p2,
  const vgl_point_3d<double>& b_p3);


//=======================================================================
//: Compute the area of a triangle
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
double vgl_triangle_3d_area(
  const vgl_point_3d<double> &p0,
  const vgl_point_3d<double> &p1,
  const vgl_point_3d<double> &p2 );

//=======================================================================
//: Compute the aspect ratio of a triangle
//  The triangle is represented by its vertices \a p1, \a p2, \a p3
double vgl_triangle_3d_aspect_ratio(
  const vgl_point_3d<double> &p0,
  const vgl_point_3d<double> &p1,
  const vgl_point_3d<double> &p2 );

#endif // VGL_TRIANGLE_3D_H_