core/vgl/vgl_triangle_3d.h File Reference

Some helpful functions when working with triangles. More...

#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>

Go to the source code of this file.

Enumerations
enum	vgl_triangle_3d_intersection_t { None = 0, Skew, Coplanar }
Functions
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 for coincident edges of triangles a and b.
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 the given point is inside the triangle.
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)
	Check if point i_pnt is inside the 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 the intersection point between the line segment and triangle.
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 if the given triangles a and b intersect.
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 intersection line of the given triangles.
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 line of intersection of the given triangle and plane.
double	vgl_triangle_3d_longest_side (const vgl_point_3d< double > &p1, const vgl_point_3d< double > &p2, const vgl_point_3d< double > &p3)
	Compute the longest side of the given triangle.
double	vgl_triangle_3d_shortest_side (const vgl_point_3d< double > &p1, const vgl_point_3d< double > &p2, const vgl_point_3d< double > &p3)
	Compute the shortest side of the given triangle.
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 closest point on a triangle to a reference point.
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)
	Compute the distance to the closest point on a triangle from a reference point.
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)
	Check if the two triangles are coplanar.
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 area of a triangle.
double	vgl_triangle_3d_aspect_ratio (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.

---

Detailed Description

Some helpful functions when working with triangles.

Author:

Kieran O'Mahony

Date:

21 June 2007

Definition in file vgl_triangle_3d.h.

---

Enumeration Type Documentation

enum vgl_triangle_3d_intersection_t

Enumerator:

None
Skew
Coplanar

Definition at line 16 of file vgl_triangle_3d.h.

---

Function Documentation

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 area of a triangle.

The triangle is represented by its vertices p1, p2, p3

Definition at line 1303 of file vgl_triangle_3d.cxx.

double vgl_triangle_3d_aspect_ratio	(	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 p1, p2, p3

Compute the aspect ratio of a triangle.

The triangle is represented by its vertices p1, p2, p3

Definition at line 1325 of file vgl_triangle_3d.cxx.

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 closest point on a triangle to a reference point.

The triangle is represented by its vertices p1, p2, p3.

Parameters:

q	The reference point.

Returns:

The closest point on the triangle. This may be inside the triangle, or it may be a point on one of the triangle edges.

Definition at line 1198 of file vgl_triangle_3d.cxx.

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 for coincident edges of triangles a and b.

Returns:

a vector of the coincident edges

Definition at line 26 of file vgl_triangle_3d.cxx.

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
	)

Compute the distance to the closest point on a triangle from a reference point.

The triangle is represented by its vertices p1, p2, p3.

Parameters:

q	The reference point.

Returns:

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.)

Definition at line 1274 of file vgl_triangle_3d.cxx.

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
	)

Compute the intersection point between the line segment and triangle.

The triangle is represented by its vertices p1, p2, p3

Returns:

true if line intersects triangle

The triangle is represented by its vertices p1, p2, p3

Returns:

intersection type

Definition at line 221 of file vgl_triangle_3d.cxx.

double vgl_triangle_3d_longest_side	(	const vgl_point_3d< double > &	p1,
		const vgl_point_3d< double > &	p2,
		const vgl_point_3d< double > &	p3
	)		[inline]

Compute the longest side of the given triangle.

The triangle is represented by its vertices p1, p2, p3

Returns:

length of the longest side

Definition at line 102 of file vgl_triangle_3d.h.

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 line of intersection of the given triangle and plane.

The triangle is represented by its vertices p1, p2, p3

Returns:

intersection type

Note:

an intersection line is not defined (NaN) for a coplanar intersection

The triangle is represented by its vertices p1, p2, p3

Returns:

intersection type

Note:

an intersection line is not defined (vgl_vgl_nan) for a coplanar intersection

Definition at line 1104 of file vgl_triangle_3d.cxx.

double vgl_triangle_3d_shortest_side	(	const vgl_point_3d< double > &	p1,
		const vgl_point_3d< double > &	p2,
		const vgl_point_3d< double > &	p3
	)		[inline]

Compute the shortest side of the given triangle.

The triangle is represented by its vertices p1, p2, p3

Returns:

length of the longest side

Definition at line 115 of file vgl_triangle_3d.h.

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 the given point is inside the triangle.

The triangle is represented by its vertices p1, p2, p3

Returns:

true if point is inside

Definition at line 80 of file vgl_triangle_3d.cxx.

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
	)

Check if point i_pnt is inside the triangle.

The triangle is represented by its vertices p1, p2, p3

Returns:

true if point is inside

Note:

this method uses the less efficient 'angles' method which requires 3 calls to acos()

Definition at line 167 of file vgl_triangle_3d.cxx.

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
	)

Check if the two triangles are coplanar.

The triangles are represented by their respective vertices a_p1, a_p2, a_p3 and b_p1, b_p2, b_p3

Definition at line 1287 of file vgl_triangle_3d.cxx.

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 if the given triangles a and b intersect.

The triangles are represented by their respective vertices a_p1, a_p2, a_p3 and b_p1, b_p2, b_p3

Returns:

intersection type

The triangle are represented by their respective vertices a_p1, a_p2, a_p3 and b_p1, b_p2, b_p3

Returns:

intersection type

Definition at line 754 of file vgl_triangle_3d.cxx.

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 intersection line of the given triangles.

See also:

vgl_triangle_3d_triangle_intersection()

Note:

an intesection line is not computed for a coplanar intersection

Compute the intersection line of the given triangles.

See also:

vgl_triangle_3d_triangle_intersection()

Note:

an intesection line is not computed for a coplanar intersection

Definition at line 327 of file vgl_triangle_3d.cxx.