CGAL Kernel Reference Manual: Triangle

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3D Triangle (Triangle_3)

Definition

An object

t of the class Triangle_3 is a triangle in the three-dimensional Euclidean space

³. As the triangle is not a full-dimensional object there is only a test whether a point lies on the triangle or not.

#include <CGAL/Triangle_3.h>

Creation

Triangle_3<R> t ( Point_3<R> p, Point_3<R> q, Point_3<R> r);
introduces a triangle t with vertices p, q and r.

Operations

bool t == t2 Test for equality: two triangles t and t₂ are equal, iff there exists a cyclic permutation of the vertices of t2, such that they are equal to the vertices of t.

bool t != t2 Test for inequality.

Point_3<R> t.vertex ( int i) returns the i'th vertex modulo 3 of t.

Point_3<R> t [ int i] returns vertex(int i).

Plane_3<R> t.supporting_plane ()
returns the supporting plane of t, with same orientation.

Predicates

bool t.is_degenerate () t is degenerate if its vertices are collinear.

bool t.has_on ( Point_3<R> p)
A point is on t, if it is on a vertex, an edge or the face of t.

Miscellaneous

Bbox_3 t.bbox () returns a bounding box containing t.

Triangle_3<R> t.transform ( Aff_transformation_3<R> at)
returns the triangle obtained by applying at on the three vertices of t.

Next: Class declaration of Tetrahedron_3<R>

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The GALIA project. Jan 18, 2000.

Triangle_3<R> t ( Point_3<R> p, Point_3<R> q, Point_3<R> r);
	introduces a triangle t with vertices p, q and r.

bool	t == t2	Test for equality: two triangles t and t₂ are equal, iff there exists a cyclic permutation of the vertices of t2, such that they are equal to the vertices of t.

bool	t != t2	Test for inequality.

Point_3<R>	t.vertex ( int i)	returns the i'th vertex modulo 3 of t.

Point_3<R>	t [ int i]	returns vertex(int i).

Plane_3<R>	t.supporting_plane ()
		returns the supporting plane of t, with same orientation.

bool	t.is_degenerate ()	t is degenerate if its vertices are collinear.

bool	t.has_on ( Point_3<R> p)
		A point is on t, if it is on a vertex, an edge or the face of t.

Bbox_3	t.bbox ()	returns a bounding box containing t.

Triangle_3<R>	t.transform ( Aff_transformation_3<R> at)
		returns the triangle obtained by applying at on the three vertices of t.