The requirements for the geometric traits class of the basic triangulation class Triangulation_2<Gt, Tds> are kept rather light. Essentially, a geometric traits class Geom_traits has to provide some type for points, segments and triangles, and a few geometric predicates: coordinate comparison and orientation tests.

Types

Geom_traits::Point
	The type must provide a copy constructor and assignment operator.
Geom_traits::Segment
	The type must provide a constructor that takes two points as argument.
Geom_traits::Triangle
	The type must provide a constructor that takes three points as argument.

Creation

Only a default constructor and an assignement operator are required. Note that further constructors can be provided.

Geom_traits gt;
	A default constructor.

Geom_traits

gt = gtr

Assignment operator.

Predicates

Comparison_result	gt.compare_x ( Point p0, Point p1)
		Compares the x-coordinates.
Comparison_result	gt.compare_y ( Point p0, Point p1)
		Compares the y-coordinates.
bool	gt.compare ( Point p0, Point p1)
		True if compare_x(p0,p1) and compare_y(p0,p1) return EQUAL.
Orientation	gt.orientation ( Point p0, Point p1, Point p2)
		Orientation test.
Oriented_side	gt.side_of_oriented_circle ( Point p, Point q, Point r, Point s)
		Returns the oriented side of the query point s with respect to the oriented circle going through p,q,r in that order. This predicates is required only if the function oriented_side(const Face_handle& f, const Point &p) is explicitely called by the user.

Construction