Rational Triangles ( rat_triangle )

Definition

An instance t of the data type rat_triangle is an oriented triangle in the two-dimensional plane with rational coordinates. A rat_triangle t splits the plane into one bounded and one unbounded region. If t is positively oriented, the bounded region is to the left of it, if it is negatively oriented, the unbounded region is to the left of it. t is called degenerate, if the 3 vertices of t are collinear.

#include < LEDA/geo/rat_triangle.h >

Types

rat_triangle::coord_type	the coordinate type (rational).
rat_triangle::point_type	the point type (rat_point).

Creation

rat_triangle	t	introduces a variable t of type rat_triangle. t is initialized to the empty triangle.
rat_triangle	t(const rat_point& p, const rat_point& q, const rat_point& r)
		introduces a variable t of type rat_triangle. t is initialized to the triangle [p, q, r].
rat_triangle	t(const rational& x1, const rational& y1, const rational& x2, const rational& y2, const rational& x3, const rational& y3)
		introduces a variable t of type rat_triangle. t is initialized to the triangle [(x1, y1),(x2, y2),(x3, y3)].
rat_triangle	t(const triangle& t, int prec = rat_point::default_precision)
		introduces a variable t of type rat_triangle. t is initialized to the triangle obtained by approximating the three defining points of t.

Operations

void	t.normalize()	simplifies the homogenous representation by calling p.normalize() for every vertex of t.
rat_point	t.point1()	returns the first vertex of triangle t.
rat_point	t.point2()	returns the second vertex of triangle t.
rat_point	t.point3()	returns the third vertex of triangle t.
rat_point	t[int i]	returns the i-th vertex of t. Precondition 1 < = i < = 3.
int	t.orientation()	returns the orientation of t.
rational	t.area()	returns the signed area of t (positive, if orientation(a, b, c) > 0, negative otherwise).
bool	t.is_degenerate()	returns true if the vertices of t are collinear.
int	t.side_of(const rat_point& p)
		returns +1 if p lies to the left of t, 0 if p lies on t and -1 if p lies to the right of t.
region_kind	t.region_of(const rat_point& p)
		returns BOUNDED$\_$REGION if p lies in the bounded region of t, ON$\_$REGION if p lies on t and UNBOUNDED$\_$REGION if p lies in the unbounded region.
bool	t.inside(const rat_point& p)
		returns true, if p lies to the left of t.
bool	t.outside(const rat_point& p)
		returns true, if p lies to the right of t.
bool	t.on_boundary(const rat_point& p)
		decides whether p lies on the boundary of t.
bool	t.contains(const rat_point& p)
		decides whether t contains p.
bool	t.intersection(const rat_line& l)
		decides whether the bounded region or the boundary of t and l intersect.
bool	t.intersection(const rat_segment& s)
		decides whether the bounded region or the boundary of t and s intersect.
rat_triangle	t.translate(rational dx, rational dy)
		returns t translated by vector (dx, dy).
rat_triangle	t.translate(const rat_vector& v)
		returns t + v, i.e., t translated by vector v. Precondition v.dim() = 2.
rat_triangle	t + const rat_vector& v	returns t translated by vector v.
rat_triangle	t - const rat_vector& v	returns t translated by vector - v.
rat_triangle	t.rotate90(const rat_point& q, int i=1)
		returns t rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
rat_triangle	t.rotate90(int i=1)	returns t.rotate90(t.source(),i).
rat_triangle	t.reflect(const rat_point& p, const rat_point& q)
		returns t reflected across the straight line passing through p and q.
rat_triangle	t.reflect(const rat_point& p)
		returns t reflected across point p.
rat_triangle	t.reverse()	returns t reversed.