Rational Simplices ( d3_rat_simplex )

Definition

An instance of the data type d3_rat_simplex is a simplex in 3d space. The simplex is defined by four points p1,p2,p3,p4 with rational coordinates (d3_rat_points). We call the simplex degenerate, if the four defining points are coplanar.

#include < LEDA/geo/d3_rat_simplex.h >

Types

d3_rat_simplex::coord_type	the coordinate type (rational).
d3_rat_simplex::point_type	the point type (d3_rat_point).

Creation

d3_rat_simplex	S(const d3_rat_point& a, const d3_rat_point& b, const d3_rat_point& c, const d3_rat_point& d)
		creates the simplex (a,b,c,d).
d3_rat_simplex	S	creates the simplex ((0,0,0),(1,0,0),(0,1,0),(0,0,1) ).

Operations

d3_simplex	S.to_d3_simplex()	returns a floating point approximation of S.
d3_rat_point	S.point1()	returns p1.
d3_rat_point	S.point2()	returns p2.
d3_rat_point	S.point3()	returns p3.
d3_rat_point	S.point4()	returns p4.
d3_rat_point	S[int i]	returns pi. Precondition i>0 and i<5.
int	S.index(const d3_rat_point& p)
		returns 1 if p==p1, 2 if p==p2, 3 if p==p3, 4 if p==p4, 0 otherwise.
bool	S.is_degenerate()	returns true if S is degenerate and false otherwise.
d3_rat_sphere	S.circumscribing_sphere()	returns a d3_rat_sphere through (p1,p2,p3,p4) (precondition: the d3_rat_simplex is not degenerate).
bool	S.in_simplex(const d3_rat_point& p)
		returns true, if p is contained in the simplex.
bool	S.insphere(const d3_rat_point& p)
		returns true, if p lies in the interior of the sphere through p1,p2,p3,p4.
rational	S.vol()	returns the signed volume of the simplex.
d3_rat_simplex	S.reflect(const d3_rat_point& p, const d3_rat_point& q, const d3_rat_point& v)
		returns S reflected across the plane through (p,q,v).
d3_rat_simplex	S.reflect(const d3_rat_point& p)
		returns S reflected across point p.
d3_rat_simplex	S.translate(const rat_vector& v)
		returns S translated by vector v. Precond.: v.dim()=3.
d3_rat_simplex	S.translate(rational dx, rational dy, rational dz)
		returns S translated by vector (dx,dy,dz).
d3_rat_simplex	S.translate(integer dx, integer dy, integer dz, integer dw)
		returns S translated by vector (dx/dw,dy/dw,dz/w).
d3_rat_simplex	S + const rat_vector& v	returns S translated by vector v.
d3_rat_simplex	S - const rat_vector& v	returns S translated by vector - v.