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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.


next up previous contents index
Next: 3D Convex Hull Algorithms Up: Basic Data Types for Previous: Rational Spheres ( d3_rat_sphere   Contents   Index
root 2008-01-09