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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/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(d3_rat_point a, d3_rat_point b, d3_rat_point c, 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(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(d3_rat_point p)
    returns true, if p is contained in the simplex.

bool  S.insphere(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(d3_rat_point p, d3_rat_point q, d3_rat_point v)
    returns S reflected across the plane through (p,q,v).

d3_rat_simplex  S.reflect(d3_rat_point p) returns S reflected across point p.

d3_rat_simplex  S.translate(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 + rat_vector v returns S translated by vector v.

d3_rat_simplex S - 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

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2002-10-16