Definition
An instance of the data type d3_simplex is a simplex in 3d space. The simplex is defined by four points p1,p2,p3,p4 (d3_points). We call the simplex degenerate, if the four defining points are coplanar.
#include < LEDA/d3 _simplex.h >
Creation
| d3_simplex | S(d3_point a, d3_point b, d3_point c, d3_point d) | |
| creates the simplex (a,b,c,d). | ||
| d3_simplex | S | creates the simplex ((0,0,0),(1,0,0),(0,1,0),(0,0,1)). |
Operations
| d3_point | S.point1() | returns p1. |
| d3_point | S.point2() | returns p2. |
| d3_point | S.point3() | returns p3. |
| d3_point | S.point4() | returns p4. |
| int | S.index(d3_point p) | returns 1 if p==p1, 2 if p==p2, 3 if p==p3, 4 if p==p4, and 0 otherwise. |
| bool | S.is_degenerate() | returns true if S is degenerate and false otherwise. |
| d3_sphere | S.circumscribing_sphere() | returns a d3_sphere through (p1,p2,p3,p4) (precondition: the d3_simplex is not degenerate). |
| bool | S.in_simplex(d3_point p) | returns true, if p is contained in the simplex. |
| bool | S.insphere(d3_point p) | returns true, if p lies in the interior of the sphere through p1,p2,p3,p4. |
| double | S.vol() | returns the signed volume of the simplex. |
| d3_simplex | S.reflect(d3_point p, d3_point q, d3_point v) | |
| returns S reflected across the plane through (p,q,v). | ||
| d3_simplex | S.reflect(d3_point p) | returns S reflected across point p. |
| d3_simplex | S.translate(vector v) | returns S translated by vector v. Precond.: v.dim()=3. |
| d3_simplex | S.translate(double dx, double dy, double dz) | |
| returns S translated by vector (dx,dy,dz). | ||
| d3_simplex | S + vector v | returns S translated by vector v. |
| d3_simplex | S - vector v | returns S translated by vector - v. |