Definition
An instance of the data type d3_rat_sphere is an oriented sphere in 3d space. The sphere is defined by four points p1,p2,p3,p4 with rational coordinates (d3_rat_points).
#include < LEDA/d3 _rat _sphere.h >
Creation
| d3_rat_sphere | S(d3_rat_point p1, d3_rat_point p2, d3_rat_point p3, d3_rat_point p4) | |
| introduces a variable S of type d3_rat_sphere. S is initialized to the sphere through points p1,p2,p3,p4. | ||
Operations
| d3_sphere | S.to_float() | returns a floating point approximation of S. |
| bool | S.contains(d3_rat_point p) | |
| returns true, if p is on the sphere, false otherwise. | ||
| bool | S.inside(d3_rat_point p) | returns true, if p is inside the sphere, false otherwise. |
| bool | S.outside(d3_rat_point p) | returns true, if p is outside the sphere, false otherwise. |
| 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. |
| bool | S.is_degenerate() | returns true, if the 4 defining points are coplanar. |
| d3_rat_point | S.center() | returns the center of the sphere. |
| rational | S.sqr_radius() | returns the square of the radius. |
| d3_rat_sphere | S.translate(rat_vector v) | translates the sphere by vector v and returns a new d3_rat_sphere. |
| d3_rat_sphere | S.translate(rational r1, rational r2, rational r3) | |
| translates the sphere by vector (r1,r2,r3) and returns a new d3_rat_sphere. | ||