Next: Rational Simplices ( d3_rat_simplex Up: Basic Data Types for Previous: Rational Planes ( d3_rat_plane   Contents   Index

# Rational Spheres ( d3_rat_sphere )

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/geo/d3_rat_sphere.h >

Creation

 d3_rat_sphere S(const d3_rat_point& p1, const d3_rat_point& p2, const d3_rat_point& p3, const 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(const d3_rat_point& p) returns true, if p is on the sphere, false otherwise. bool S.inside(const d3_rat_point& p) returns true, if p is inside the sphere, false otherwise. bool S.outside(const 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(const rat_vector& v) translates the sphere by vector v and returns a new d3_rat_sphere. d3_rat_sphere S.translate(const rational& r1, const rational& r2, const rational& r3) translates the sphere by vector (r1,r2,r3) and returns a new d3_rat_sphere.

Next: Rational Simplices ( d3_rat_simplex Up: Basic Data Types for Previous: Rational Planes ( d3_rat_plane   Contents   Index
Christian Uhrig 2017-04-07