\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Boolean Operations on Nef Polygons Embedded on the Sphere

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CGAL::Nef_polyhedron_S2< Traits >::Sphere_point Class Reference
2D Boolean Operations on Nef Polygons Embedded on the Sphere Reference

`#include <CGAL/Nef_polyhedron_S2.h>`

## Definition

An object `p` of type `Sphere_point<R>` is a point on the surface of a unit sphere.

Such points correspond to the nontrivial directions in space and similarly to the equivalence classes of all nontrivial vectors under normalization.

Operations

Access to the coordinates is provided by the following operations. Note that the vector \( (x,y,z)\) is not normalized.

## Types
typedef unspecified_type | RT
| ring number type.

## Creation
| Sphere_point ()
| creates some sphere point.
| Sphere_point (RT x, RT y, RT z)
| creates a sphere point corresponding to the point of intersection of the ray starting at the origin in direction \( (x,y,z)\) and the surface of \( S_2\).

## Operations
RT | x ()
| the \( x\)-coordinate.
RT | y ()
| the \( y\)-coordinate.
RT | z ()
| the \( z\)-coordinate.
bool | operator== (const Nef_polyhedron_S2< Traits >::Sphere_point &q)
| Equality.
bool | operator!= (const Nef_polyhedron_S2< Traits >::Sphere_point &q)
| Inequality.
Sphere_point | antipode ()
| returns the antipode of `p`.