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

CGAL 4.8 - 2D and 3D Linear Geometry Kernel

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CGAL::Homogeneous< RingNumberType > Class Template Reference
Kernel Classes

`#include <CGAL/Homogeneous.h>`

## Definition

A model for a `Kernel` using homogeneous coordinates to represent the geometric objects.

In order for `Homogeneous` to model Euclidean geometry in \( E^2\) and/or \( E^3\), for some mathematical ring \( E\) (e.g., the integers \(\mathbb{Z}\) or the rationals \(\mathbb{Q}\)), the template parameter `RingNumberType` must model the mathematical ring \( E\). That is, the ring operations on this number type must compute the mathematically correct results. If the number type provided as a model for `RingNumberType` is only an approximation of a ring (such as the built-in type `double`), then the geometry provided by the kernel is only an approximation of Euclidean geometry.

Is Model Of:
  `Kernel`

Implementation

This model of a kernel uses reference counting.

See Also
  `CGAL::Cartesian<FieldNumberType>`
  `CGAL::Simple_cartesian<FieldNumberType>`
  `CGAL::Simple_homogeneous<RingNumberType>`

## Types
typedef Quotient< RingNumberType > | FT
typedef RingNumberType | RT