CGAL 4.7 - 3D Spherical Geometry Kernel: SphericalKernel::Equal_3 Concept Reference

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

CGAL 4.7 - 3D Spherical Geometry Kernel

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SphericalKernel::Equal_3 Concept Reference
Geometric Concepts

## Definition

Testing equality between objects.

Refines:
  `Kernel::Equal_3`

See Also
  `SphericalKernel::CompareX_3`
  `SphericalKernel::CompareY_3`
  `SphericalKernel::CompareZ_3`
  `SphericalKernel::CompareXY_3`
  `SphericalKernel::CompareXYZ_3`

## Operations

An object of this type must provide in addition:
bool | operator() (const SphericalKernel::Circular_arc_point_3 &p0, const SphericalKernel::Circular_arc_point_3 &p1)
| For two points.
bool | operator() (const SphericalKernel::Circular_arc_3 &a0, const SphericalKernel::Circular_arc_3 &a1)
| For two arcs. More...
bool | operator() (const SphericalKernel::Line_arc_3 &a0, const SphericalKernel::Line_arc_3 &a1)
| For two segments. More...

## Member Function Documentation

bool SphericalKernel::Equal_3::operator() | ( | const SphericalKernel::Circular_arc_3 & | a0,
|  | const SphericalKernel::Circular_arc_3 & | a1
| ) |  |

For two arcs.

Two arcs are equal, iff their non-oriented supporting planes are equal, and the centers and squared radii of their respective supporting circles are equal, and their sources and targets are equal.

bool SphericalKernel::Equal_3::operator() | ( | const SphericalKernel::Line_arc_3 & | a0,
|  | const SphericalKernel::Line_arc_3 & | a1
| ) |  |

For two segments.

Two segments are equal, iff their non-oriented supporting lines are equal (i.e. they define the same set of points), and their endpoints are the same.