CGAL 6.1.2 - 3D Spherical Geometry Kernel: SphericalKernel::IsThetaMonotone_3 Concept Reference

CGAL 6.1.2 - 3D Spherical Geometry Kernel

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SphericalKernel::IsThetaMonotone_3 Concept Reference
Reference Manual » Geometric Concepts

## Definition

See also
  `SphericalKernel::MakeThetaMonotone_3`

## Operations
An object of this type must provide:
bool | operator() (const SphericalKernel::Circular_arc_3 &a)
| Tests whether the arc `a` is \( \theta\)-monotone, i.e. the intersection of any meridian anchored at the poles of the context sphere used by the function `SphericalKernel::is_theta_monotone_3_object` and the arc `a` is reduced to at most one point in general, and two points if a pole of that sphere is an endpoint of `a`.

## Member Function Documentation

## ◆ operator()()

bool SphericalKernel::IsThetaMonotone_3::operator() | ( | const SphericalKernel::Circular_arc_3 & | a | ) |

Tests whether the arc `a` is \( \theta\)-monotone, i.e. the intersection of any meridian anchored at the poles of the context sphere used by the function `SphericalKernel::is_theta_monotone_3_object` and the arc `a` is reduced to at most one point in general, and two points if a pole of that sphere is an endpoint of `a`.

Note that a bipolar circle has no such arcs.

Precondition
  `a` lies on the context sphere used by the function `SphericalKernel::is_theta_monotone_3_object`, and the supporting circle of `a` is not bipolar.