CGAL 4.12 - 3D Spherical Geometry Kernel
SphericalKernel::CompareZAtTheta_3 Concept Reference

## Definition

SphericalKernel::CompareZToRight_3

## Operations

An object of this type must provide:

Comparison_result operator() (const SphericalKernel::Circular_arc_3 &a0, const SphericalKernel::Circular_arc_3 &a1, const SphericalKernel::Vector_3 &m)
compares the $$z$$-coordinates of the two intersections points of a0 and a1 with the meridian defined by m (see Section Spherical Kernel Objects). More...

Comparison_result operator() (const SphericalKernel::Circular_arc_point_3 &p, const SphericalKernel::Circular_arc_3 &a)
given a meridian anchored at the poles of the context sphere used by the function SphericalKernel::compare_z_at_theta_3_object, and passing through point p, compares the $$z$$-coordinate of point p and that of the intersection of the meridian with a. More...

## ◆ operator()() [1/2]

 Comparison_result SphericalKernel::CompareZAtTheta_3::operator() ( const SphericalKernel::Circular_arc_3 & a0, const SphericalKernel::Circular_arc_3 & a1, const SphericalKernel::Vector_3 & m )

compares the $$z$$-coordinates of the two intersections points of a0 and a1 with the meridian defined by m (see Section Spherical Kernel Objects).

Precondition
a0 and a1 lie on the context sphere used by the function SphericalKernel::compare_z_at_theta_3_object. m $$\neq(0,0,0)$$ and the $$z$$-coordinate of m is $$0$$. Arcs a0 and a1 are $$\theta$$-monotone and both intersected by the meridian defined by m(see Section Spherical Kernel Objects).

## ◆ operator()() [2/2]

 Comparison_result SphericalKernel::CompareZAtTheta_3::operator() ( const SphericalKernel::Circular_arc_point_3 & p, const SphericalKernel::Circular_arc_3 & a )

given a meridian anchored at the poles of the context sphere used by the function SphericalKernel::compare_z_at_theta_3_object, and passing through point p, compares the $$z$$-coordinate of point p and that of the intersection of the meridian with a.

Precondition
a and p lie on the context sphere used by the function SphericalKernel::compare_z_at_theta_3_object, arc a is $$\theta$$-monotone and the meridian passing through p intersects arc a.