 CGAL 4.14 - 3D Spherical Geometry Kernel
SphericalKernel::CompareTheta_3 Concept Reference

## Definition

SphericalKernel::CompareThetaZ_3
SphericalKernel::CompareX_3
SphericalKernel::CompareY_3
SphericalKernel::CompareZ_3
SphericalKernel::CompareXY_3
SphericalKernel::CompareXYZ_3
SphericalKernel::Equal_3

## Operations

An object of this type must provide:

Comparison_result operator() (const SphericalKernel::Circular_arc_point_3 &p, const SphericalKernel::Circular_arc_point_3 &q)
Compares the $$\theta$$-coordinates of p and q in the cylindrical coordinate system relative to the context sphere used by the function SphericalKernel::compare_theta_3_object. More...

Comparison_result operator() (const SphericalKernel::Circular_arc_point_3 &p, const SphericalKernel::Vector_3 &m)
Compares the $$\theta$$-coordinates of p and of the meridian defined by m (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to the context sphere used by the function SphericalKernel::compare_theta_3_object. More...

Comparison_result operator() (const SphericalKernel::Vector_3 &m, const SphericalKernel::Circular_arc_point_3 &p)
Same as previous, with opposite result.

Comparison_result operator() (const SphericalKernel::Vector_3 &m1, const SphericalKernel::Vector_3 &m2)
Compares the $$\theta$$-coordinates of the meridians defined by m1 and by m2 (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to the context sphere used by the function SphericalKernel::compare_theta_3_object. More...

## ◆ operator()() [1/3]

 Comparison_result SphericalKernel::CompareTheta_3::operator() ( const SphericalKernel::Circular_arc_point_3 & p, const SphericalKernel::Circular_arc_point_3 & q )

Compares the $$\theta$$-coordinates of p and q in the cylindrical coordinate system relative to the context sphere used by the function SphericalKernel::compare_theta_3_object.

Precondition
p and q lie on the context sphere used by the function SphericalKernel::compare_theta_3_object, but do not coincide with its poles.

## ◆ operator()() [2/3]

 Comparison_result SphericalKernel::CompareTheta_3::operator() ( const SphericalKernel::Circular_arc_point_3 & p, const SphericalKernel::Vector_3 & m )

Compares the $$\theta$$-coordinates of p and of the meridian defined by m (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to the context sphere used by the function SphericalKernel::compare_theta_3_object.

Precondition
p lies on the context sphere used by the function SphericalKernel::compare_theta_3_object, but does not coincide with its poles. m $$\neq(0,0,0)$$ and the $$z$$-coordinate of m is $$0$$.

## ◆ operator()() [3/3]

 Comparison_result SphericalKernel::CompareTheta_3::operator() ( const SphericalKernel::Vector_3 & m1, const SphericalKernel::Vector_3 & m2 )

Compares the $$\theta$$-coordinates of the meridians defined by m1 and by m2 (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to the context sphere used by the function SphericalKernel::compare_theta_3_object.

m1 $$\neq(0,0,0)$$, m2 $$\neq(0,0,0)$$ and the $$z$$-coordinate of m1 and m2 is $$0$$.