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CGAL 4.5.1 - 3D Spherical Geometry Kernel
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SphericalKernel::CompareTheta_3 Concept Reference
Geometric Concepts

Definition

See Also
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...
 

Member Function Documentation

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.
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 \( 0\).
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 \( 0\).