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CGAL 4.8.1 - 3D Spherical Geometry Kernel
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SphericalKernel::CompareZAtTheta_3 Concept Reference
Geometric Concepts

Definition

See Also
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...
 

Member Function Documentation

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).
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.