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CGAL 5.0 - 2D and 3D Linear Geometry Kernel
Kernel::PowerSideOfBoundedPowerCircle_2 Concept Reference

Definition

Refines:
AdaptableFunctor (with four arguments)
See also
CGAL::Weighted_point_2<Kernel>
ComputePowerProduct_2 for the definition of orthogonality for power distances.
PowerSideOfOrientedPowerCircle_2

Operations

A model of this concept must provide:

CGAL::Bounded_side operator() (const Kernel::Weighted_point_2 &p, const Kernel::Weighted_point_2 &q, const Kernel::Weighted_point_2 &r, const Kernel::Weighted_point_2 &t)
 Let \( {z(p,q,r)}^{(w)}\) be the power circle of the weighted points \( (p,q,r)\). More...
 
CGAL::Bounded_side operator() (const Kernel::Weighted_point_2 &p, const Kernel::Weighted_point_2 &q, const Kernel::Weighted_point_2 &t)
 returns the sign of the power test of t with respect to the smallest circle orthogonal to p and q. More...
 
CGAL::Bounded_side operator() (const Kernel::Weighted_point_2 &p, const Kernel::Weighted_point_2 &t)
 returns the sign of the power test of t with respect to the smallest circle orthogonal to p.
 

Member Function Documentation

◆ operator()() [1/2]

CGAL::Bounded_side Kernel::PowerSideOfBoundedPowerCircle_2::operator() ( const Kernel::Weighted_point_2 p,
const Kernel::Weighted_point_2 q,
const Kernel::Weighted_point_2 r,
const Kernel::Weighted_point_2 t 
)

Let \( {z(p,q,r)}^{(w)}\) be the power circle of the weighted points \( (p,q,r)\).

This method returns:

  • ON_BOUNDARY if t is orthogonal to \( {z(p,q,r)}^{(w)}\),
  • ON_UNBOUNDED_SIDE if t lies outside the bounded circle of center \( z(p,q,r)\) and radius \( \sqrt{ w_{z(p,q,r)}^2 + w_t^2 }\) (which is equivalent to \( \Pi({t}^{(w)},{z(p,q,r)}^{(w)}) > 0\)),
  • ON_BOUNDED_SIDE if t lies inside this bounded circle.

The order of the points p, q, and r does not matter.

Precondition
p, q, and r are not collinear.

If all the points have a weight equal to 0, then power_side_of_bounded_power_circle_2(p,q,r,t) == side_of_bounded_circle(p,q,r,t).

◆ operator()() [2/2]

CGAL::Bounded_side Kernel::PowerSideOfBoundedPowerCircle_2::operator() ( const Kernel::Weighted_point_2 p,
const Kernel::Weighted_point_2 q,
const Kernel::Weighted_point_2 t 
)

returns the sign of the power test of t with respect to the smallest circle orthogonal to p and q.

Precondition
p and q have different bare points.