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.