Kernel::PowerSideOfBoundedPowerSphere_3 Concept Reference

Definition

Refines

AdaptableQuinaryFunction

See also

CGAL::Weighted_point_3<Kernel>

ComputePowerProduct_3 for the definition of orthogonality for power distances.

PowerSideOfOrientedPowerSphere_3

Operations
A model of this concept must provide:
CGAL::Bounded_side	operator() (const Kernel::Weighted_point_3 &p, const Kernel::Weighted_point_3 &q, const Kernel::Weighted_point_3 &r, const Kernel::Weighted_point_3 &s, const Kernel::Weighted_point_3 &t)
	Let \( {z(p,q,r,s)}^{(w)}\) be the power sphere of the weighted points \( (p,q,r,s)\). More...
CGAL::Bounded_side	operator() (const Kernel::Weighted_point_3 &p, const Kernel::Weighted_point_3 &q, const Kernel::Weighted_point_3 &r, const Kernel::Weighted_point_3 &t)
	returns the sign of the power test of t with respect to the smallest sphere orthogonal to p, q, and r. More...
CGAL::Bounded_side	operator() (const Kernel::Weighted_point_3 &p, const Kernel::Weighted_point_3 &q, const Kernel::Weighted_point_3 &t)
	returns the sign of the power test of t with respect to the smallest sphere orthogonal to p and q. More...
CGAL::Bounded_side	operator() (const Kernel::Weighted_point_3 &p, const Kernel::Weighted_point_3 &t)
	returns the sign of the power test of t with respect to the smallest sphere orthogonal to p.

Member Function Documentation

operator()() [1/3]

CGAL::Bounded_side Kernel::PowerSideOfBoundedPowerSphere_3::operator()	(	const Kernel::Weighted_point_3 &	p,
		const Kernel::Weighted_point_3 &	q,
		const Kernel::Weighted_point_3 &	r,
		const Kernel::Weighted_point_3 &	s,
		const Kernel::Weighted_point_3 &	t
	)

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

This method returns:

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

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

Precondition

p, q, r, s are not coplanar.

If all the points have a weight equal to 0, then power_side_of_bounded_power_sphere_3(p,q,r,s,t) == side_of_bounded_sphere(p,q,r,s,t).

operator()() [2/3]

CGAL::Bounded_side Kernel::PowerSideOfBoundedPowerSphere_3::operator()	(	const Kernel::Weighted_point_3 &	p,
		const Kernel::Weighted_point_3 &	q,
		const Kernel::Weighted_point_3 &	r,
		const Kernel::Weighted_point_3 &	t
	)

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

Precondition

p, q, r are not collinear.

operator()() [3/3]

CGAL::Bounded_side Kernel::PowerSideOfBoundedPowerSphere_3::operator()	(	const Kernel::Weighted_point_3 &	p,
		const Kernel::Weighted_point_3 &	q,
		const Kernel::Weighted_point_3 &	t
	)

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

Precondition

p and q have different bare points.