Kernel::PowerSideOfOrientedPowerSphere_3 Concept Reference

Definition

Refines

AdaptableQuinaryFunction

See also

CGAL::Weighted_point_3<Kernel>

ComputePowerProduct_3 for the definition of power distance.

PowerSideOfBoundedPowerSphere_3

Operations
A model of this concept must provide:
Oriented_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) const
	Let \( {z(p,q,r,s)}^{(w)}\) be the power sphere of the weighted points \( (p,q,r,s)\).

Member Function Documentation

operator()()

Oriented_side Kernel::PowerSideOfOrientedPowerSphere_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 ) const

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

Returns

• ON_ORIENTED_BOUNDARY if t is orthogonal to \( {z(p,q,r,s)}^{(w)}\),
• ON_NEGATIVE_SIDE if t lies outside the oriented 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_POSITIVE_SIDE if t lies inside this oriented sphere.

The order of the points p, q, r and s is important, since it determines the orientation of the implicitly constructed power sphere.

Precondition

p, q, r, s are not coplanar.

If all the points have a weight equal to 0, then power_side_of_oriented_power_sphere_3(p,q,r,s,t) = side_of_oriented_sphere(p,q,r,s,t).