CGAL 4.14 - 2D and 3D Linear Geometry Kernel
Kernel::PowerSideOfOrientedPowerSphere_3 Concept Reference

## Definition

Refines:
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 $$(p,q,r,s)$$. More...

## ◆ 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).