CGAL 5.3 - 2D and 3D Linear Geometry Kernel
Kernel::PowerSideOfBoundedPowerSphere_3 Concept Reference

## Definition

Refines:
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.

## ◆ 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.