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CGAL 6.0 - 2D and 3D Linear Geometry Kernel
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AdaptableQuinaryFunction 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 \( (p,q,r,s)\). | |
| 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. | |
| 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. | |
| 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. | |
| 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.
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).
| 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.
p, q, r are not collinear. | 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.
p and q have different bare points.