CGAL 4.10 - 2D and 3D Linear Geometry Kernel
|
AdaptableFunctor
(with five arguments)CGAL::Weighted_point_3<Kernel>
ComputePowerProduct_3
for the definition of orthogonal. Operations | |
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) |
returns the sign of the power test of the last weighted point with respect to the smallest sphere orthogonal to the others. 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) |
Analogous to the previous method, with the power sphere \( {z(p,q,r)}^{(w)}\) of the points \( (p,q,r)\). More... | |
CGAL::Bounded_side | operator() (const Kernel::Weighted_point_3 &p, const Kernel::Weighted_point_3 &q, const Kernel::Weighted_point_3 &t) |
Analogous to the previous method, where \( {z(p,q)}^{(w)}\) is the power sphere of p and q . More... | |
CGAL::Bounded_side | operator() (const Kernel::Weighted_point_3 &p, const Kernel::Weighted_point_3 &q) |
Analogous to the previous method, where \( {z(p)}^{(w)}\) of the power sphere of p , that is the sphere with the bare point of p as center, and \( -w_p\) as weight. More... | |
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 | ||
) |
returns the sign of the power test of the last weighted point with respect to the smallest sphere orthogonal to the others.
Let \( {z(p,q,r,s)}^{(w)}\) be the power sphere of the weighted points \( (p,q,r,s)\). 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 oriented sphere.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 | ||
) |
Analogous to the previous method, with the power sphere \( {z(p,q,r)}^{(w)}\) of the points \( (p,q,r)\).
p, q, r
are not collinear.If all the points have a weight equal to 0, then power_side_of_bounded_power_sphere_3(p,q,r,t)
== side_of_bounded_sphere(p,q,r,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 & | t | ||
) |
Analogous to the previous method, where \( {z(p,q)}^{(w)}\) is the power sphere of p
and q
.
p
and q
have different bare points.If all points have a weight equal to 0, then power_side_of_bounded_power_sphere_3(p,q,t)
gives the same answer as the kernel predicate s(p,q).has_on(t)
would give, where s(p,q)
denotes the segment with endpoints p
and q
.
CGAL::Bounded_side Kernel::PowerSideOfBoundedPowerSphere_3::operator() | ( | const Kernel::Weighted_point_3 & | p, |
const Kernel::Weighted_point_3 & | q | ||
) |
Analogous to the previous method, where \( {z(p)}^{(w)}\) of the power sphere of p
, that is the sphere with the bare point of p
as center, and \( -w_p\) as weight.
When p
and q
have equal bare points, then it returns the comparison of the weights (ON_BOUNDED_SIDE
when q
is heavier than p
).