mirror of https://github.com/CGAL/cgal
reorder things
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@ -7993,91 +7993,6 @@ public:
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}; /* end Kernel::HasOn_3 */
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/*!
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\ingroup PkgKernel23ConceptsFunctionObjects
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\cgalConcept
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\cgalRefines `AdaptableFunctor` (with five arguments)
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\sa `CGAL::Weighted_point_3<Kernel>`
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\sa `ComputePowerProduct_3` for the definition of orthogonal.
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*/
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class PowerSideOfBoundedPowerSphere_3 {
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public:
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/// \name Operations
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/// A model of this concept must provide:
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/// @{
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/*!
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returns the sign of the power test of the last weighted point
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with respect to the smallest sphere orthogonal to the others.
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Let \f$ {z(p,q,r,s)}^{(w)}\f$ be the power sphere of the weighted points
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\f$ (p,q,r,s)\f$. Returns
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- `ON_BOUNDARY` if `t` is orthogonal to
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\f$ {z(p,q,r,s)}^{(w)}\f$,
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- `ON_UNBOUNDED_SIDE` if `t` lies outside the bounded sphere of
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center \f$ z(p,q,r,s)\f$ and radius \f$ \sqrt{ w_{z(p,q,r,s)}^2 + w_t^2 }\f$
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(which is equivalent to \f$ \Pi({t}^{(w)},{z(p,q,r,s)}^{(w)} >0\f$)),
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- `ON_BOUNDED_SIDE` if `t` lies inside this oriented sphere.
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\pre `p, q, r, s` are not coplanar.
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If all the points have a weight equal to 0, then
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`power_side_of_bounded_power_sphere_3(p,q,r,s,t)` == `side_of_bounded_sphere(p,q,r,s,t)`.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q,
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const Kernel::Weighted_point_3 & r,
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const Kernel::Weighted_point_3 & s,
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const Kernel::Weighted_point_3 & t);
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/*!
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Analogous to the previous method, for coplanar points,
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with the power circle \f$ {z(p,q,r)}^{(w)}\f$.
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\pre `p, q, r` are not collinear.
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If all the points have a weight equal to 0, then
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`power_side_of_bounded_power_sphere_3(p,q,r,t)` == `side_of_bounded_sphere(p,q,r,t)`.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q,
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const Kernel::Weighted_point_3 & r,
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const Kernel::Weighted_point_3 & t);
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/*!
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which is the same for collinear points, where \f$ {z(p,q)}^{(w)}\f$ is the
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power segment of `p` and `q`.
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\pre `p` and `q` have different bare points.
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If all points have a weight equal to 0, then
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`power_side_of_bounded_power_sphere_3(p,q,t)` gives the same answer as the kernel predicate
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`s(p,q).has_on(t)` would give, where `s(p,q)` denotes the
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segment with endpoints `p` and `q`.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q,
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const Kernel::Weighted_point_3 & t);
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/*!
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which is the same for equal points, that is when `p` and `q`
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have equal coordinates, then it returns the comparison of the weights
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(`ON_BOUNDED_SIDE` when `q` is heavier than `p`).
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\pre `p` and `q` have equal bare points.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q);
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/// @}
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}; /* end Kernel::Intersect_2 */
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/*!
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\ingroup PkgKernel23ConceptsFunctionObjects
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\cgalConcept
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@ -8790,6 +8705,89 @@ public:
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}; /* end Kernel::LessZ_3 */
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/*!
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\ingroup PkgKernel23ConceptsFunctionObjects
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\cgalConcept
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\cgalRefines `AdaptableFunctor` (with five arguments)
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\sa `CGAL::Weighted_point_3<Kernel>`
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\sa `ComputePowerProduct_3` for the definition of orthogonal.
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*/
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class PowerSideOfBoundedPowerSphere_3 {
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public:
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/// \name Operations
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/// A model of this concept must provide:
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/// @{
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/*!
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returns the sign of the power test of the last weighted point
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with respect to the smallest sphere orthogonal to the others.
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Let \f$ {z(p,q,r,s)}^{(w)}\f$ be the power sphere of the weighted points
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\f$ (p,q,r,s)\f$. Returns
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- `ON_BOUNDARY` if `t` is orthogonal to
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\f$ {z(p,q,r,s)}^{(w)}\f$,
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- `ON_UNBOUNDED_SIDE` if `t` lies outside the bounded sphere of
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center \f$ z(p,q,r,s)\f$ and radius \f$ \sqrt{ w_{z(p,q,r,s)}^2 + w_t^2 }\f$
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(which is equivalent to \f$ \Pi({t}^{(w)},{z(p,q,r,s)}^{(w)} >0\f$)),
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- `ON_BOUNDED_SIDE` if `t` lies inside this oriented sphere.
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\pre `p, q, r, s` are not coplanar.
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If all the points have a weight equal to 0, then
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`power_side_of_bounded_power_sphere_3(p,q,r,s,t)` == `side_of_bounded_sphere(p,q,r,s,t)`.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q,
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const Kernel::Weighted_point_3 & r,
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const Kernel::Weighted_point_3 & s,
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const Kernel::Weighted_point_3 & t);
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/*!
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Analogous to the previous method, for coplanar points,
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with the power circle \f$ {z(p,q,r)}^{(w)}\f$.
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\pre `p, q, r` are not collinear.
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If all the points have a weight equal to 0, then
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`power_side_of_bounded_power_sphere_3(p,q,r,t)` == `side_of_bounded_sphere(p,q,r,t)`.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q,
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const Kernel::Weighted_point_3 & r,
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const Kernel::Weighted_point_3 & t);
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/*!
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which is the same for collinear points, where \f$ {z(p,q)}^{(w)}\f$ is the
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power segment of `p` and `q`.
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\pre `p` and `q` have different bare points.
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If all points have a weight equal to 0, then
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`power_side_of_bounded_power_sphere_3(p,q,t)` gives the same answer as the kernel predicate
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`s(p,q).has_on(t)` would give, where `s(p,q)` denotes the
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segment with endpoints `p` and `q`.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q,
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const Kernel::Weighted_point_3 & t);
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/*!
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which is the same for equal points, that is when `p` and `q`
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have equal coordinates, then it returns the comparison of the weights
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(`ON_BOUNDED_SIDE` when `q` is heavier than `p`).
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\pre `p` and `q` have equal bare points.
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*/
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CGAL::Bounded_side
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operator()(const Kernel::Weighted_point_3 & p,
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const Kernel::Weighted_point_3 & q);
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/// @}
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}; /* end Kernel::PowerSideOfBoundedPowerSphere_3 */
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/*!
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\ingroup PkgKernel23ConceptsFunctionObjects
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