CGAL 5.4.4 - 2D Movable Separability of Sets

These functions determine whether a cavity (of a mold in the plane) that has the shape of a given polygon could be casted in the mold and then pulled out of the mold in a given direction without colliding into the mold (but possibly sliding along the mold boundary).

## Functions

template<typename CastingTraits_2 >
CGAL::Polygon_2< CastingTraits_2 >::Edge_const_iterator CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction (const CGAL::Polygon_2< CastingTraits_2 > &polygon, const typename CastingTraits_2::Direction_2 &d, const CastingTraits_2 &traits=CastingTraits_2())
Given a simple polygon and a direction, this function determines whether a cavity (of a mold in the plane) that has the shape of the polygon could be casted in the mold and then pulled out of the mold in the given direction without colliding into the mold (but possibly sliding along the mold surface). More...

template<typename CastingTraits_2 >
CGAL::Polygon_2< CastingTraits_2 >::Edge_const_iterator CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction (const CGAL::Polygon_2< CastingTraits_2 > &polygon, const typename CastingTraits_2::Direction_2 &d, CGAL::Orientation orientation, const CastingTraits_2 &traits=CastingTraits_2())
Same as above with the additional orientation argument. More...

template<typename CastingTraits_2 >
bool CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction (const CGAL::Polygon_2< CastingTraits_2 > &polygon, const typename CGAL::Polygon_2< CastingTraits_2 >::Edge_const_iterator &it, const typename CastingTraits_2::Direction_2 &d, const CastingTraits_2 &traits=CastingTraits_2())
Given a simple polygon, an edge of the polygon, and a direction, this function determines whether a cavity (of a mold in the plane) that has the shape of the polygon can be used so that the polygon could be casted in the mold and then pulled out of the mold in the given direction such that the given edge is used as the top edge without colliding into the mold (but possibly sliding along the mold surface). More...

template<typename CastingTraits_2 >
bool CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction (const CGAL::Polygon_2< CastingTraits_2 > &polygon, const typename CGAL::Polygon_2< CastingTraits_2 >::Edge_const_iterator &it, const typename CastingTraits_2::Direction_2 &d, CGAL::Orientation orientation, const CastingTraits_2 &traits=CastingTraits_2())
Same as above with the additional orientation argument. More...

## ◆ is_pullout_direction() [1/4]

template<typename CastingTraits_2 >
 CGAL::Polygon_2::Edge_const_iterator CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction ( const CGAL::Polygon_2< CastingTraits_2 > & polygon, const typename CastingTraits_2::Direction_2 & d, const CastingTraits_2 & traits = CastingTraits_2() )

#include <CGAL/Set_movable_separability_2/Single_mold_translational_casting/is_pullout_direction.h>

Given a simple polygon and a direction, this function determines whether a cavity (of a mold in the plane) that has the shape of the polygon could be casted in the mold and then pulled out of the mold in the given direction without colliding into the mold (but possibly sliding along the mold surface).

If the polygon is not castable at all, the function returns false whatsoever.

The type that substitutes the template parameter CastingTraits_2 must be a model of the concept CastingTraits_2.

Parameters
 polygon the input polygon. d the inspected direction. traits the traits to use.
Returns
if polygon can be pullout in the d direction the iterator of the corresponding top edge, otherwise, polygon.edges_end().
Precondition
polygon must be non-degenerate (has at least 3 vertices) and simple, and it does not have three consecutive collinear vertices.
Examples:
Set_movable_separability_2/is_pullout_direction_single_mold_trans_cast.cpp.

## ◆ is_pullout_direction() [2/4]

template<typename CastingTraits_2 >
 CGAL::Polygon_2::Edge_const_iterator CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction ( const CGAL::Polygon_2< CastingTraits_2 > & polygon, const typename CastingTraits_2::Direction_2 & d, CGAL::Orientation orientation, const CastingTraits_2 & traits = CastingTraits_2() )

#include <CGAL/Set_movable_separability_2/Single_mold_translational_casting/is_pullout_direction.h>

Same as above with the additional orientation argument.

If the orientation of the polygon is known upon invocation, specify it. Otherwise, it has to be computed. Note that finding the orientation of a polygon requires time linear in the number of edges.

Parameters
 polygon the input polygon. d the inspected direction. orientation the orientation of polygon. traits the traits to use.
Returns
if polygon can be pullout in the d direction the iterator of the corresponding top edge, otherwise, polygon.edges_end().
Precondition
polygon must be non-degenerate (has at least 3 vertices) and simple, and it does not have three consecutive collinear vertices.

## ◆ is_pullout_direction() [3/4]

template<typename CastingTraits_2 >
 bool CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction ( const CGAL::Polygon_2< CastingTraits_2 > & polygon, const typename CGAL::Polygon_2< CastingTraits_2 >::Edge_const_iterator & it, const typename CastingTraits_2::Direction_2 & d, const CastingTraits_2 & traits = CastingTraits_2() )

#include <CGAL/Set_movable_separability_2/Single_mold_translational_casting/is_pullout_direction.h>

Given a simple polygon, an edge of the polygon, and a direction, this function determines whether a cavity (of a mold in the plane) that has the shape of the polygon can be used so that the polygon could be casted in the mold and then pulled out of the mold in the given direction such that the given edge is used as the top edge without colliding into the mold (but possibly sliding along the mold surface).

Observe, that if polygon can be pulled out in the given direction, but with a top edge different than the given one, the function returns false.

The type that substitutes the template parameter CastingTraits_2 must be a model of the concept CastingTraits_2.

Parameters
 polygon the input polygon. it an iterator to an edge in polygon. d the tested direction. traits the traits to use.
Returns
true if polygon can be pulled out in the d direction with the edge identified by i being the top edge, and false otherwise.
Precondition
polygon must be non-degenerate (has at least 3 vertices) and simple, and it does not have three consecutive collinear vertices.

## ◆ is_pullout_direction() [4/4]

template<typename CastingTraits_2 >
 bool CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction ( const CGAL::Polygon_2< CastingTraits_2 > & polygon, const typename CGAL::Polygon_2< CastingTraits_2 >::Edge_const_iterator & it, const typename CastingTraits_2::Direction_2 & d, CGAL::Orientation orientation, const CastingTraits_2 & traits = CastingTraits_2() )

#include <CGAL/Set_movable_separability_2/Single_mold_translational_casting/is_pullout_direction.h>

Same as above with the additional orientation argument.

If the orientation of the polygon is known upon invocation, specify it. Otherwise, it has to be computed. Note that finding the orientation of a polygon requires time linear in the number of edges.

Parameters
 polygon the input polygon. it an iterator to an edge in polygon. d the tested direction. orientation the orientation of polygon. traits the traits to use.
Returns
true if polygon can be pulled out in the d direction with the edge identified by i being the top edge, and false otherwise.
Precondition
polygon must be non-degenerate (has at least 3 vertices) and simple, and it does not have three consecutive collinear vertices.