2D Movable Separability of Sets Reference

Shahar Shamai and Efi Fogel

Movable Separability of Sets [2] is a class of problems that deal with moving sets of objects, such as polygons in the plane; the challenge is to avoid collisions between the objects while considering different kinds of motions and various definitions of separation.

Introduced in: CGAL 4.12
Depends on: 2D Polygons
BibTeX: cgal:sf-sms2-24a
License: GPL

At this point this package consists of the implementations of various predicates and constructions related to castings of polygonal objects. In particular, it can be used to determine whether a feasible mold for a polygonal object does exist. If a mold exists, the package can also be used to compute all possible orientations of the feasible molds and the corresponding motions needed to remove the casted object from the mold.

Classified Reference Pages

Casting Functions

• CGAL::Set_movable_separability_2::Single_mold_translational_casting::top_edges()
• CGAL::Set_movable_separability_2::Single_mold_translational_casting::pullout_directions()
• CGAL::Set_movable_separability_2::Single_mold_translational_casting::is_pullout_direction()

Casting Concepts

• CastingTraits_2

Modules
	Top Edges
	These function 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 without colliding into the mold (but possibly sliding along the mold boundary).
	Is Pullout Direction
	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).
	Pullout Directions
	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 using a given edge as the top edge and then pulled out of the mold without colliding into the mold (but possibly sliding along the mold boundary).
	Concepts