\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.14 - 2D Movable Separability of Sets
Modules
2D Movable Separability of Sets Reference

Casting_2.png
Shahar Shamai, 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-sms2-19a
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

Casting Concepts

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