BijectiveDigitzedRigidMotions is a set of Mathematica packages for which the main objective is to implement algorithms used in the study of bjective digitized rigid motions. The algorithms were described/introduced in: Kacper Pluta , Pascal Romon, Yukiko Kenmochi, Nicolas Passat,Bijective Rigid Motions of the 2D Cartesian Grid, DGCI2016, Springer 2016 (free preprint); Kacper Pluta, Pascal Romon, Yukiko Kenmochi, Nicolas Passat. Bijectivity certification of 3D digitized rotations, CTIC2016, Springer 2016 (free preprint).
- Download or clone the repository
- Install the packages
To check if a 2D digitized rigid motion is bijective while restricted to a finite digital set S while using ForwardAlgorithm:
Needs["ForwardAlgorithm`"];
CheckInjectivity[4, 1, {1/3, 1/2}, S]
To check if a 2D digitized rigid motion is bijective while restricted to a finite digital set S while using BackwardAlgorithm:
Needs["BackwardAlgorithm`"];
S = Rectangle[{-10, -10}, {10, 10}];
IntersectionSetLatticesNonInjective[4, 1, {1/3, 1/2}, S]
To check if a 3D digitized rotation given by a Lipschitz quaternion is bijective:
Needs["QuaternionCertification`"];
CertifyQuaternion[{3,0,0,1}]
The algorithms were implemented in Mathematica 10, therefore, Mathematica 10 or higher is required.
Any result obtained with the official release should be cited while using a DOI number. The DOI number of the newest release is:
