The ultimate planar convex hull algorithm
SIAM Journal on Computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Computing in nonlinear media and automata collectives
Computing in nonlinear media and automata collectives
Cellular Automata: A Discrete Universe
Cellular Automata: A Discrete Universe
Integer Gradient for Cellular Automata: Principle and Examples
SASOW '08 Proceedings of the 2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems Workshops
Gabriel Graphs in Arbitrary Metric Space and their Cellular Automaton for Many Grids
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
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In the cellular automata domain, the discrete convex hull computation rules proposed until now only deal with a connected set of seeds in infinite space, or with distant set of seeds in finite space. We present a cellular automata rule that constructs the discrete convex hull of arbitrary set of seeds in infinite spaces. The rule is expressed using intrinsic and general properties of the cellular spaces, considering them as metric spaces. In particular, this rule is a direct application of metric Gabriel graphs. This allows the rule and its components to be used on all common 2D and 3D grids used in cellular automata.