Abstract
Although space-filling curves are well known, and have many applications in parallel computing and data mapping, there is a need for a space-filling surface that is a continuous mapping from two-dimensional domain onto the unit cube. This would allow efficient implementation of a 2D problem on parallel processors which are interconnected into a 3D grid. Such a surface is presented in this paper, which uses Hilbert’s geometric approach to generate a mapping from a unit square to a triangular prism. Using two such mappings we can create a mapping from a rectangle to a unit cube. To culminate, we use the mapping to produce a continuous omnichromatic picture, that is, one for which the colors change continuously, and under sufficient resolution, contains every possible RGB value.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
