On the construction and display of a polytopal mesh for the N-dimensional hypercube and (N + 1) simplex |
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| Affiliation: | 1. Weill Cornell Medicine, Department of Healthcare Policy & Research, New York, NY, United States of America;2. RTI International, Behavioral Health Research Division, Research Triangle Park, NC, United States of America;3. Office of the Assistant Secretary for Planning and Evaluation, US Department of Health & Human Services, Washington, DC, United States of America |
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| Abstract: | By considering the analytical properties of polytopes it is possible to design a general data structure, a polytopal mesh, to represent such N-dimensional objects. Further investigation of the N-dimensional hypercube leads to the construction of a ternary code for representing the hypercube and the interconnection between levels of the polytopal mesh. This technique has been extended to other convex polytopes and specific examples of the N-dimensional cross polytope and simplex are given. Various projection techniques are used to display the convex polytopes on a two dimensional viewport. |
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