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This paper shows the usefulness of discrete differential geometry inglobal analysis. Using the discrete differential geometry of triangles, we couldconsider the global structure of closed trajectories of triangles on atriangular mesh consisting of congruent isosceles triangles. As an example, weperform global analysis of an Escher-style trick art, i.e., a simpler version of -Ascending and Descending-. Afterdefining the local structure on the trick art, we analyze its global structureand attribute its paradox to a singular point i.e., a singular triangle at the center. Then, the endless-Penrose stairs- is described as a closed trajectory around the isolatedsingular point. The approach fits well with graphical projection and gives asimple and intuitive example of the interaction between global and localstructures. We could deal with higher dimensional objects as well byconsidering n-simplices n > 2 instead of triangles.

KEYWORDS

Discrete Differential Geometry, Triangle Mesh, Global Analysis, Singular Point, Penrose Stairs

Cite this paper

Morikawa, N. 2016 Discrete Differential Geometry of Triangles and Escher-Style Trick Art. Open Journal of Discrete Mathematics, 6, 161-166. doi: 10.4236-ojdm.2016.63013.





Autor: Naoto Morikawa

Fuente: http://www.scirp.org/



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