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Meyer, M., Desbrun, M., Schroder, P. and Barr, A.H. (2003) Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. In: Hege, H.-C. and Polthier, K., Eds., Visualization and Mathematics III, Springer-Verlag, Berlin, 35-57.

has been cited by the following article:

• TITLE: Discrete Differential Geometry of Triangles and Escher-Style Trick Art

  AUTHORS: Naoto Morikawa

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

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.6 No.3, July 5, 2016

  ABSTRACT: This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles) on a triangular mesh consisting of congruent isosceles triangles. As an example, we perform global analysis of an Escher-style trick art, i.e., a simpler version of “Ascending and Descending”. After defining the local structure on the trick art, we analyze its global structure and 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 isolated singular point. The approach fits well with graphical projection and gives a simple and intuitive example of the interaction between global and local structures. We could deal with higher dimensional objects as well by considering n-simplices (n > 2) instead of triangles.