Affiliation:
1. Department of Mathematics, Northeastern University, Shenyang 110004, P. R. China
Abstract
In this paper, we define the notion of affine curvatures on a discrete planar curve. By the moving frame method, they are in fact the discrete Maurer–Cartan invariants. It shows that two curves with the same curvature sequences are affinely equivalent. Conditions for the curves with some obvious geometric properties are obtained and examples with constant curvatures are considered. On the other hand, by using the affine invariants and optimization methods, it becomes possible to collect the IFSs of some self-affine fractals with desired geometrical or topological properties inside a fixed area. In order to estimate their Hausdorff dimensions, GPUs can be used to accelerate parallel computing tasks. Furthermore, the method could be used to a much broader class.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Cited by
3 articles.
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