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Approximate convex hull of affine iterated function system attractors

Anton Mishkinis 1 Christian Gentil 1 Sandrine Lanquetin 1 Dmitry Sokolov 2 
2 ALICE - Geometry and Lighting
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximation of the convex hull without loss of accuracy.
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Submitted on : Thursday, November 22, 2012 - 9:47:46 AM
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Anton Mishkinis, Christian Gentil, Sandrine Lanquetin, Dmitry Sokolov. Approximate convex hull of affine iterated function system attractors. Chaos, Solitons & Fractals, 2012, 45 (11), pp.1444-1451. ⟨10.1016/j.chaos.2012.07.015⟩. ⟨hal-00755842⟩



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