Approximate convex hull of affine iterated function system attractors |
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| Authors: | Anton Mishkinis Christian Gentil Sandrine Lanquetin Dmitry Sokolov |
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| Institution: | 1. Department of Genetics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA;2. GeneDx, Gaithersburg, MD, USA;3. Baylor College of Medicine, Houston, TX, USA;4. Brigham and Women’s Hospital and Harvard Medical School, Boston, MA, USA;5. Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Parkville, Victoria, Australia;6. Memorial Sloan Kettering Cancer Center, New York, NY, USA;7. University of Vermont, Larner College of Medicine, Burlington, VT, USA;8. Mayo Clinic, Rochester, MN, USA. |
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| 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 approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy. |
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