0000000000739412
AUTHOR
Anton Mishkinis
Méthodes d’approximation d’opérations géométriques sur des objets fractals
National audience
Extension des méthodes de géométrie algorithmique aux structures fractales
Defining shapes by iteration allows us to generate new structures with specific properties (roughness,lacunarity), which cannot be achieved with classic modelling.For developing an iterative modeller to design fractals described by a BCIFS, we developed a set oftools and algorithms that permits one to evaluate, to characterize and to analyse different geometricproperties (localisation, convex hull, volume, fractal dimension) of fractals. We identified properties ofstandard CAD operations (intersection, union, offset, . . . ) allowing us to approximate them for fractalsand also to optimize these approximation algorithms.In some cases, it is possible to construct a CIFS with generalised HUTCH…
Approximation de l'enveloppe convexe de l'attracteur d'un IFS affine
International audience
Approximate convex hull of affine iterated function system attractors
International audience; 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 additio…