0000000000739412

AUTHOR

Anton Mishkinis

showing 4 related works from this author

Méthodes d’approximation d’opérations géométriques sur des objets fractals

2015

National audience

[INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR][ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR][INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]ComputingMilieux_MISCELLANEOUS
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Extension des méthodes de géométrie algorithmique aux structures fractales

2013

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…

[SPI.OTHER]Engineering Sciences [physics]/OtherConception assistée par ordinateur[ SPI.OTHER ] Engineering Sciences [physics]/Other[SPI.OTHER] Engineering Sciences [physics]/Other[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM][INFO.INFO-OH]Computer Science [cs]/Other [cs.OH]Informatique graphiqueComputer-aided design[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Géométrie algorithmiqueComputational geometryModélisation géométrique[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH]Computer graphics[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM][ INFO.INFO-OH ] Computer Science [cs]/Other [cs.OH]FractalGeometric modelling
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Approximate convex hull of affine iterated function system attractors

2012

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…

Discrete mathematicsConvex hull0209 industrial biotechnologyGeneral MathematicsApplied Mathematics010102 general mathematicsProper convex functionConvex setMathematicsofComputing_GENERALGeneral Physics and AstronomyStatistical and Nonlinear Physics02 engineering and technology[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR]01 natural sciences[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]020901 industrial engineering & automationAffine hullTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYConvex polytopeOutput-sensitive algorithmConvex combination0101 mathematicsConvex conjugateMathematics
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Approximation de l'enveloppe convexe de l'attracteur d'un IFS affine

2012

International audience

[INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR]ComputingMilieux_MISCELLANEOUS[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]
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