Tangents to fractal curves and surfaces

Dmitry Sokolov 1 Christian Gentil 2 Hicham Bensoudane 2
1 ALICE - Geometry and Lighting
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunarity (size and distribution of holes). In this context we intend to develop differential calculus tools for fractal curves and surfaces defined by IFS. Using local fractional derivatives, we show that, even if most fractal curves are nowhere differentiable, they admit a left and right half-tangents, what gives us an additional parameter to characterize shapes.
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Dmitry Sokolov, Christian Gentil, Hicham Bensoudane. Tangents to fractal curves and surfaces. Curves and Surfaces, 2012, 6920, pp.663-680. ⟨hal-00798910⟩



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