Alexander A. Pasko

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Concepts of functionally based geometric modeling including sets of objects, operations, and relations are discussed. Transformations of a defining real function are described for set-theoretic operations, blending, offsetting, bijective mapping, projection, cartesian products, and metamorphosis. Inclusion, point membership, and intersection relations are(More)
This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality The volume spline is based on use of the Green’s function for interpolation of scalar function values of a chosen “carrier” solid. Our algorithm is capable(More)
This paper presents a project devoted to developing an open system architecture for functionally based (implicit or more generally F-rep) shape modeling and its applications. The software tools are built around the shape models written in a highlevel programming language called HyperFun. A model in HyperFun can serve as a protocol for exchanging F-rep(More)
Alexander Pasko , Valery Adzhiev β , Benjamin Schmitt and C. Schlick α Department of Digital Media, Hosei University 3-7-2 Kajino-cho Koganei-shi ,Tokyo 184-8584 Japan. β The National Centre for Computer Animation, Bournemouth Media School, Bournemouth University, Poole, Dorset BH12 5BB, United Kingdom. γ LaBRI, Laboratoire Bordelais de Recherche(More)
Surface creases provide us with important information about the shapes of objects and can be intuitively defined as curves on a surface along which the surface bends sharply. Our mathematical description of such surface creases is based on study of extrema of the principal curvatures along their curvature lines. On a smooth generic surface we define ridges(More)
Yutaka Ohtake Alexander Belyaev Alexander Pasko Computer Graphics Group, Max-Planck-Institut für Informatik Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany E-mails: ohtake,belyaev @mpi-sb.mpg.de Shape Modeling Lab, University of Aizu, Aizu-Wakamatsu 965-8580, Japan E-mail: belyaev@u-aizu.ac.jp Department of Digital Media, Faculty of Computer and(More)
We present an approach to constructive modeling of FRep solids [2] defined by real-valued functions using 4D uniform rational cubic Bspline volumes as primitives. While the first three coordinates are used to represent the spatial component of the volume to be sculpted, the fourth coordinate is used as a scalar, which corresponds to a function value or a(More)
We present a general mathematical framework for transforming functionally defined shapes. The proposed model of extended space mappings considers transformations of a hypersurface in coordinate-function space with its projection onto geometric space. This model covers coordinate space mappings, metamorphosis, and algebraic operations on defining functions,(More)
There are limitations to the current BRep based “model then animate” paradigm when animating time-dependent (dynamic) objects. This paper describes an approach to modeling dynamic objects directly in space-time or even higher dimensional space. The use of the function representation (FRep) is proposed due to the ease with which it handles higher dimensions.(More)