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- Alexander A. Pasko, Valery Adzhiev, Alexei Sourin, Vladimir V. Savchenko
- The Visual Computer
- 1995

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 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 high-level programming language called HyperFun. A model in HyperFun can serve as a protocol for exchanging F-rep… (More)

- Vladimir V. Savchenko, Alexander A. Pasko, Oleg G. Okunev, Tosiyasu L. Kunii
- Comput. Graph. Forum
- 1995

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)

- Yutaka Ohtake, Alexander G. Belyaev, Alexander A. Pasko
- Shape Modeling International
- 2001

The paper presents a novel approach for accurate polygo-nization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals.

- Alexander A. Pasko, Valery Adzhiev, Benjamin Schmitt, Christophe Schlick
- Graphical Models
- 2001

This paper deals with modeling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real/abstract object or process under consideration. An attribute is a mathematical model of an object property of arbitrary nature (material, photometric, physical, statistical, etc.) defined at any point of the… (More)

- Vladimir V. Savchenko, Alexander A. Pasko
- The Visual Computer
- 1998

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)

- Alexander G. Belyaev, Alexander A. Pasko, Tosiyasu L. Kunii
- Computer Graphics International
- 1998

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 G. Belyaev, Alexander A. Pasko
- The Visual Computer
- 2003

The paper presents a novel approach for accurate polygo-nization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals. Given an initial polygonization of an implicit surface, a mesh evolution process initialized by the… (More)

- Valery Adzhiev, Elena L. Kartasheva, Tosiyasu L. Kunii, Alexander A. Pasko, Benjamin Schmitt
- Symposium on Solid Modeling and Applications
- 2002

The paper presents an approach to modeling heterogeneous objects as multidimensional point sets with multiple attributes (hypervolumes). A theoretical framework is based on a hybrid model of hypervolumes combining a cellular representation and a constructive representation using real-valued functions. This model allows for independent but unifying… (More)

- Tosiyasu L. KUNII, Masumi IBUSUKI, Galina I. PASKO, Alexander A. PASKO, Daisuke TERASAKI, Hiroshi HANAIZUMI
- 2003

Member Summary Recent advances of Web information systems such as e-commerce and e-learning have created very large but hidden demands on conceptual multiresolution analysis for more generalized information analysis, cognition and modeling. To meet the demands in a general way, its modeling is formulated based on modern algebraic topology. To be specific,… (More)