Publications(January 2002 - December 2002)

1. B. Schmitt, A. Pasko, V. Adzhiev, C. Schlick, Constructive texturing based on hypervolume modeling, Journal of Visualization and Computer Animation, vol. 12, No. 5, 2001, pp. 297-310 (published in June 2002).
   Abstract - The concept of solid texturing is extended in two directions: constructive modeling of space partitions for texturing and modeling of multidimensional textured objects called hypervolumes. A hypervolume is considered as a point set with attributes of both physical (density, temperature, etc.) and photometric (color, transparency, diffuse and specular reflections, etc.) nature. The point set geometry and attributes are modeled independently using real-valued scalar functions of several variables. The concept of constructive hypervolume textures is independent of the geometry representation. We provide examples of textured Frep and BRep objects as illustrations.
2. A. Pasko, V. Adzhiev, B. Schmitt, C. Schlick, Constructive hypervolume modeling, Graphical Models, special issue on Volume Modeling, vol. 63, No. 6, November 2001, pp. 413-442 (published in August 2002).
   Abstract - In this paper, we deal 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 point set. We provide a brief survey of different modeling techniques related to point sets with attributes. It spans such different areas as solid modeling, heterogeneous objects modeling, scalar fields or "implicit surface" modeling, and volume graphics. Then, on the basis of this survey we formulate requirements to a general model of hypervolumes (multidimensional point sets with multiple attributes). A general hypervolume model and its components such as objects, operations, and relations are introduced and discussed. A function representation (FRep) is used as the basic model for the point set geometry and attributes represented independently using real-valued scalar functions of several variables. Each function defining the geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This reflects the constructive nature of the symmetric approach to modeling geometry and associated attributes in multidimensional space. To demonstrate a particular application of the proposed general model, we consider in detail the problem of texturing, introduce a model of constructive hypervolume texture, and then discuss its implementation, as well as the special modeling language we used for modeling hypervolume objects.
3. G. Pasko, A. Pasko, M. Ikeda, T. Kunii, Bounded blending operations, Shape Modeling International 2002, Banff (Canada, May 17-22), IEEE Computer Society, 2002, pp. 95-103.
   Abstract - New analytical formulations of bounded blending for functionally defined set-theoretic operations are proposed. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional bounding solid. The proposed blending using a bounding solid can be applied to a single selected edge or a vertex. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. It is shown to have versatile applications in interactive design.
4. V. Adzhiev, E. Kartasheva, T. Kunii, A. Pasko, B. Schmitt, Cellular-functional modeling of heterogeneous objects, Proc. 7th ACM Symposium on Solid Modeling and Applications, Saarbrucken, Germany (June 17 - 21, 2002), Konwoo Lee and N.M. Patrikalakis (Eds.), ACM Press, 2002, pp. 192-203.
   Abstract - 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 representation of geometry and attributes, and makes it possible to represent dimensionally non-homogeneous entities and their cellular decompositions. Hypervolume model components such as objects, operations and relations are introduced and outlined. The framework's inherent multidimensionality allowing, in particular, to deal naturally with time dependence promises to model complex dynamic objects composed of different materials with constructive building of their geometry and attributes. Attributes given at each point can represent properties of arbitrary nature (material, photometric, physical, statistical, etc.). To demonstrate a particular application of the proposed framework, we present an example of multimaterial modeling - a multilayer geological structure with cavities and wells. Another example illustrating the treatment of attributes other than material distributions is concerned with time-dependent adaptive mesh generation where function representation is used to describe object geometry and density of elements in the cellular model of the mesh. The examples have been implemented by using a specialized modeling language and software tools being developed by the authors.
5. R. Cartwright, V. Adzhiev, A. Pasko, Y. Goto, T. L. Kunii, Web-based shape modeling with HyperFun, Technical Report HCIS-2002-02, Hosei University, Tokyo, Japan, 2002, 16 p.
   Abstract - We present an approach to collaborative Web based modeling using functionally defined shapes specified in the high level language HyperFun. The EmpiricalHyperFun shape modeling system based on Empirical Modeling principles provides users with an unusual degree of mutual interaction through the Web.

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