Publications(January 2002 - December 2002)
- 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
- 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.
- 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
- 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.
- 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,
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