/ V. V. Savchenko / Professor
/ Valery Adzhiev / Visiting Researcher
/ Alexander A. Pasko / Assistant Professor
The laboratory's research and development project is devoted to developing an open system architecture for functionally based volume modeling and its applications. The software tools are built around the volume models written in a high-level modeling language called HyperFun. A model in HyperFun can serve as a protocol for exchanging models between users, modeling systems, or networked computers. HyperFun models can be collected in application-specific libraries. The basic set of system components: an interpreter for parsing and function evaluation; F-rep system libraries; a modeler with an extendible graphical user interface; a multidimensional modeler with a symbolic user interface providing means for interpreting multidimensional coordinates and constructing scenes; applications for visualization (polygonization, VRML generation, ray-tracing), animation, voxelization and others; a collaborative Internet-based modeler including a HyperFun-to-Java translator and advanced interactive techniques based on the "empirical modeling" paradigm (collaboration work with University of Warwick, UK).
Refereed Journal Papers
A general mathematical frame-work for transforming functionally defined shapes is presented. The proposed model of extended space mappings considers transformations of a hypersurface in coordinate-function space with its projection onto geometric space.
Several techniques of computer-aided synthetic carving are presented. We describe procedural methods for relief carvings and patterned lattices, and interactive carving with chisels.
Different approaches to volume modeling are considered. A hybrid system based on voxel data and function representation is proposed and discussed.
The paper deals with the Minkowski sum operation in the context of geometric modeling with real functions. We formulate the Minkowski sum as the Cartesian product resulting in a higher dimensional object and a mapping to the initial space.
Several techniques of computer-aided synthetic carving are presented. We describe procedural methods for relief carvings and patterned lattices, and interactive carving with chisels. All proposed methods are based on the function representation of geometric objects.
The problem of implementation of interpolating functions for scattered data is considered. We sketch an algorithm for particle-based simulation of a hypothetical comet, apply the developed tool for visualization of a particle flow of a cometary coma.
The paper presents our approach to volume modeling which combines volume representations by voxel data and by continuous real functions. We illustrate the approach by several advanced operations on a volumetric object.
R-functions introduced by V. Rvachev in 60-s have some properties valuable for computer modeling of two-, three-dimensional, and time-dependent shapes. We observe applications of them under the unified shape model called the function representation.
We describe several advanced shape modeling techniques such as polygon-to-function conversion, pattern dependent interpolation of scattered data, and reconstruction from medial axis. These techniques are applied to model complex shapes for computer art works. Procedural and interactive approaches to synthetic carving are described. All introduced techniques are united under the shapes representation by real-valued functions.
The paper deals with simulation and characterization of a growing mammalian cell colony. Modelled cells were compared to AHH-1 human lymphocyte culture cells with the help of the fractal analysis methods.
We discuss the main differences between direct volume visualization and modeling with voxel data, and discuss some results and questions about a software/hardware combination to speed up solving volume modeling problems.
On a smooth generic surface we define ridges to be the local positive maxima of the maximal principal curvature along its associated curvature line and ravines to be the local negative minima of the minimal principal curvature along its associated curvature line. The ridges and ravines are important for shape analysis and possess remarkable mathematical properties. For example, they correspond to the end points of shape skeletons. In this paper we derive a formula and develop software to detect the ridges and ravines on a surface given in implicit form.
An algorithm of polygonization of trimmed implicit surfaces yielding surface sheets is presented. These two- dimensional manifolds with boundaries result from the set-theoretic difference of an implicit surface and a solid. The algorithm generates the polygonal approximation of the trimmed surface with the mesh adaptation to the manifold boundary.
An approach to model multidimensional shapes using the function representation is discussed. The modelled shapes are mapped onto so-called "multimedia coordinates" to generate animation, time-dependent spreadsheets and other miltimedia objects.
This paper presents a project devoted to developing an open system architecture for functionally based shape modeling and applications. The software tools are built around the shape models written in a high-level language called HyperFun (see http://www.hyperfun.org). A model in HyperFun can serve as a lightweight communication protocol to exchange models between users, modeling systems, and networked computers.