/ V. V. Savchenko / Professor
/ Kenjiro T. Miura / Associate Professor
/ Alexander A. Pasko / Assistant Professor
Research activity of the Shape Modeling Laboratory is concerned with developing new paradigm of modeling highly complex objects and scenes. This paradigm includes different models defined by real functions. Recently we have studied new operations, primitives, and applications of this approach.
The projection operation is important while solving the following geometric problems: bullet 3D to 2D projection; bullet 4D to 3D projection for sweeping by a moving solid; bullet Reconstruction from the medial axis transformation; bullet Construction of an envelope of a parametric family; bullet Implicitization of parametric curves and surfaces; bullet Calculation of the surface area by integration. We analyzed several approaches to projection: analytical methods, approximate projections and global maximum searches. With this methods the projection operation becomes closed on the representation by real functions.
We have extended the set of primitives by including functionally defined 2D polygons. This polygon-to-function conversion is useful in sweeping, reconstruction, synthetic carving, animation and other applications.
The approach and specific techniques proposed by our laboratory and collaborators are presented in the Web site Shape Modeling and Computer Graphics with Real Functions http://www.u-aizu.ac.jp/public/www/labs/sw-sm/FrepWWW/F-rep.html This approach is becoming internationally recognizable. It was presented in the tutorial course on implicit surfaces at SIGGRAPH'96 conference (New Orleans, USA) and referenced as ``an attempt to step to a more general modeling scheme using real functions." Our submission has received ``Best WWW award" for innovation technologies in computer graphics at Eurographics'96 conference in France.
We have organized the Shape Modeling International '97 conference held at the University of Aizu in March 1997. The SMI'97 was a truly international conference. The 18 contributed papers were selected, after peer review, from a total of 38 papers submitted from 12 different countries (Australia, Canada, France, Germany, Hong Kong, Hungary, Italy, Japan, Korea, Russia, UK, USA). Eight world leading specialists delivered invited talks and courses. The proceedings were published by IEEE Computer Society Press.
Refereed Journal Papers
We consider a long-standing problem, hair modeling, and show how easy and effectively our functionally based model can be applied there. Modeling hair, we represent it with solid noise and subsequently unify it with the solid being made hairy. The hair and the solid are defined by real functions and the resultant hairy solid is in turn functionally defined and can be an argument for other operations. We are able to control length, thickness and curliness of hair and to obtain different hairstyles varying defining functions and applying set-theoretic operations to solid hair.
The paper studies a function representation of point sets swept by moving solids. We have reduced the problem of swept solid description to global extremum search by t variable. Examples of self-intersections, moving CSG solids and NC machining are given.
We discuss different techniques to projecting geometric objects defined by real functions of several variables. The result of this operation is an object of the lower dimension with its own defining function. We discuss several approaches: analytical methods, approximate projections and global maximum searches. The accuracy is compared for two algorithms: the union of maximal cross-sections and the global search with the quadratic interpolation. The following applications are illustrated: 3D solid projection onto a 2D plane; 4D to 3D projection for sweeping by a moving solid; 3D reconstruction from the medial axis.
This paper deals with an approach to the representation of polygons by real functions and its applications in geometric modeling. We combine an algorithm employing a monotone function of a Boolean operation, with R-functions. This method results in a continuous function F(x,y) with zero value at polygon edges. We discuss and illustrate different sweeping techniques and reconstruction from cross-sections.
In this invited STAR report we present a survey of our project on the function representation (F-rep) in shape modeling. Modeling concepts include sets of objects, operations and relations. Transformations of a defining function are described for the basic and advanced operations: deformation with space mappings and algebraic sums controlled by arbitrary points, reconstruction of solids from surface points and contours, sweeping by a moving solid. We introduce high-level geometric language that provides extendibility of a modeling system by input symbolic descriptions of primitives, operations and predicates. Applications of this language in teaching geometric modeling are illustrated. Application examples of aesthetic design, collisions simulation, facial expressions simulation, NC machining, range data processing, 3D reconstruction from cross-sections, artificial life, and 3D texture generation are given.
Modeling of the occlusal surface of teeth is an important problem in computer-aided design of dental restorations. The designed shape must fit the existing jaw articulation. Also, the design process must be fast to be practical in clinical applications. In this paper we present techniques for automatic adjustment of the occlusal surface of restorations based on the results of articulation simulation. The shape of restorations is changed to avoid interpenetrations with the opponent teeth during functional jaw movements. The 3-D space mapping method is used which guarantees the surface smoothness and preservation of the main topological features of the occlusal surface. To speedup calculations we use rasterrizing graphics hardware for computationally involved collision detection between surfaces of teeth.
In massively parallel and distributed systems, as they grow along with the complexity of the tasks they solve, the share of multi-task regimes, such as real-time control problems, multimedia, signal and image analysis and processing, increases. In the presented paper we discuss a mathematical framework for the organization of resource sharing to attain global maximum in computer performance when we have limited resources, such as common memory, channels and so forth. Local strategy of optimization is considered that leads to the optimal distribution of common resources.
The paper presents a project devoted to the implementation of the "empirical" approach to geometric modelling in the form of the definitive programming environment. The notion of the Kernel Geometric Interactive environment is introduced. Its characteristic feature called "inherent symbolic interactivity" is supported by a high-level definitive languageof point-sets HyperJazz.
This is an extended version of the invited paper from the GraphiCon'96 International Conference. We review the basics of F-rep paradigm in shape modeling, describe primitive solids, basic ana advanced operations, and applications.