/ V. V. Savchenko / 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 Proceeding Papers
The projection operation in multidimensional space is discussed. Several numerical methods are compared. Examples of applications in sweeping, reconstruction from medial axis aaand 2D to 3D projection are given.
The goal of the proposed project is to design a new modeling and visualization system (integrated software/hardware computing system) incorporating a digital signal processor array within a personal computer host. The system also includes application specific integrated circuits and characterized by high parallelism and homogeneity of vector computations. It results in superior performance along with comparatively low cost. In the proposed system the following main problems have to be solved: combination of implicit freeform surfaces, height and volume data; atmospheric effects (fog, haze, rain, snow, layered atmospheric effects, round earth, sky illumination); animation, deformation and 3D morphing.
The problem of implementation of interpolating functions for scattered data is considered. A basic idea of the variational schema, formulas and description of the developed algorithm are given.