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Gross -1 
3D Modeling and Approximation for Visualization 
and Simulation 
M. H. Gross 
Computer Science Department 
Swiss Federal Institute of Technology 
ETH-Zentrum 
8092 Zurich 
Tel: +41 1 632 7114 
Fax: +41 1 632 1172 
E-mail: grossm@infethz.ch 
Abstract 
This paper elucidates the role of modeling from the point of view of visualization and 
visual simulation. In a more general understanding, it exemplifies the increasingly growing 
relationship of visualization on the one side, and of vision and electronic photogrammetry 
on the other. Both research disciplines, which developed almost independently in the past, 
can benefit from each other because the complexity of todays and tomorrows advanced ap 
plications requires methods comprising algorithms and techniques from both disciplines. 
Particular emphasis is given here to modeling, which plays a key role in both areas and 
stands for the mutual fertilization to be achieved. 
Especially, graphics models are stressed and it is illustrated, how to use them for effi 
cient approximation and coding of 3D shapes. The scope ranges from the traditional para 
metric B-spline model, via wavelet-based models to the physically-based shape coding 
approach of deformable models. Where B-splines are still a flexible and easy to handle tool 
for shape description the power of wavelet bases comes along with their inherent hierarchi 
cal organization and their localization properties. Consequently, wavelet-based models 
gain much attraction for coding and representation of very large data sets, such as digital 
terrain models or remotely sensed images. Even more elaborated, deformable models in 
corporate physics and are computed most elegantly in the space of finite elements. They 
allow for the simulation of the behavior of complex 3D shapes under external forces. All 
these paradigms are illustrated by various examples and it is outlined, what the key issues 
of graphics and visualization modeling are and how electronic photogrammetry can help 
to approach them.