Gross - 3 
Needless to say that the latter one stands for a large variety of representations encompas 
sing surface deformations as well as light and material properties. Conversely, the data 
modeling issue stems from the strong demand for real-time interaction with complex geo 
metric models including the constraints of preserving consistency, fast access and object 
orientation. In this context, the well known boundary descriptions, CSG, or for instance 
the winged-edge data structure had been developed [4]. 
The following survey is focussed on geometric models in computer graphics and it is 
pointed out, how they can be combined efficiently with image processing methods to form 
elaborated solutions of complex problems. Along these lines, particular emphasis is given 
to various parametric, nonparametric and implicit models based on: 
• NURBS: The traditional way of describing 3D-shapes via B-splines has 
approved to provide a flexible scheme and can be employed immediately 
for visualization. 
• Wavelets and multiresolution modeling: Parametric, nonparametric or 
implicit curve and surface modeling using wavelet bases incorporates the 
multiresolution paradigm into the model and still provides consistent de 
scriptions within well-defined error bounds. Wavelets not only provide 
hierarchical bases for data approximation, but moreover, they inherently 
carry out some local spectral estimates of the data. This important prop 
erty can be harvested for pattern recognition tasks, such as texture analy 
sis. Since wavelets gain more and more attraction in shape modeling, 
they will be stressed more detailed. 
• Physically-based models: Another sophisticated approach to the geo 
metric modeling problem of nonrigid and deformable objects came out 
with snakes [12] and deformable models. They allow to integrate physi 
cal behavior into the model - a very important step in animation as well 
as in nonrigid motion detection. 
2 The Traditional B-Spline Model 
Parametric spline-based curve and surface models have been elaborated and investi 
gated quite intensively during the past decades. From the Bézier-type to the rational 
B-spline on nonuniform knots (NURB) a rich variety of methods was provided to solve 
even very complex modeling tasks in free-form design [3]. As a consequence, B-spline 
surface tools are part of most modem modeling and CAD systems. Beside of the standard 
tensor product surface, Bézier- and B-splines had also been extended onto triangular 
patches and barycentric combinations, which turn out to be topologically more liberate. To 
gether with a bundle of numerically stable and robust algorithms the B-splines figure out 
a powerful and flexible tool for geometric modeling. In particular, B-splines based shape