Gross - 7 
x(s,t) = 
(4) 
'x(s, t)" 
y(s , t) 
z(s, t) 
Z Z Z C W Vpq( s ,t) 
m q p 
where m,p and g denote the discrete scaling and shifting parameters and c the coeffi 
cients. Now, filtering the coefficients controls the approximation. 
[7] used this model to build a fast and adaptive meshing method for surfaces, which 
bases on the approximation behavior and error bounds of the wavelet theory. Especially, 
the localization properties of the WT and straightforwardly the ability to define local level- 
of-detail filters motivated to use the above paradigm for modeling very large scale data 
sets, such as DTMs. Figure 4a illustrates the local approximation properties of the method, 
where the digital terrain model of mount Matterhorn was reconstructed perfectly within the 
elliptic region only. The same holds for the triangle mesh, depicted in fig. 4b. Taking advan 
tage from level-of-detail filtering the initial data as well as the number of graphics primi 
tives, i.e. triangles could be reduced massively. Special emphasis is given to real-time ap 
plications, like interactive data exploration or flight simulation. 
Fig. 4 Wavelet-based digital terrain models: 
a) Local level-of-detail control. 
b) Adaptive meshing of the DTM. 
(data source: courtesy Bundesamt fiir Landestopographie, Switzerland, from [7]) 
Volume data can also be expanded using 3D wavelets and, correspondingly, the shapes 
of isosurfaces in volumes. They are defined implicitly, as: 
f(x,y,z) - r = 0 
(5)