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410 16. Implicit Modeling
Figure 16.28. “Spiral Stairs.” A complex BlobTree implicit model created in Erwin DeGroot’s
BlobTree.net system. (See also Plate VI.)
• union: max(f(L(N),M),f(R(N),M));
• intersection: min(f(L(N),M),f(R(N),M));
• difference: min(f (L(N),M), −f(R(N),M)).
A complex BlobTree model showing many of the features that have been in-
tegrated is shown in Figure 16.28.
16.9 Interactive Implicit Modeling Systems
Early sketch-based modeling systems, such as Teddy (Igarashi et al., 1999), used
a few drawn strokes from the user to infer a polygonal model in 3-space. With
better hardware and improved algorithms, sketch-based implicit modeling sys-
tems are now possible. Shapeshop uses implicit sweep surfaces to manufacture
Figure 16.29. Outlines
are inflated.
Image cour-
tesy Erwin DeGroot
.
3D strokes from 2D user strokes and also preserves the hierarchy of the BlobTree
unlike the early systems that produced homogeneous meshes (Schmidt, Wyvill,
Sousa, & Jorge, 2005). This enables a user to produce complex models of ar-
bitrary topology from a few simple strokes. The margin figures show a closed