__abstract:__

In this paper we introduce a 3D shape representation that is based solely
on mesh connectivity -- the *connectivity shape*. Given a
connectivity, we define its natural geometry as a smooth
embedding in space with uniform edge lengths and describe efficient techniques
to compute it. Furthermore, we show how to generate connectivity
shapes that approximate given shapes. Applications of connectivity
shapes to modeling, mesh coding and graph drawing are described.

__publication:__

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Imagine all edges of the cow being springs of the same equilibrium length. In the embedding (b) we forced the spring system into a high energy state. In (c) we released all vertices and the spring system relaxed into a low energy state, with more or less uniform edge lengths. This is the connectivity's natural shape. More poetically, the sphere embedding in (b) has the

We can also to generate connectivity shapes that approximate given shapes. This is done by (re)meshing the given shape with uniform edge lengths. For example, the connectivity shape in (d) bears a striking resemblance to the original (a). The only information in this mesh is its connectivity, in the sense that it induces the mesh geometry.

__Connectivity Creatures:__