Skeletal Reconstruction of Branching Shapes

We present a new method for the implicit reconstruction of branching shapes from a set of scattered data points. The method is based on the computation of a geometric skeleton inside the data set. This skeleton is simplified in order to filter noise and converted into skeletal elements – a graph of interconnected curves – that generate an implicit surface. We use Bézier triangles as extra skeletal elements to perform bulge free blends between branches while controlling the blend extent. This leads to a smooth implicit representation of the shape, directly computed in a purely geometric way.