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Abstract:
We present a shape representation, the {\em multi-level partition of unity}
implicit surface, that allows us to construct surface models from
very large sets of points. There are three key ingredients
to our approach: 1) piecewise quadratic functions that capture
the local shape of the surface, 2) weighting functions (the
partitions of unity) that blend together these local shape functions,
and 3) an octree subdivision method that adapts to variations in
the complexity of the local shape.
Our approach gives us considerable flexibility in the choice of local
shape functions, and in particular we can accurately represent sharp
features such as edges and corners by selecting appropriate shape
functions. An error-controlled subdivision leads to an adaptive approximation
whose time and memory consumption depends on the required accuracy.
Due to the separation of local approximation and local blending,
the representation is not global
and can be created and evaluated rapidly.Because our surfaces are
described using implicit functions, operations such as shape blending,
offsets, deformations and CSG are simple to perform.
