Modeling surfaces of arbitrary topology using manifolds

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Abstract
We describe an extension of B-splines to surfaces of arbitra ry topol- ogy, including arbitrary boundaries. The technique inheri ts many of the properties of B-splines: local control, a compact rep resenta- tion, and guaranteed continuity of arbitrary degree. The su rface is specified using a polyhedral control mesh instead of a rectangular one; the resulting surface approximates the polyhedral mes h much as a B-spline approximates its rectangular control mesh. Li ke a B- spline, the surface is a single, continuous object. This is a chieved by modeling the domain of the surface with a manifold whose topology matches that of the polyhedral mesh, then embedding this domain into 3-space using a basis-function/control-point formul ation. We provide a constructive approach to building a manifold.

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