It is frequently necessary to complete the design of a surface from a specication of its boundary. This paper introduces a technique for completing the surface when the boundary is described by a non-self-intersecting, closed, planar, B-spline curve. The mapping produces a tensor product B-spline surface whose outer boundary is the input curve, and whose parameterization generalizes the polar parameterization of the disc. x1. Introduction In this paper we propose a new operator for generating a planar sur- face from a closed, non-self-intersecting piecewise polynomial boundary in the plane. We consider this approach to be a novel step towards the larger goal of surface completion from a free form curve boundary. This is a com- mon problem arising in geometric modeling. Examples include \capping" extrusions and lling holes where adjacent patches come together. Holes also commonly occur in scanned datasets. There are many applications where such models must be made \watertight". Given the importance of the problem, a number of methods have been proposed for surface completion. Rather than attempt to warp a rectangular uv domain to an irregularly shaped region, a common ap- proach is to employ tensor product surfaces whose parameter domains are further restricted by trimming curves. Generally, the boundary must be densely sampled to accurately represent this subset and the parameteriza- tion originally associated with the boundary curve is lost. Moreover, the representation does not lend itself easily to further modeling operations. Several methods have been introduced for hole-lling (e.g., (1)). Often these techniques do not address the parameterization of the lled region.
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