Generating a surface including an n-sided patch so as to cover an n-sided hole

While parametric surfaces are most conveniently described by rectangular patches, most complex objects require the use of patches with other than four sides. Many methods to generate such patches are widely used, but all have drawbacks. The paper describes the creation of a surface which covers the original surface and the non-rectangular "hole" with a new smooth surface. The method employs the recursive splines described by Savva and Clapworthy (ibid., 1998) and can be used with a control mesh of arbitrary topology. Further control of the shape of the patch covering the "hole" can be achieved by user manipulation of a "controller" point on the patch.