A rational extension of Piegl’s method for filling -sided holes

Optimizing conformality of NURBS surfaces by general bilinear transformations

“…maps an elementary circle of the (u, v) domain to an elementary circle of the surface. Second, a conformal parameterization will lead to more robust and stable computations for derivative based algorithms such as surface intersection, curvature computation, and so on [1,6,9,11].…”

“…1). By surface reparameterizations [14,[11][12][13], the surface may have infinitely many different parameterizations. Depending on where and how it will be used, one may need to find a suitable or optimal parameterization out of the infinitely many, or to convert the given param- Fig.…”

“…The results of most surface algorithms [1][2][3][4][5][6][7][8][9][10][11][12][13] for surface rendering (e.g. texture mapping), tessellation and blending applications are highly dependent on the surface parameterization.…”

G n filling orbicular N-sided holes using periodic B-spline surfaces

“…Region-partition-based methods [8,9] usually generate one B-spline surface at each corner point D ij O (j = (i + 1) mod N ). These methods require that the specified boundary conditions satisfy the following compatibility conditions (see Figure 1…”

“…The third category splits the region into several untrimmed patches by connecting a central point of the region to each boundary curves, fulfilling continuity conditions between each pair of neighboring patches [6][7][8]. Piegl, Tiller [8] and Yang [9] used untrimmed Coons patches to fill N -sided holes with B-spline boundary. Their methods preserve G 0 continuity, but introduce tangential error on the boundary and inner curves, incurring the well-known twist compatibility problem.…”