A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Creating multisided rational Bézier surfaces using base points
ACM Transactions on Graphics (TOG)
Filling polygonal holes with bicubic patches
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG)
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Vertex blending: problems and solutions
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Implicit Gn-blending of vertices
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Multisided arrays of control points for multisided Bézier patches
Computer Aided Geometric Design
Simultaneous blending of convex polyhedra by S32 algebraic splines
Computer-Aided Design
Blends of canal surfaces from polyhedral medial transform representations
Computer-Aided Design
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Setbacks not only beautify the shape of polyhedral vertex blending, but also overcome the difficulties inherited from non-setback blending. However, stitching several tensor product Bezier surfaces, the existing approaches to setback vertex blending may cause twist compatibility problems and approximate solutions, especially when the vertex gathers more edges. This paper proposes a new algorithm, yielding an exact solution using a single rational S-patch. Although S-patch developers Loop and DeRose (1989) also investigated vertex blending (1990), they did not configure setback. In addition, the new algorithm reduces the depth of the S-patch and extends the edge blending surfaces to use rational Bezier representation, so that circular rounding can be made. Miscellaneous examples demonstrate that the method produces smooth and natural connecting shapes.