The authors investigate some approaches to the generation of two classes of closed smooth piecewise bicubic surfaces--the parametric bicubic B-spline surfaces in which the B-spline blending functions are defined on simple quadrilateral meshes and the control polyhedra consist only of triangular and rectangular faces, and the class of surfaces obtained directly from the closed quadrilateral control polyhedra by converting the control vertices to Bézier points. The introduction reviews the most relevant surface generation algorithms.
The concept of geometric continuity of surfaces is briefly described in the second section. Sufficient conditions for a surface to be G 1 continuous across a common boundary of two Bézier patches and around an extraordinary vertex are also given.
Based on the above conditions, the third section presents a method to assure that the surface is G 1 about a vertex. The method also permits one to compute all neighboring Bézier coefficients adjacent to a common Bézier coefficient of n bicubic Bézier patches if only three of the neighboring coefficients are known.
In the next two sections, methods for generating surfaces from the first class mentioned above are presented. First, Section 4 presents the simplest case, where the surfaces are defined on a cube and the generation is based on de Casteljau’s surface-splitting algorithm. Then, the fifth section treats the case where the surfaces are defined on large simple quadrilateral meshes. The B-spline blending functions are explicitly constructed.
The remainder of the paper deals with the second class of surfaces. In Section 6, some properties of the quadrilateral control polyhedron are examined. Sections 7, 8, and 9 examine the generation of piecewise bicubic surfaces from small, large, and degenerate quadrilateral control polyhedra, respectively.
The paper is well written, and the presentation is sustained by graphical representations and examples.
