Geometric continuity and convex combination patches

Closed surfaces defined from biquadratic splines

“…To ensure that, it is sufficient to require that the elements of S(M) satisfy certain conditions across the edges of M (see [3], [5], and [6]). We choose the simplest and most natural conditions which are sufficient for our purpose, and these we proceed to describe.…”

Smooth Parametric Surfaces and n-Sided Patches

“…Blending function methods for defining polygonal patches have been considered by Charrot and Gregory [-16,38], Gregory and Hahn [39,40,41] and Hagen [45]. We illustrate the technique by describing a GC 1 method, where the surrounding patch complex is a C 1 surface.…”

“…However, the differential geometer might well prefer to state that two such patches meet with ' contact of order k' . The idea will be explained through that of a reparameterization of the surface, see, for example, DeRose [21], Hollig [52], Gregory and Hahn [39],and Hahn [48]. Here we will summarize some of the material contained in Gregory [37] which is based on the exposition of Hahn [48].…”

“…Then the blended surface We will consider the blending function technique as one method of treating the polygonal hole problem. The difficulty of using blends for the specific polygonal hole problem is discussed in Gregory and Hahn [39].…”

An Arbitrary Mesh Network Scheme Using Rational Splines

“…It is also proposed to investigate shape control of the interior of a patch, other than through the control of its boundary. Finally, the method can be extended to the construction of higher order continous surfaces, although more care is now needed in the construction of the blends of the strip functions, as is discussed in [4] and [5].…”