A C2 polygonal surface patch

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.…”

“…Also, a specific GC 2 construction is proposed in Gregory and Hahn [41]. Alternatively, a scheme will be proposed in [42], whereby p j is defined as a reparameterization of a C k extension of the composite map (3.28) into the positive quadrant.…”

“…Let P j (u,v), u ≥ 0, v ≥ 0, denote a C 1 extension of this map into the positive quadrant. (In the papers [16], [38], [40] and [41] this is achieved by Boolean sum Taylor interpolation.) Then…”

Manifold-based surfaces with boundaries

“…Gregory and Hahn (1989) describe a C 2 hole-filling algorithm; Bohl and Reif (1997) describe C 2 conditions on degenerate patches and how N patches can be joined at a point. C 2 spline surfaces on arbitrary meshes were constructed by Peters (1996) and C d spline surfaces for general d are described by Prautzsch (1997).…”

Assembling curvature continuous surfaces from triangular patches

“…[6,2,15,21,19,3,10,11,13,5,7,8]. Here, we consider three-sided patches as in [17], corresponding to control nets with triangular facets.…”