High Order Continuous Polygonal Patches

Abstract

A polygonal patch method is described which can be used to fill a polygonal hole within a given k'th order continuous rectangular patch complex. The method is relatively easy to implement, since it only requires C k extensions of the rectangular patch complex defined in terms of the rectangular patch parameterizations. The method is illustrated by reference to C 2 bicubic B-spline surfaces.

An Arbitrary Mesh Network Scheme Using Rational Splines

“…Now each face of the mesh network is topologically equivalent to a polygonal domain and the final surface is constructed by blending the Boolean sum Taylor interpolants on each of these polygons in the following manner. This follows the approach of Charrot and Gregory [1], see also [3] and [5]. Let , denote a generic regular polygon with vertices X Ω i , i = 0,..., N -1.…”

“…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].…”

Modelado geométrico personalizado de la córnea humana y su aplicación a la detección de ectasias corneales

“…El polígono o poliedro primitivo es suavizado por partes, utilizando unos tensores de naturaleza triangular o rectangular, mediante el uso de los denominados parches. Para las superficies de Bézier, han de cumplirse las condiciones de suavidad de la curva entre los parches adyacentes (Gregory, 1982;Degen, 1990), pero para las funciones B-Spline o las NURBS, esta condición de suavidad de la función viene definida sin ninguna condición especial (Dimas y Briassoulis, 1999).…”