Karčiauskas Kȩstutis, Peters Jörg
Vilnius University, Lithuania.
University of Florida, USA.
Comput Aided Geom Des. 2020 Aug;81. doi: 10.1016/j.cagd.2020.101908. Epub 2020 Jun 8.
A polar configuration is a node surrounded by triangles. Polar configurations are common to cap off cylinders and spheres. When the triangles, interpreted as quadrilaterals with one edge collapsed, are surrounded by a quad-strip then the extended polar configuration qualifies as part of a (lqd) mesh. Recent constructions, referred to as semi-structured splines, can use lqd meshes as control nets: multi-sided configurations that merge parameter directions are covered by G-spline; and T-junctions that transition from coarse and fine are covered by GT-splines. This paper complements existing semi-structured splines by providing the missing component for polar configurations. A spectrum of constructions of differing degree are introduced, tested and compared. Bi-2 splines are extended to polar configurations covered by surfaces consisting of (macro-)patches of degree as low as bi-2. Bi-3 splines are extended to polar configurations covered by surfaces that are except for a pole and consist of (macro-)patches of degree as low as bi-3.
极坐标配置是由三角形围绕的节点。极坐标配置常用于封闭圆柱体和球体。当将三角形解释为一条边塌陷的四边形，且这些四边形被四边形条带围绕时，扩展的极坐标配置就符合（lqd）网格的一部分。最近被称为半结构化样条的构造，可以使用lqd网格作为控制网：合并参数方向的多边配置由G样条覆盖；从粗到细过渡的T型连接由GT样条覆盖。本文通过提供极坐标配置缺失的组件来补充现有的半结构化样条。引入、测试并比较了一系列不同次数的构造。双二次样条被扩展到由低至双二次（宏观）面片组成的曲面覆盖的极坐标配置。双三次样条被扩展到除一个极点外由低至双三次（宏观）面片组成的曲面覆盖的极坐标配置。
