Fair free-form surfaces that are almost everywhere parametrically C2.
Fair free-form surfaces that are almost everywhere parametrically C2.
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公平的自由曲面几乎无处不在，参数化 C2。
DOI：
10.1016/j.cam.2018.07.040
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发表时间：
2019
影响因子：
2.4
通讯作者：
Peters,Jörg
中科院分区：
文献类型：
--
作者：
Karčiauskas,Kȩstutis;Peters,Jörg
与G k连续性相比，C k连续性简化了曲面上函数的构造及其细化，例如求解曲面上的微分方程。本文介绍的自由曲面类几乎处处参数化C2。特别是，一个新的双6建设相结合的快速收缩C2引导细分曲面与一个微小的多边G1帽。帽被选择为小于对于几何建模或在表面上计算所预期的任何细化。快速收缩意味着一个细分步骤比Catmull-Clark细分的三个步骤更收缩剩余的孔。这就产生了由有限数量的零件组成的光滑表面，适用于工程实践。细分构造和帽都由参考曲面引导，该参考曲面具有不同的结构和较低的平滑度，但传达了光顺曲面的基本形状。
Compared to G k continuity, C k continuity simplifies the construction of functions on surfaces and their refinement, eg to solve differential equations on the surface. The new class of free-form surfaces introduced in this paper is almost everywhere parametrically C 2. In particular, a new bi-6 construction combines a fast-contracting C 2 guided subdivision surface with a tiny multi-sided G 1 cap. The cap is chosen to be smaller than any refinement anticipated for geometric modeling or computing on surfaces. Fast contraction means that one subdivision step shrinks the remaining hole more than three steps of Catmull–Clark subdivision. This yields smooth surfaces consisting of a finite number of pieces that are suitable for engineering practice. Both the subdivision construction and the cap are guided by a reference surface that has a different structure and lower smoothness, but conveys the basic shape of a fair surface.