细分曲面奇异点处的光滑过渡

Smooth Connection near Singular Points on Subdivision Surfaces

摘要: 首先通过引入形状调节参数c(0≤c≤1)给出了一种形状可调的C-C细分方法，基于该理论，针对细分曲面中的奇异点，本文以奇异点处的2-环作为控制网格，采用循环映射的方法，提出了一种形状可调的G²曲面造型方法，得到Bézier控制点的显式解。与以往的方法相比，生成的曲面不仅在奇异点处达到G²连续，而且解决了曲面设计的可调性问题。本文给出了算法流程和相关数据结构，也给出了相应的实例进行验证。

Abstract: This paper discusses G² smooth connection near singular points on subdivision surfaces. A shape adjustable Catmull-Clark subdivision algorithm is present by introducing subdivision shape ad-justment parameter c(0≤c≤1). Based on this, aimed at the singular points in subdivision surface, based on the 2-ring of the singular points as control mesh, adopting the method of cyclic mapping, this paper proposes a G² surface modeling method which is shape-adjustable. Then we can get the explicit solution of the Bezier control points. Compared with existing methods, the generated surface not only achieves the G² continuous at singular points, but solves the problem of the curved surface design to be adjustable. The algorithm process and data structure are present. Corresponding examples are also given in this paper.