网格曲面中孔洞的光滑填充算法研究

三角网格模型是几何描述的一种重要形式，有着广泛的应用。但三角网络模型常常会存在孔洞缺陷。这些孔洞的存在一方面影响视觉效果，另一方面会影响许多后续的操作，如快速原型制造、有限元分析等，因此有必要对这些孔洞进行修补。目前绝大多数孔洞填充算法是将网格模型中的孔洞提取成空间多边形，并对孔洞多边形进行三角化。这种处理方法的主要缺陷是没有考虑网格曲面在孔洞附近的几何形态，因而填充部分不能与整个曲面光滑地融为一体。笔者提出了一种三角网格曲面中孔洞的光滑填充算法。该算法根据孔洞周围网格曲面的几何信息来增加孔洞内部的采样点，然后再对增加的采样点进行三角化，较好地解决了填充部分与整体曲面光滑连接的问题。

A Smooth Hole Filling Algorithm for Triangle Mesh Surfaces

Triangle mesh surface is an important representation of geometry with broad applications. However, there often exist unwanted holes in triangle meshes. The holes may lead to had visualization effect and bring difficulties to rapid prototype manufacturing, finite elements analyses etc. At present, most hole-filling algorithms solve this problem by extracting and triangulating hole polygons. The limitation of this kind of methods is that they did not take the geometry of the model around the hole into consideration, and hence the filled area cannot smoothly blend with the other part of the model. In this paper, we put forward a new hole-filling algorithm which infers new sample points in the hole area from the model shape around the hole. By triangulating the added sample points, the algorithm can output the smooth hole filling result.