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中文摘要：
法向网格是一种新型的曲面多分辨率描述方式，其中每个层次都可以表示为其前一个粗糙层次的法向偏移．文中提出一种基于法向网格表示的隐式曲面多分辨率网格逼近算法．首先通过基于空间剖分技术的多边形化算法获得隐式曲面的粗糙逼近网格，并利用网格均衡化方法对粗糙网格进行优化，消除其中的狭长三角形；然后利用法向细分规则迭代地对网格中的三角面片进行细分，并利用区间算术技术沿法向方向对隐式曲面进行逼近．最终生成的隐式曲面分片线性逼近网格为法向网格．该逼近网格为隐式曲面提供了一种多分辨率表示，网格具有细分连通性，其数据量较传统的多边形化算法所生成的网格有大幅度的压缩．该算法可用于隐式曲面的多级绘制、累进传输及相关数字几何处理．
英文摘要：
Normal mesh is a now new fundamental surface description, which is multiresolution mesh where each level can be written as a normal offset from a coarser version. In this paper,we presented an algorithm to create normal mesh approximations for implicit surfaces. This algorithm begins from a coarse base mesh created from implicit surface by a space-division based polygonization method,firstly. The base mesh is then optimized by a smoothing procedure, and the aspect ratios of long and narrow triangles in the mesh are improved remarkably. Subsequently, the facets of the base mesh are subdivided normally and iteratively, and the vertices newly created are located on the implicit surface along certain normal by employing interval arithmetic technique. Finally, a piecewise-linear approximation mesh is obtained, and it is a normal mesh with subdivision connectivity and provides implicit surface a multiresolution description, naturally. The mesh also has much fewer data with respect to the traditional non-regular polygonization in sense of same approximation error. The algorithm can be used in the context of multilevel drawing, progressive transmission or other relative geometric processing of implicit surfaces.
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