Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
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DOI：
10.2312/sgp/sgp06/021-030
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发表时间：
2006-06
期刊：
影响因子：
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通讯作者：
T. Kanai;Y. Ohtake;K. Kase
中科院分区：
文献类型：
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作者：
T. Kanai;Y. Ohtake;K. Kase
本文描述了一种从多边形网格分层逼近隐式曲面的有效方法。提出了一种新的多边形网格与隐式曲面之间的误差函数。该误差函数被定义为与其全局行为无关，并且在局部区域上是区域敏感的。隐式曲面与多边形的紧密拟合可以通过最小二乘拟合方法来计算。此外，该函数可以表示为二次形式，其实现了这种误差度量的紧凑表示。我们的新算法快速构建SLIM（稀疏低程度隐式）表面，这是最近开发的非一致的层次隐式表面表示。用户可以根据SLIM曲面的误差，快速得到一组具有任意分辨率的隐式曲面。
This paper describes an efficient method for the hierarchical approximation of implicit surfaces from polygonal meshes. A novel error function between a polygonal mesh and an implicit surface is proposed. This error function is defined so as to be scale-independent from its global behavior as well as to be area-sensitive on local regions. An implicit surface tightly-fitted to polygons can be computed by the least-squares fitting method. Furthermore, this function can be represented as the quadric form, which realizes a compact representation of such an error metric. Our novel algorithm rapidly constructs a SLIM (Sparse Low-degree IMplicit) surface which is a recently developed non-conforming hierarchical implicit surface representation. Users can quickly obtain a set of implicit surfaces with arbitrary resolution according to errors from a SLIM surface.