Non-convex hull surfaces
Non-convex hull surfaces
复制标题
非凸船体表面
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
G. Taubin
中科院分区：
文献类型：
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作者：
G. Taubin
我们提出了一种新的算法来重建近似水密表面有限定向点云。任意点集的凸包船体（CH）由所有支撑线性半空间的交构成，是一个分段线性水密曲面，但通常是采样曲面的差逼近。我们引入了非凸船体（NCH）的有向点云作为交叉的互补支持球面半空间，每点一个。该集的边界曲面是一个分段二次插值曲面，它也可以被描述为NCH符号距离函数的零水平集。我们在体积网格（规则或自适应）的顶点上评估NCH有符号距离函数，并使用等值面算法为NCH曲面生成近似多边形网格。尽管它的简单性，这个简单的算法产生高质量的多边形网格与那些国家的最先进的算法产生的竞争。描述了与中轴变换的关系。
We present a new algorithm to reconstruct approximating watertight surfaces from finite oriented point clouds. The Convex Hull (CH) of an arbitrary set of points, constructed as the intersection of all the supporting linear half spaces, is a piecewise linear watertight surface, but usually a poor approximation of the sampled surface. We introduce the Non-Convex Hull (NCH) of an oriented point cloud as the intersection of complementary supporting spherical half spaces; one per point. The boundary surface of this set is a piecewise quadratic interpolating surface, which can also be described as the zero level set of the NCH Signed Distance function. We evaluate the NCH Signed Distance function on the vertices of a volumetric mesh, regular or adaptive, and generate an approximating polygonal mesh for the NCH Surface using an isosurface algorithm. Despite its simplicity, this simple algorithm produces high quality polygon meshes competitive with those generated by state-of-the-art algorithms. The relation to the Medial Axis Transform is described.