An improved Marching Cube algorithm for 3D data segmentation

Abstract The marching cube algorithm is one of the most popular algorithms for isosurface triangulation. It is based on a division of the data volume into elementary cubes, followed by a standard triangulation inside each cube. In the original formulation, the marching cube algorithm is based on 15 basic triangulations and a total of 256 elementary triangulations are obtained from the basic ones by rotation, reflection, conjugation, and combinations of these operations. The original formulation of th... Title of program: TRIANGOLATE Catalogue Id: AENS_v1_0 Nature of problem Given a scalar field Μ(x,y,z) sampled on a 3D regular grid, build a discrete model of the isosurface associated to the isovalue Μ Iso , which is defined as the set of points that satisfy the equation Μ(x,y,z) = Μ Iso . Versions of this program held in the CPC repository in Mendeley Data AENS_v1_0; TRIANGOLATE; 10.1016/j.cpc.2012.09.030 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要 移动立方体算法（Marching Cube Algorithm）是目前最主流的等值面三角剖分（isosurface triangulation）算法之一。其核心思路是将数据体划分为若干基本立方体，随后在每个立方体内执行标准化的三角剖分操作。在原始的算法框架中，移动立方体算法基于15种基础三角剖分模式，通过旋转、反射、共轭操作及其组合，可由这15种基础模式衍生出总计256种基本三角剖分结果。 本算法的原始表述…… 程序名称：TRIANGOLATE 目录编号：AENS_v1_0 问题本质 给定在三维规则网格（3D regular grid）上采样得到的标量场（scalar field） Μ(x,y,z)，构建与等值值 Μ_Iso 相关联的等值面（isosurface）的离散模型。该等值面被定义为满足方程 Μ(x,y,z) = Μ_Iso 的所有点构成的集合。 存放在Mendeley数据集中的CPC程序库版本 AENS_v1_0；TRIANGOLATE；10.1016/j.cpc.2012.09.030 本程序源自贝尔法斯特女王大学所维护的CPC程序库（1969-2018）