In this paper, we give a stable and efficient method for fixing self-intersections and non-manifold parts in a given embedded simplicial complex. In addition, we show how symmetric properties can be used for further optimisation. We prove an initialisation criterion for computation of the outer hull of an embedded simplicial complex. To regularise the outer hull of the retriangulated surface, we present a method to remedy non-manifold edges and points. We also give a modification of the outer hull algorithm to determine chambers of complexes which gives rise to many new insights. All of these methods have applications in many areas, for example in 3D-printing, artistic realisations of 3D models or fixing errors introduced by scanning equipment applied for tomography. Implementations of the proposed algorithms are given in the computer algebra system GAP4. For verification of our methods, we use a data-set of highly self-intersecting symmetric icosahedra.

翻译：本文提出一种稳定高效的方法，用于修复嵌入单纯复形中的自交与非流形部分，并进一步展示了如何利用对称性质进行优化。我们证明了计算嵌入单纯复形外凸包的初始化准则。为规整重新三角化曲面的外凸包，提出了一种修复非流形边与点的处理方法。同时改进了外凸包算法以确定复形的腔室结构，由此产生多项新见解。上述方法可广泛应用于三维打印、三维模型艺术实现，以及纠正层析成像扫描设备引入的误差等场景。文中算法已在计算机代数系统GAP4中实现，并通过高自交对称二十面体数据集验证了方法的有效性。