Surface offsetting is a crucial operation in digital geometry processing and computer-aided design, where an offset is defined as an iso-value surface of the distance field. A challenge emerges as even smooth surfaces can exhibit sharp features in their offsets due to the non-differentiable characteristics of the underlying distance field. Prevailing approaches to the offsetting problem involve approximating the distance field and then extracting the iso-surface. However, even with dual contouring (DC), there is a risk of degrading sharp feature points/lines due to the inaccurate discretization of the distance field. This issue is exacerbated when the input is a piecewise-linear triangle mesh. This study is inspired by the observation that a triangle-based distance field, unlike the complex distance field rooted at the entire surface, remains smooth across the entire 3D space except at the triangle itself. With a polygonal surface comprising n triangles, the final distance field for accommodating the offset surface is determined by minimizing these n triangle-based distance fields. In implementation, our approach starts by tetrahedralizing the space around the offset surface, enabling a tetrahedron-wise linear approximation for each triangle-based distance field. The final offset surface within a tetrahedral range can be traced by slicing the tetrahedron with planes. As illustrated in the teaser figure, a key advantage of our algorithm is its ability to precisely preserve sharp features. Furthermore, this paper addresses the problem of simplifying the offset surface's complexity while preserving sharp features, formulating it as a maximal-clique problem.

中文翻译：

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PCO：具有尖锐特征的精确可控偏移表面


表面偏移是数字几何处理和计算机辅助设计中的一项关键操作，其中偏移定义为距离场的等值表面。一个挑战出现了，因为由于底层距离场的不可微分特性，即使是光滑的表面也会在其偏移中表现出尖锐的特征。解决偏移问题的主要方法包括近似距离场，然后提取等值面。然而，即使使用双等值线 （DC），由于距离场的离散化不准确，也存在降低尖锐特征点/线的风险。当 input 是分段线性三角形网格时，此问题会加剧。这项研究的灵感来自于以下观察结果：与根植于整个表面的复杂距离场不同，基于三角形的距离场在整个 3D 空间中保持平滑，但三角形本身除外。对于包含 n 个三角形的多边形表面，容纳偏移表面的最终距离场是通过最小化这 n 个基于三角形的距离场来确定的。在实现中，我们的方法首先将偏移表面周围的空间四面体化，从而为每个基于三角形的距离场实现四面体方向的线性近似。四面体范围内的最终偏移曲面可以通过用平面对四面体进行切片来追踪。如预告图所示，我们算法的一个关键优势是它能够精确保留清晰的特征。此外，本文还解决了简化偏移曲面复杂性同时保留尖锐特征的问题，将其表述为最大-团问题。