Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface. Commonly, existing approaches yield medial-axis surfaces with various artifacts, including zigzag boundaries, bumpy surfaces, unwanted spikes, and non-smooth stitching curves. Considering that the surface of a CAD model can be easily decomposed into a collection of surface patches, its 3D medial axis can be extracted by computing the Voronoi diagram of these surface patches, where each surface patch serves as a generator. However, no solver currently exists for accurately computing such an extended Voronoi diagram. Under the assumption that each generator defines a linear distance field over a sufficiently small range, our approach operates by tetrahedralizing the region of interest and computing the medial axis within each tetrahedral element. Just as SurfaceVoronoi computes surface-based Voronoi diagrams by cutting a 3D prism with 3D planes (each plane encodes a linear field in a triangle), the key operation in this paper is to conduct the hyperplane cutting process in 4D, where each hyperplane encodes a linear field in a tetrahedron. In comparison with the state-of-the-art, our algorithm produces better outcomes. Furthermore, it can also be used to compute the offset surface.

翻译：高保真三维中轴提取是CAD领域的关键操作。当输入为多边形模型时，由于网格表面固有的离散化误差，确保结果的精确性与规整性变得极具挑战。现有方法通常生成存在多种瑕疵的中轴曲面，包括锯齿状边界、凹凸不平的表面、多余尖刺以及非光滑拼接曲线。考虑到CAD模型的表面可被轻松分解为曲面片集合，其三维中轴可通过计算这些曲面片的Voronoi图来提取，其中每个曲面片作为生成元。然而，目前尚不存在能够精确计算此类扩展Voronoi图的求解器。在假设每个生成元在足够小的范围内定义线性距离场的前提下，本方法通过对感兴趣区域进行四面体剖分，并在每个四面体单元内计算中轴。正如SurfaceVoronoi通过三维平面对三维棱柱进行切割（每个平面对应三角形内的线性场）来计算基于曲面的Voronoi图，本文的核心操作是在四维空间执行超平面切割过程，其中每个超平面对应四面体内的线性场。与现有最优方法相比，本算法能产生更优结果。此外，该方法也可用于计算偏置曲面。