A detail-preserving method for medial mesh computation in triangular meshes

Abstract

The medial axis transform (MAT) of an object is the set of all points inside the object that have more than one closest point on the object’s boundary. Representing sharp edges and corners of triangular meshes using MAT poses a complex challenge. While some researchers have proposed using zero-radius medial spheres to depict these features, they have not clearly articulated how to establish proper connections among them. In this paper, we propose a novel framework for computing MAT of a triangular mesh while preserving its features. The initial medial axis mesh obtained may contain erroneous edges, which are discussed and addressed in Section 3.3. Furthermore, during the simplification process, it is crucial to ensure that the medial spheres remain within the confines of the triangular mesh. Our algorithm excels in preserving critical features throughout the simplification procedure, consistently ensuring that the spheres remain enclosed within the triangular mesh. Experiments on various types of 3D models demonstrate the robustness, shape fidelity, and efficiency in representation achieved by our algorithm.