In the research of computer vision and machine perception, 3D objects are usually represented by 2-manifold triangular
meshes M. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors, and Voronoi diagrams of
point sites onM, based on an exact geodesic metric. Compared to euclidean metric spaces, the Voronoi diagrams onMexhibit many
special properties that fail all of the existing euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesicmetric-
based Voronoi diagrams onM, this paper studies the analytic structure of iso-contours, bisectors, and Voronoi diagrams onM.
After a necessary preprocessing of model M, practical algorithms are proposed for quickly obtaining full information about
iso-contours, bisectors, and Voronoi diagrams on M. The complexity of the construction algorithms is also analyzed. Finally, three
interesting applications—surface sampling and reconstruction, 3D skeleton extraction, and point pattern analysis—are presented that
show the potential power of the proposed algorithms in pattern analysis.