Discrete bi-Laplacians and biharmonic b-splines
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Least squares quasi-developable mesh approximation
Computer Aided Geometric Design
Constructing common base domain by cues from Voronoi diagram
Graphical Models
Q-Complex: Efficient non-manifold boundary representation with inclusion topology
Computer-Aided Design
Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh
Computer Graphics Forum
Analytic Curve Skeletons for 3D Surface Modeling and Processing
Computer Graphics Forum
2D-line-drawing-based 3d object recognition
CVM'12 Proceedings of the First international conference on Computational Visual Media
The complexity of geodesic Voronoi diagrams on triangulated 2-manifold surfaces
Information Processing Letters
Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures
Computer-Aided Design
Saddle vertex graph (SVG): a novel solution to the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Parallel chen-han (PCH) algorithm for discrete geodesics
ACM Transactions on Graphics (TOG)
Technical note: Kinematic skeleton extraction from 3D articulated models
Computer-Aided Design
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In the research of computer vision and machine perception, 3D objects are usually represented by 2-manifold triangular meshes {\cal M}. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors, and Voronoi diagrams of point sites on {\cal M}, based on an exact geodesic metric. Compared to euclidean metric spaces, the Voronoi diagrams on {\cal M} exhibit many special properties that fail all of the existing euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesic-metric-based Voronoi diagrams on {\cal M}, this paper studies the analytic structure of iso-contours, bisectors, and Voronoi diagrams on {\cal M}. After a necessary preprocessing of model {\cal M}, practical algorithms are proposed for quickly obtaining full information about iso--contours, bisectors, and Voronoi diagrams on {\cal 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.