Computational geometry: an introduction
Computational geometry: an introduction
Algorithms for clustering data
Algorithms for clustering data
Symbolic treatment of geometric degeneracies
Journal of Symbolic Computation
Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
3D Symmetry Detection Using The Extended Gaussian Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Strategies for polyhedral surface decomposition: an experimental study
Computational Geometry: Theory and Applications
Optimal slicing of free-form surfaces
Computer Aided Geometric Design
Robot Motion Planning
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Partitioning 3D Surface Meshes Using Watershed Segmentation
IEEE Transactions on Visualization and Computer Graphics
Modeling and Rendering of Points with Local Geometry
IEEE Transactions on Visualization and Computer Graphics
The Complex EGI: A New Representation for 3-D Pose Determination
IEEE Transactions on Pattern Analysis and Machine Intelligence
Orientation-Based Differential Geometric Representations for Computer Vision Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation and geometric computation using the extended Gaussian image
Pattern Recognition Letters
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Complex shape modeling with point sampled geometry
Complex shape modeling with point sampled geometry
EC-EGI: enriched complex EGI for 3D shape registration
Machine Vision and Applications
Least squares quasi-developable mesh approximation
Computer Aided Geometric Design
Computing feasible toolpaths for 5-axis machines
Theoretical Computer Science
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Partitioning free-form surfaces into sub-patches and finding optimal representative normal for each patch to maximize a global objective function is an important two-level operation in diverse industrial applications. In this paper, by solving a maximum hemispherical partitioning problem raised from a weighted Gaussian image, an optimization algorithm is proposed to partition a free-form surface into two sub-patches and simultaneously report the optimal representative normals. By discretizing the free-form surface with W sample points and clustering normals on the surface with m distinct sample normals, the proposed algorithm is designed, in general, with O(m2W2) time complexity and O(W2) space complexity, and in particular, if the surface is convex, in O(m2 logm) time complexity. Case studies with four representative examples are presented and a real world application is exploited to demonstrate the effectiveness and usefulness of the proposed algorithm.