Computational Geometry: Theory and Applications
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Filling gaps in the boundary of a polyhedron
Computer Aided Geometric Design
On triangulating three-dimensional polygons
Proceedings of the twelfth annual symposium on Computational geometry
An efficient volumetric method for building closed triangular meshes from 3-D image and point data
Proceedings of the conference on Graphics interface '97
Optimal surface reconstruction from planar contours
Communications of the ACM
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Almost-Delaunay simplices: Robust neighbor relations for imprecise 3D points using CGAL
Computational Geometry: Theory and Applications
Shape reconstruction from unorganized cross-sections
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Developable surfaces from arbitrary sketched boundaries
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
ILoveSketch: as-natural-as-possible sketching system for creating 3d curve models
Proceedings of the 21st annual ACM symposium on User interface software and technology
Fixing geometric errors on polygonal models: a survey
Journal of Computer Science and Technology
Minimum weight triangulation by cutting out triangles
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Design-driven quadrangulation of closed 3D curves
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Polygon mesh repairing: An application perspective
ACM Computing Surveys (CSUR)
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We present an algorithm for obtaining a triangulation of multiple, non-planar 3D polygons. The output minimizes additive weights, such as the total triangle areas or the total dihedral angles between adjacent triangles. Our algorithm generalizes a classical method for optimally triangulating a single polygon. The key novelty is a mechanism for avoiding non-manifold outputs for two and more input polygons without compromising optimality. For better performance on real-world data, we also propose an approximate solution by feeding the algorithm with a reduced set of triangles. In particular, we demonstrate experimentally that the triangles in the Delaunay tetrahedralization of the polygon vertices offer a reasonable trade off between performance and optimality.