Validation and Storage of Polyhedra through Constrained Delaunay Tetrahedralization
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Boundary recovery for Delaunay tetrahedral meshes using local topological transformations
Finite Elements in Analysis and Design
Constrained Delaunay tetrahedral mesh generation and refinement
Finite Elements in Analysis and Design
Motion planning with dynamics by a synergistic combination of layers of planning
IEEE Transactions on Robotics
Three-dimensional constrained boundary recovery with an enhanced Steiner point suppression procedure
Computers and Structures
A faster circle-sweep Delaunay triangulation algorithm
Advances in Engineering Software
3D topographic data modelling: why rigidity is preferable to pragmatism
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
Differential constraints for bounded recursive identification with multivariate splines
Automatica (Journal of IFAC)
Accelerating ray tracing using constrained tetrahedralizations
EGSR'08 Proceedings of the Nineteenth Eurographics conference on Rendering
Modelling higher dimensional data for GIS using generalised maps
ICCSA'13 Proceedings of the 13th international conference on Computational Science and Its Applications - Volume 1
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Two-dimensional constrained Delaunay triangulations are geometric structures that are popular for interpolation and mesh generation because they respect the shapes of planar domains, they have “nicely shaped” triangles that optimize several criteria, and they are easy to construct and update. The present work generalizes constrained Delaunay triangulations (CDTs) to higher dimensions and describes constrained variants of regular triangulations, here christened weighted CDTs and constrained regular triangulations. CDTs and weighted CDTs are powerful and practical models of geometric domains, especially in two and three dimensions. The main contributions are rigorous, theory-tested definitions of CDTs and piecewise linear complexes (geometric domains that incorporate nonconvex faces with “internal” boundaries), a characterization of the combinatorial properties of CDTs and weighted CDTs (including a generalization of the Delaunay Lemma), the proof of several optimality properties of CDTs when they are used for piecewise linear interpolation, and a simple and useful condition that guarantees that a domain has a CDT. These results provide foundations for reasoning about CDTs and proving the correctness of algorithms. Later articles in this series discuss algorithms for constructing and updating CDTs.