Computational geometry: an introduction
Computational geometry: an introduction
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Computational geometry in C
Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials
Computer Aided Geometric Design
Scattered Data Interpolation Using C2 Supersplines of Degree Six
SIAM Journal on Numerical Analysis
Minimum strictly convex quadrangulations of convex polygons
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Characterizing and efficiently computing quadrangulations of planar point sets
Computer Aided Geometric Design
Converting triangulations to quadrangulations
Computational Geometry: Theory and Applications
Filling polygonal holes using C1 cubic triangular spline patches
Computer Aided Geometric Design
Convex preserving scattered data interpolation using bivariate C1 cubic splines
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Quadrangulations of Planar Sets
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
No Quadrangulation is Extremely Odd
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Hamilton Triangulations for Fast Rendering
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Improved Approximations for Minimum Cardinality Quadrangulations of Finite Element Meshes
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Implementation of algorithms for maximum matching on nonbipartite graphs.
Implementation of algorithms for maximum matching on nonbipartite graphs.
Graph Theory With Applications
Graph Theory With Applications
An adaptive numerical integration algorithm for polygons
Applied Numerical Mathematics
Computing convex quadrangulations
Discrete Applied Mathematics
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We consider the problem of obtaining "nice" quadrangulations of planar sets of points. For many applications "nice" means that the quadrilaterals obtained are convex if possible and as "fat" or squarish as possible. For a given set of points a quadrangulation, if it exists, may not admit all its quadrilaterals to be convex. In such cases we desire that the quadrangulations have as many convex quadrangles as possible. Solving this problem optimally is not practical. Therefore we propose and experimentally investigate a heuristic approach to solve this problem by converting "nice" triangulations to the desired quadrangulations with the aid of maximum matchings computed on the dual graph of the triangulations. We report experiments on several versions of this approach and provide theoretical justification for the good results obtained with one of these methods. The results of our experiments are particularly relevant for those applications in scattered data interpolation which require quadrangulations that should stay faithful to the original data.