Intersection algorithms for lines and circles
ACM Transactions on Graphics (TOG)
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A new and simple algorithm for quality 2-dimensional mesh generation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Optimal point placement for mesh smoothing
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Mesh generation for domains with small angles
Proceedings of the sixteenth annual symposium on Computational geometry
Sink-insertion for mesh improvement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
A time efficient Delaunay refinement algorithm
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A time-optimal delaunay refinement algorithm in two dimensions
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Lepp terminal centroid method for quality triangulation
Computer-Aided Design
Lepp terminal centroid method for quality triangulation: a study on a new algorithm
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Algorithms and theory of computation handbook
Fully Generalized Two-Dimensional Constrained Delaunay Mesh Refinement
SIAM Journal on Scientific Computing
A review on delaunay refinement techniques
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
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We present two new Delaunay refinement algorithms, the second an extension of the first. For a given input domain (a set of points in the plane or a planar straight line graph), and a threshold angle α, the Delaunay refinement algorithms compute triangulations that have all angles at least α. Our algorithms have the same theoretical guarantees as the previous Delaunay refinement algorithms. The original Delaunay refinement algorithm of Ruppert is proven to terminate with size-optimal quality triangulations for α ≤ 20.7°. In practice, it generally works for α ≤ 34° and fails to terminate for larger constraint angles. The new Delaunay refinement algorithm generally terminates for constraint angles up to 42°. Experiments also indicate that our algorithm computes significantly (almost by a factor of two) smaller triangulations than the output of the previous Delaunay refinement algorithms.