On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
SIAM Journal on Computing
Fat triangles determine linearly many holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Applications of a new space-partitioning technique
Discrete & Computational Geometry
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Handbook of discrete and computational geometry
Robot Motion Planning
Speeding Up the Incremental Construction of the Union of Geometric Objects in Practice
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Counting and representing intersections among triangles in three dimensions
Computational Geometry: Theory and Applications
Speeding up the incremental construction of the union of geometric objects in practice
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
Counting and representing intersections among triangles in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Counting and representing intersections among triangles in three dimensions
Computational Geometry: Theory and Applications
Towards faster linear-sized nets for axis-aligned boxes in the plane
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
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We present an efficient algorithm for the following problem: Given a collection T = {Δ1.....,Δn} of n triangles in the plane, such that there exists a subset S ⊂ T (unknown to us), of ∪Δ ∈ S Δ = ∪ΔΔ∈TΔ n triangles, such that ζ « construct efficiently the union of the triangles in T. We show that this problem can be solved in subquadratic time. In our solution, we use the approximate Disjoint-Cover (DC) algorithm, presented as a heuristics in [9]. We present a detailed implementation of this method, which combines a variety of techniques related to range-searching in two dimensions. We provide a rigorous analysis of its performance in the above setting, showing that it does indeed run in subquadratic time (for a reasonable range of ζ).