Proceedings of the twenty-second annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Decompositions and Boundary Coverings of Non-convex Fat Polyhedra
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Small-size ε-nets for axis-parallel rectangles and boxes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Decompositions and boundary coverings of non-convex fat polyhedra
Computational Geometry: Theory and Applications
Connect the Dot: Computing Feed-Links with Minimum Dilation
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
On the union of fat tetrahedra in three dimensions
Journal of the ACM (JACM)
Better bounds on the union complexity of locally fat objects
Proceedings of the twenty-sixth annual symposium on Computational geometry
Approximating the Fréchet distance for realistic curves in near linear time
Proceedings of the twenty-sixth annual symposium on Computational geometry
Tangencies between families of disjoint regions in the plane
Proceedings of the twenty-sixth annual symposium on Computational geometry
A note about weak ε-nets for axis-parallel boxes in d-space
Information Processing Letters
A note on the perimeter of fat objects
Computational Geometry: Theory and Applications
Small-Size $\eps$-Nets for Axis-Parallel Rectangles and Boxes
SIAM Journal on Computing
Tangencies between families of disjoint regions in the plane
Computational Geometry: Theory and Applications
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
Jaywalking your dog: computing the Fréchet distance with shortcuts
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved bound for the union of fat triangles
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Improved bounds on the union complexity of fat objects
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Triangulating and guarding realistic polygons
Computational Geometry: Theory and Applications
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An $(\alpha,\beta)$-covered object is a simply connected planar region $c$ with the property that for each point $p\in\partial c$ there exists a triangle contained in $c$ and having $p$ as a vertex, such that all its angles are at least $\alpha0$ and all its edges are at least $\beta\cdot{\rm \diam}(c)$-long. This notion extends that of fat convex objects. We show that the combinatorial complexity of the union of $n$ $(\alpha,\beta)$-covered objects of "constant description complexity" is $O(\lambda_{s+2}(n) \log^2n\log\log n)$, where $s$ is the maximum number of intersections between the boundaries of any pair of given objects, and $\lambda_s(n)$ denotes the maximum length of an $(n,s)$-Davenport--Schinzel sequence. Our result extends and improves previous results concerning convex $\alpha$-fat objects.