On the union of κ-curved objects

A (not necessarily convex) object C in the plane is -curved for some constant 0<< 1, if it has constant description complexity, and for each pointp on the boundary ofC, one can place a diskBC of radius diam.C/ whose boundary passes throughp. We prove that the combinatorial complexity of the boundary of the union of a set C ofn-curved objects (e.g., fat ellipses or rounded heart-shaped objects) is O.s.n/ logn/, for some constants. © 1999 Elsevier Science B.V. All rights reserved.

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