Abstract
In this paper we introduce a new algorithm for planar orthogonal drawing of complete binary trees on the surface of a given simple rectilinear polygon. Our algorithm aims to uniformly distribute the vertices of the given tree on the given surface and to reduce the total number of edge bends as much as possible. We also introduce a new linear time algorithm for bisecting simple (rectilinear) polygons, assuming the straight skeletons of the polygons are given. To our knowledge, this paper and the previous works of the authors are the first attempts for developing algorithms that draw trees on 2D surfaces which are bounded by simple (rectilinear) polygons.
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