1-Bend 3-D Orthogonal Box-Drawings: Two Open Problems Solved

1-bend 3-D orthogonal drawings: two open problems solved

A New Algorithm and Open Problems in Three-Dimensional Orthogonal Graph Drawing

In this paper we present an algorithm for 3-D orthogonal drawing of arbitrary degree n-vertex m-edge multigraphs with O(m 2 = p n) bounding box volume and 6 bends per edge route. This is the smallest known bound on the bounding box volume of 3-D orthogonal multigraph drawings. We continue the study of the tradeoo between bounding box volume and the number of bends in orthogonal graph drawings t...

Two Algorithms for Three Dimensional Orthogonal Graph Drawing

We use basic results from graph theory to design two algorithms for constructing 3-dimensional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. Our first algorithm gives drawings bounded by an O(x/~ ) • O(x/~ • O(v~ ) box; each edge route contains at most 7 bends. The best previous result generated edge routes containing up to 16 bends per route. Our second al...

Capturing Lombardi Flow in Orthogonal Drawings by Minimizing the Number of Segments

Inspired by the artwork of Mark Lombardi, we study the problem of constructing orthogonal drawings where a small number of horizontal and vertical line segments covers all vertices. We study two problems on orthogonal drawings of planar graphs, one that minimizes the total number of line segments and another that minimizes the number of line segments that cover all the vertices. We show that th...

Three-dimensional orthogonal graph drawing algorithms

We use basic results from graph theory to design algorithms for constructing three-dimensional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. The best previous result generated a drawing bounded by an O( √ n) × O( √ n) × O( √ n) box, with each edge route containing up to 16 bends. Our algorithms initiate the study of bend=bounding box trade-o issues for thre...