Planar Polyline Drawings with Good Angular Resolution

We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree n on a (2n - 5) × (3/2n - 7/2) grid with at most 5n - 15 bends and minimum angle > 2/d. In the constructed drawings, every edge has at most three bends and length O(n). To our best knowledge, this algorithm achieves the best simultaneous bounds concerning the grid size, angular resolution, and number of bends for planar grid drawings of high-degree planar graphs. Besides the nice theoretical features, the practical drawings are aesthetically very pleasing. An implementation of our algorithm is available with the AGD-Library (Algorithms for Graph Drawing) [2, 1]. Our algorithm is based on ideas by Kant for polyline grid drawings for triconnected plane graphs [23]. In particular, our algorithm significantly improves upon his bounds on the angular resolution and the grid size for non-triconnected plane graphs. In this case, Kant could show an angular resolution of 4/3d+7 and a grid size of (2n - 5) × (3n - 6), only.

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