Topic
Angular resolution (graph drawing)
About: Angular resolution (graph drawing) is a research topic. Over the lifetime, 40 publications have been published within this topic receiving 707 citations.
Papers published on a yearly basis
Papers
1 Aug 1998
TL;DR: In this paper, 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 was constructed.
Abstract: 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
75 citations
26 Sep 1994
TL;DR: In this paper, the angular resolution of planar straight-line drawings of graphs with large angles between the edges is studied, defined as the smallest angle formed by two incident edges.
Abstract: We investigate the problem of constructing planar straightline drawings of graphs with large angles between the edges. Namely, we study the angular resolution of planar straight-line drawings, defined as the smallest angle formed by two incident edges. We prove the first nontrivial upper bound on the angular resolution of planar straight-line drawings, and show a continuous trade-off between the area and the angular resolution. We also give linear-time algorithms for constructing planar straight-line drawings with high angular resolution for various classes of graphs, such as series-parallel graphs, outerplanar graphs, and triangulations generated by nested triangles. Our results are obtained by new techniques that make extensive use of geometric constructions.
69 citations
59 citations
29 Sep 2004
TL;DR: This work presents a method for modifying a force-directed graph drawing algorithm into an algorithm for drawing graphs with curved lines based on embedding control points as dummy vertices so that edges can be drawn as splines.
Abstract: We present a method for modifying a force-directed graph drawing algorithm into an algorithm for drawing graphs with curved lines. Our method is based on embedding control points as dummy vertices so that edges can be drawn as splines. Our experiments show that our method yields aesthetically pleasing curvilinear drawing with improved angular resolution. Applying our method to the GEM algorithm on the test suite of the “Rome Graphs” resulted in an average improvement of 46% in angular resolution and of almost 6% in edge crossings.
55 citations
TL;DR: The results explore what is achievable with straight-line drawings and what more is achieving with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.
Abstract: We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show:
1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area.
2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution.
3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.
46 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 51 |
| 2024 | 71 |
| 2023 | 189 |
| 2022 | 525 |
| 2021 | 7 |