Angular resolution, area and the number of bends are some important aesthetic criteria of a polyline drawing. Although trade-offs among these criteria have been examined over the past decades, many of these trade-offs are still not known to be optimal. In this paper we give a new technique to compute polyline drawings for planar trian-gulations. Our algorithm is simple and intuitive, yet implies significant improvement over the known results. We present the first smooth tradeoff between the area and angular resolution for 2-bend polyline drawings of any given planar graph. Specifically, for any given n-vertex triangula-tion, our algorithm computes a drawing with angular resolution r/d(υ) at each vertex υ, and area f(n, r), for any r ∈ (0,1], where d(υ) denotes the degree at υ. For r ＜ 0.389 or r ＞ 0.5, f(n, r) is less than the drawing area required by previous algorithms; f(n, r) ranges from 7.12n~2 when r ≤ 0.3 to 32.12n~2 when r = 1.
展开▼
