For an angle $\alpha\in (0,\pi)$, we consider plane graphs and multigraphs in which the edges are either (i) one-bend polylines with an angle $\alpha$ between the two edge segments, or (ii) circular arcs of central angle $2(\pi-\alpha)$. We derive upper and lower bounds on the maximum density of such graphs in terms of $\alpha$. As an application, we improve upon bounds for the number of edges in $\alpha AC_1^=$ graphs (i.e., graphs that can be drawn in the plane with one-bend edges such that any two crossing edges meet at angle $\alpha$). This is the first improvement on the size of $\alpha AC_1^=$ graphs in over a decade.

翻译：对于角度$\alpha\in (0,\pi)$，我们考虑边为以下两种形式之一的平面图和多重图：(i) 两条边段夹角为$\alpha$的单折折线，或 (ii) 中心角为$2(\pi-\alpha)$的圆弧。我们推导了此类图的最大密度关于$\alpha$的上下界。作为应用，我们改进了$\alpha AC_1^=$图（即能用单折边绘制且任意两条交叉边夹角为$\alpha$的平面图）中边数的界。这是十多年来$\alpha AC_1^=$图规模研究中的首次改进。