A 2-dimensional direction-length framework is a collection of points in the plane which are linked by pairwise constraints that fix the direction or length of the line segments joining certain pairs of points. We represent it as a pair $(G,p)$, where $G=(V;D,L)$ is a ‘mixed’ graph and $p:V\to {\mathbb{R}}^2$ is a point configuration for V. It is globally rigid if every direction-length framework $(G,q)$ which satisfies the same constraints can be obtained from $(G,p)$ by a translation or a rotation by 180°. We characterise the mixed graphs G with the property that every generic framework $(G,p)$ is globally rigid.

中文翻译：

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方向长度框架的整体刚性

二维方向长度框架是平面中点的集合，这些点通过成对约束进行链接，成对约束固定连接某些成对点的线段的方向或长度。我们将其表示为一对$（G，p）$，在哪里 $G=（V;d，\mathrm{大号}）$ 是一个“混合”图，并且 $p：V\to {\mathbb{[R}}^2$是V的点配置。如果每个方向长度的框架都具有全局刚性$（G，q）$ 可以从中获得满足相同约束的条件 $（G，p）$平移或旋转180°。我们用每个通用框架的特性来描述混合图G$（G，p）$ 具有全球刚性。