The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length.

We also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics.

基尔霍夫杆模型描述了细长弹性杆在三个维度上的弯曲和扭转，并已得到广泛研究，可以在给定几何形状和边界条件的情况下预测杆将如何变形。在这项工作中，我们研究了许多反问题，目的是计算直杆的几何形状，在将其端点连接到支撑结构后，该直杆将自动变形以匹配弯曲的目标形状。我们的解决方案使我们能够通过改变沿其长度的横截面轮廓来精细地控制杆的静态平衡状态。

我们还表明，物理上可实现的平衡状态集允许用线性线复合体进行简洁的几何描述，这导致非常有效的计算设计算法。它们通过交互式软件工具实现，使我们能够将三维手绘样条曲线转换为弹性杆，并实时反馈设计的可行性和实用性。我们通过设计和制造几个应用于室内设计和软机器人的物理原型来证明我们方法的有效性。