A crossing-free morph is a continuous deformation between two graph drawings that preserves straight-line pairwise noncrossing edges. Motivated by applications in 3D morphing problems, we initiate the study of morphing graph drawings in the plane in the presence of stationary point obstacles, which need to be avoided throughout the deformation. As our main result, we prove that it is NP-hard to decide whether such an obstacle-avoiding 2D morph between two given drawings of the same graph exists. This is in sharp contrast to the classical case without obstacles, where there is an efficiently verifiable (necessary and sufficient) criterion for the existence of a morph.

翻译：无交叉变形是指两个图绘制之间的连续形变，其始终保持直线边对之间无交叉。受3D变形问题应用的启发，我们开始研究在平面静止点障碍物（需在整个形变过程中避开）存在的情况下，图绘制的变形问题。作为主要结果，我们证明判断同一图的两个给定绘制之间是否存在此类避障2D变形是NP难的。这与经典的无障碍物情形形成鲜明对比，后者存在一个可高效验证的（必要且充分的）变形存在性判别准则。