Testing a rotation axis to drain a 3D workpiece

Given a triangular mesh defining the geometry of a 3D workpiece filled with water, we propose an algorithm to test whether, for an arbitrary given axis, the workpiece will be completely drained under gravity when the rotation axis is set parallel to the ground and the workpiece is rotated around the axis. Observing that all water traps contain a concave vertex, we solve our problem by constructing and analyzing a directed “draining graph” whose nodes correspond to concave vertices of the geometry and whose edges are set according to the transition of trapped water when we rotate the workpiece around the given axis. Our algorithm to test whether or not a given rotation axis drains the workpiece outputs a result in about a second for models with more than 100,000 triangles after a few seconds of preprocessing.