Testing an axis of rotation for 3D workpiece draining

Abstract

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 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 check 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.