Abstract: Boolean operation is a common approach for constructing complex solid geometries in
computer-aided geometric design. Since it was introduced in the 1880s, most of the research on it is
trading off between efficiency and robustness. And most of the algorithms require strictly that input
meshes have no cavity and boundary edges, which ensures that inputs can serve as boundary
representations for some solids. Quite different from the methods mentioned above, this paper
proposes an efficient, robust and wildly-adaptive method of Boolean operation, which could be
applied to non-solid meshes. Firstly, we merge input meshes into one mesh, then split it into different
patches along non-manifold edges after resolving the intersection issue of the merge, and identify all
cells surrounded by those patches. Next, we calculate the winding number of each cell by adding
virtual patches, tag the special properties of the cell in every input mesh, and consequently acquire the
correct result of Boolean operation.

Key words: mesh, Boolean operation, non-closed, winding number