Robust and Accurate Boolean Operations on Polygonal Models

We present a new sampling-based method for the efficient and reliable calculation of boundary surface defined by a Boolean operation of given polygonal models. We first construct uniform volumetric cells with sampling points for each geometric element of polygonal models. We then calculate an error-minimizing point in each cell based on a quadratic error function (QEF). Based on a novel adaptive sampling condition, we construct adaptive octree cells such that a QEF point in each cell can capture the shape of all the geometric elements inside the cell. Finally we reconstruct a polygonal model from the volumetric grids and QEF points for approximating the boundary of a solid defined by the Boolean operation. Our method is robust since we can handle different types of topological inconsistency including non-manifold configurations. It is also accurate since we guarantee the boundary approximation has the same topology as the exact surface, and the maximum approximation error from the exact surface is bounded by a user specified tolerance. The efficient hierarchical scheme based on octree enables using sufficient grid resolutions on a commodity PC. We demonstrate our algorithm for a number of test cases and report experimental results.