A Point-Based Offsetting Method of Polygonal Meshes

We address the delicate problem of offsetting polygonal meshes. Offsetting is important for stereolithography, NC machining, rounding corners, collision avoidance, and Hausdorff error calculation. We introduce a new fast, and very simple method for offsetting (growing and shrinking) a solid model by arbitrary distance r. Our approach is based on a hybrid data structure combining point samples, voxels, and continuous surfaces. Each face, edge, and vertex of the original solid generate a set of offset points spaced along the (pencil of) normals associated with it. The offset points and normals are sufficiently dense to ensure that all voxels between the original and the offset surfaces are properly labeled as either too close to the original solid or possibly containing the offset surface. Then the offset boundary is generated as the isosurface using these voxels and the associated offset points. We provide a tight error bound on the resulting surface and report experimental results on a variety of CAD models.