Interference-free construction of beveled offset triangular mesh

Abstract

In this dissertation, an exact beveled offsetting method of triangular mesh is presented. Though the main target application is machining tool path generation, the suggested method can also be applied to other fields such as shelling/hollowing of solid objects, collision avoidance in robot path planning, and so on. Two main steps, constructing a vertex split mesh and event-based mesh offsetting, for obtaining an exact offset triangular mesh which has theoretically no offset error and doesn’t require any post processing to remove interferences are suggested. Beveled offsetting method is also introduced to create fewer gap filling triangles than existing round offsetting method and to support generating a tool path which reduces the number of tool’s intermission. For the fast construction of beveled offset triangular mesh, simple vertex split operation and a modified version of quadric error metric (QEM) is applied. During the vertex split operation, every sharp edge which has bigger dihedral angle than threshold value given by user is searched and split to insert a virtual face. We can get beveled offset mesh from this simple process. A modified QEM is for robust computation of the offset vertex position which minimizes the sum of squared distance error from the faces around the original mesh vertex. Even though this approach gives us beveled offset mesh, it provides incomplete mesh due to the much interference since we don’t consider offsetting concave edges. And the result mesh has intrinsic offset error while it satisfies the user’s requirement. As a first step for obtaining an exact beveled offset triangular mesh which has no interference, an elaborate algorithm for the construction of vertex split mesh is devised. In this step, we search a vertex including n, more than 3, incident faces and split it into (n-2) vertices in which each of split vertexes has exactly 3 incident faces. To get this vertex split topology, a vertex and its incident faces are ins...