A Least-Squares Optimization Model for Quad Mesh Offset

This article presents a least-squares optimization model for quad mesh offset. Starting from an initial offset mesh generated from the base mesh, the method improves offset quality by introducing tangential corrections at offset vertices and solving for them globally. Each correction is represented by two scalar variables associated with two independent directions taken from the corresponding base quad, so that the optimization preserves the intended offset distance while allowing the offset mesh to adjust tangentially. For each quad, the objective function is constructed from several local shape-preservation terms together with a center-consistency term, so that the optimized offset quad remains as consistent as possible with the shape and size of the base quad while reducing crimping and shearing. The resulting formulation is a global least-squares problem over the mesh, leading to a sparse linear system. Examples show that the method can significantly improve the quality of quad-mesh offsets in both convex and concave regions, and can be applied iteratively for further improvement.