Optimization Model for Polyline Offset

This paper presents a least-squares optimization formulation for improving polyline offset quality through tangential displacement of offset vertices. The resulting sparse tridiagonal linear system computes the global minimizer of the proposed objective and can be solved in O(n) time. Experimental examples demonstrate significant reduction of quadrilateral distortion and correction of inverted configurations. The formulation has also been extended to quadrilateral mesh surface offsets and may be applicable to broader geometric optimization problems. Keywords: optimization model, least square, rectangle quad