Polyline Offset with Optimized Rectangularity

Abstract

This article presents an interesting approach to offset a polyline, such as mesh boundary, so that the offset quads are as rectangular as possible, which is a frequent request for some applications. This article is turning this request to a math model, or error measurement function, which is optimized to achieve the goal. This polyline can be in 2D, or the boundary of a 3D mesh. The method is based on a natural offset in the normal direction of the boundary polyline, and then building a least squares model to optimize the offset quads, which push towards the request for better rectangularized.

Keywords: rectangle quad, optimization