Abstract
Recently computational methods have been improved to convert triangular meshes into quadrilateral meshes so that the generated quadrilateral elements well capture principal curvature directional fields of the surface and intrinsically have surface parametric values. It has been also suggested to use such quadrilateral mesh for reverse engineering, that is, an application to generate a parametric surface model from the mesh. In this paper, we propose an algorithm to segment a given quadrilateral mesh for generating a parametric surface model. We use a quadrilateral mesh generated by mixed integer quadrangulation by Bommes. We first segment the quadrilateral mesh into quadrangular regions to each of which we fit a parametric surface using motorcycle graph algorithm of Eppstein. However, the resulting segmentation is not necessarily appropriate for fitting a surface because the regions can involve unsmooth quadrilateral elements as the motorcycle graph algorithm of Eppstein does not take into account the geometry of the mesh. In this paper we propose a method to extend the motorcycle graph algorithm of Eppstein and other methods so as to generate regions each of which are suitable for fitting a surface. Depending on demand of a user, our method can also generate non-quadrangular region to which a trimmed surface is generated. We demonstrate our results with several models varying from mechanical to organic samples.
