Template-based Quadrilateral Meshing J. Daniels II 1 , M. Lizier 2 , M. Siqueira 3 , C. T. Silva 1 , and L. G. Nonato 4 1 SCI Institute, University of Utah, United States of America 2 Departamento de Computac ¸˜ ao, Universidade Federal de S˜ ao Carlos, Brazil 3 Departamento de Inform´ atica e Matem´ atica Aplicada, Universidade Federal do Rio Grande do Norte, Brazil 4 Instituto de Ciˆ encias Matem´ aticas e de Computac ¸˜ ao, Universidade de S˜ ao Paulo, Brazil Abstract Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthog- onality, alignment and adaptivity; however, they can not make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computer Graph- ics/Computational Geometry and Object Modeling—Curve, surface, solid and object representations 1. Introduction Generating quad meshes is a central problem in cur- rent geometry processing research, as many important applications, including texture and spline-based surface modeling, greatly benefit from a quad structure. Anima- tion artists, in general, prefer quad over triangle meshes. This is partially attributed to the ability of quad elements to naturally align to principal curvature directions and feature curves that, for example, facilitates the modeling of character limbs. Further, joints, articulations and skin bends can be modeled with quad edge polylines ending in extraordinary vertices (i.e., vertices of valence other than 4), because these polyline structures behave like a hinge to improve deformations. Although quad meshes are highly desired for the aforementioned applications, designing fully automatic techniques to produce suitable quad meshes is still a dif- ficult task. This is partially due to the fact that fun- damental quality criteria, i.e., mesh regularity (domi- nated by valence 4 vertices), orthogonality (rectangular quad elements), alignment (respecting principal curva- ture and surface features), and adaptivity (relating quad sizes to local curvature variations and anisotropy), can be in conflict with each other. Furthermore, application specific criteria, for which the mesh is targeted, may re- quire design decisions that cannot be automatically an- ticipated. On the one hand, there are well-known automatic techniques to describe the surface features of a model, and some of them have been incorporated within fully automatic quad mesh generation approaches. On the other hand, subjective design decisions require user in- puts. There are a few quad meshing approaches that of- fer some mechanisms to include the user in the mesh generation process. However, these approaches may not ensure the desired mesh alignment with surface fea- tures; may not provide necessary or easy to use inputs to control subjective design decisions; or may require a large amount of user interaction. This paper describes a new approach for generat- ing all-quad meshes from triangle surfaces. Our ap- proach offers a flexible mechanism to allow external in- put, through the definition of surface features that are Preprint submitted to SMI 2011 April 15, 2011