A Divide-and-Conquer Approach to Quad Remeshing

Abstract

Abstract-Many natural and man-made objects consist of simple primitives, similar components, and various symmetry structures. This paper presents a divide-and-conquer quadrangulation approach that exploits such global structural information. Given a model represented in triangular mesh, we first segment it into a set of submeshes, and compare them with some predefined quad mesh templates. For the submeshes that are similar to a predefined template, we remesh them as the template up to a number of subdivisions. For the others, we adopt the wave-based quadrangulation technique to remesh them with extensions to preserve symmetric structure and generate compatible quad mesh boundary. To ensure that the individually remeshed submeshes can be seamlessly stitched together, we formulate a mixed-integer optimization problem and design a heuristic solver to optimize the subdivision numbers and the size fields on the submesh boundaries. With this divider-and-conquer quadrangulation framework, we are able to process very large models that are very difficult for the previous techniques. Since the submeshes can be remeshed individually in any order, the remeshing procedure can run in parallel. Experimental results showed that the proposed method can preserve the high-level structures, and process large complex surfaces robustly and efficiently.Index Terms-Quad remeshing, divide-and-conquer, segmentation, mixed-integer optimization Ç 1I NTRODUCTION Q UAD mesh is very useful for its bilinear nature and superior performance in many graphics and scientific computing applications. However, it is very challenging to remesh a surface into a provably high-quality quad mesh, because there are very diverse requirements on the shape, the orientation and the size of the quads, the alignment of features, and the regularity of the mesh in term of singularity points. Some of the recently developed methods [1], [2] take into account these low-level requirements via global optimization techniques; however, the optimization cost may increase rapidly, and even become unacceptable, when processing large complex models.On the other hand, many natural and man-made objects consist of simple primitives, similar components, and various symmetric structures. Taking advantages of the high-level structural information would be helpful for developing a better quadrangulation method. However, the previous methods are not aware of such high-level structural information. They conduct the same kind of computation on all components, which wastes a lot of computation resources. Moreover, the global structure might not be preserved because different results might be generated for those similar parts.In this paper, we propose a top-down quadrangulation method that exploits the high-level structural information. Our primary goal is to develop a practical solution to robust and efficient remesh large complex surfaces with many components and regular structures. The basic idea to achieve this goal is "divide and conquer," i.e., segmenting the input surface into sma...

Cost Minimizing Local Anisotropic Quad Mesh Refinement

“…Thus, automatic generation of quad meshes, typically from a given triangle mesh, has been a well researched topic in the past decade [KNP07, BZK09, ZHLB10, ZHLB13, BCE∗13, MPZ14, CBK15, JTPSH15, LHJ∗15, HZN∗18]. Some methods also offer control over quad sizing and may produce anisotropic meshes [PPTSH14, JFH∗15, FBT∗18].…”

A sample implementation for parallelizing Divide-and-Conquer algorithms on the GPU

“…Among those efforts, probably the most valuable ones are the parallelization of D&C sorting algorithms [18] and scan algorithm [19] on the GPU. Other efforts were also carried out to parallelize the D&C mesh generation [20] , [21] , [22] , convex hull calculation [23] , [24] , [25] , multibody system dynamics [26] , [27] , etc.…”

“…We develop a Sample GPU implementation of a classical D&C algorithm (i.e., Quickhull) by following Tzeng and Owens's paradigm. We hope this will be helpful for interested readers to develop their own efficient GPU implementations of D&C algorithms with fewer efforts and in less time, for example, to develop efficient D&C algorithms in mesh generation [20] , [21] , [22] , convex hull calculation [23] , [24] , [25] , multibody system dynamics [26] , [27] , etc.…”