A Robust Two‐Step Procedure for Quad‐Dominant Remeshing

Abstract

We propose a new technique for quad-dominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches which capture the global structure of the processed object. Then we compute an optimized quad-mesh for every patch by generating a finite set of candidate curves and applying a combinatorial optimization procedure. Since the optimization is performed independently for each patch, we can afford more complex operations while keeping the overall computation times at a reasonable level. Our quad-meshing technique is robust even for noisy meshes and meshes with isotropic or flat regions since it does not rely on the generation of curves by integration along estimated principal curvature directions. Instead we compute a conformal parametrization for each patch and generate the quad-mesh from curves with minimum bending energy in the 2D parameter domain. Mesh consistency between patches is guaranteed by simply using the same set of sample points along the common boundary curve. The resulting quad-meshes are of highquality locally (shape of the quads) as well as globally (global alignment) which allows us to even generate fairly coarse quad-meshes that can be used as Catmull-Clark control meshes.

Exploring quadrangulations

“…Complexity of the Enumeration: The only competing approach, that we are aware of, is the brute-force enumeration of all possible connections of inward edges, e.g., [Marinov and Kobbelt 2006]. For simplicity, we present an example where the number of inner irregular vertices of the patch is minimal, a 100 by 100 2-sided patch (T V D = 2).…”

“…The three most related concepts for the exploration of quad mesh topologies are curve sampling [Marinov and Kobbelt 2006], connectivity editing [Maza et al 1999;Peng et al 2011], and advancing fronts (paving) [Blacker and Stephenson 1991;White and Kinney 1997;Park et al 2007]. Marinov and Kobbelt [2006] connect the boundary vertices of a patch by curves and propose an algorithm to generate a layout and another algorithm to mutate an existing layout. The purpose of the algorithm is quad mesh generation, but it could also be used to explore quad mesh topologies.…”

Design-driven quadrangulation of closed 3D curves

“…Many recent publications addresses quad meshing of existing 3D surfaces [Bommes et al 2011;Daniels et al 2009;Kälberer et al 2007;Levy and Liu 2010;Tong et al 2006;Bommes et al 2010;Marinov and Kobbelt 2006]. These methods aim to align the output quad meshes with the principal curvature directions in anisotropic regions generating smooth orthogonal families of flow-lines.…”

A wave-based anisotropic quadrangulation method

“…We will review some of the most related ones by how a global quadrilateral structure is constructed, since it is a very important issue for quadrangulation. Marinov and Kobbelt [2006] developed a variational shape approximation method to partition the input mesh into nearly developable regions. The regions are then individually remeshed into quads with constraints on the region boundaries to ensure a consistent remeshing.…”