Connectivity Control for Quad-Dominant Meshes

abstract: Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh. Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Quad Meshing

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing

Quad Dominant 2-Manifold Mesh Modeling

In this dissertation, I present a modeling framework that provides modeling of 2D smooth meshes in arbitrary topology without any need for subdivision. In the framework, each edge of a quad face is represented by a smooth spline curve, which can be manipulated using edge vertices and additional tangential points. The overall smoothness is achieved by interpolating all four edges of any given quad across the quad surface. The framework consists of simple quad preserving operations that manipulate the principal curves of the smooth model. These operations are all variants of a generic “Curve Split" and its inverse, “Region Collapse". By only using these sets of simple operations, it is possibly to model any desired shape conveniently. I also provide implementation guidelines for these operations. In the results of this dissertation, I present three main applications for this modeling framework. The major application is modeling Mock3D shapes; shapes with well defined interior normals by interpolating the normals at the boundaries of the shape across its surface which can serve as a mock 3D model to mimic a 3D CGI look. As a second application, the framework can be used in origami modeling by allowing assignment of crease patterns across the surface of 2D shapes modelled. Finally, vectorization of reference photos via modeling figures by following their contours is presented as a third application