Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

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

Closed-form Quadrangulation of N-Sided Patches

We analyze the problem of quadrangulating a $n$-sided patch, each side at its boundary subdivided into a given number of edges, using a single irregular vertex (or none, when $n = 4$) that breaks the otherwise fully regular lattice. We derive, in an analytical closed-form, (1) the necessary and sufficient conditions that a patch must meet to admit this quadrangulation, and (2) a full description of the resulting tessellation(s)

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

Composing quadrilateral meshes for animation

The modeling-by-composition paradigm can be a powerful tool in modern animation pipelines. We propose two novel interactive techniques to compose 3D assets that enable the artists to freely remove, detach and combine components of organic models. The idea behind our methods is to preserve most of the original information in the input characters and blend accordingly where necessary. The first method, QuadMixer, provides a robust tool to compose the quad layouts of watertight pure quadrilateral meshes, exploiting the boolean operations defined on triangles. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving the shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. The resulting meshes preserve the originally designed edge flows that, by construction, are captured and incorporated into the new quads. SkinMixer extends this approach to compose skinned models, taking into account not only the surface but also the data structures for animating the character. We propose a new operation-based technique that preserves and smoothly merges meshes, skeletons, and skinning weights. The retopology approach of QuadMixer is extended to work on quad-dominant and arbitrary complex surfaces. Instead of relying on boolean operations on triangle meshes, we manipulate signed distance fields to generate an implicit surface. The results preserve most of the information in the input assets, blending accordingly in the intersection regions. The resulting characters are ready to be used in animation pipelines. Given the high quality of the results generated, we believe that our methods could have a huge impact on the entertainment industry. Integrated into current software for 3D modeling, they would certainly provide a powerful tool for the artists. Allowing them to automatically reuse parts of their well-designed characters could lead to a new approach for creating models, which would significantly reduce the cost of the process

Generating patterns on clothing for seamless design

Symmetric patterns are used widely in clothing manufacture. However, the discontinuity of patterns at seams can disrupt the visual appeal of clothing. While it is possible to align patterns to conceal such pattern breaks, it is hard create a completely seamless garment in terms of pattern continuity. In this thesis, we explore computational methods to parameterize the clothing pieces relative to a pattern’s coordinate system to achieve pattern continuity over garments. We review previous work related to pattern alignment on clothing. We also review surface quadrangulation methods. With a suitable quadrangulation, we can map any planar pattern with fourfold rotations into each quad, and achieve a seamless design. With an understanding of previous work, we approached the problems from three angles. First, we mapped patterns with sixfold rotations onto clothing by triangulating the clothing pieces and ensuring consistency of triangle vertices on both sides of a seam. We also mapped patterns with fourfold rotations onto clothing by optimizing the shape of each clothing piece in the texture domain. Lastly, we performed quadrangulation guided by cross fields, and mapped fourfold pattern units into each quad. We assembled and simulated the texture mapped clothing in Blender to visualize the results