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

Simple quad domains for field aligned mesh parametrization

We present a method for the global parametrization of meshes that preserves alignment to a cross field in input while obtaining a parametric domain made of few coarse axis-aligned rectangular patches, which form an abstract base complex without T-junctions. The method is based on the topological simplification of the cross field in input, followed by global smoothing

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

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

Surface Shape Perception in Volumetric Stereo Displays

In complex volume visualization applications, understanding the displayed objects and their spatial relationships is challenging for several reasons. One of the most important obstacles is that these objects can be translucent and can overlap spatially, making it difficult to understand their spatial structures. However, in many applications, for example medical visualization, it is crucial to have an accurate understanding of the spatial relationships among objects. The addition of visual cues has the potential to help human perception in these visualization tasks. Descriptive line elements, in particular, have been found to be effective in conveying shape information in surface-based graphics as they sparsely cover a geometrical surface, consistently following the geometry. We present two approaches to apply such line elements to a volume rendering process and to verify their effectiveness in volume-based graphics. This thesis reviews our progress to date in this area and discusses its effects and limitations. Specifically, it examines the volume renderer implementation that formed the foundation of this research, the design of the pilot study conducted to investigate the effectiveness of this technique, the results obtained. It further discusses improvements designed to address the issues revealed by the statistical analysis. The improved approach is able to handle visualization targets with general shapes, thus making it more appropriate to real visualization applications involving complex objects

Retopology: a comprehensive study of current automation solutions from an artist’s workflow perspective

Dissertação de mestrado em Engenharia InformáticaTopology (the density, organization and flow of a 3D mesh’s connectivity) constrains the suitability of a 3D model for any given purpose, be it surface showcasing through renders, use in real-time engines, posing or animation. While some of these use cases might not have very strict topology requirements, others may demand optimized polygon counts for performance reasons, or even specific geometry distribution in order to take deformation directions into account. Many processes for creating 3D models such as sculpting try to make the user unaware of the inner workings of geometry, by providing flexible levels of surface detailing through dynamic geometry allocation. The resulting models have a dense, unorganized topology that is inefficient and unfit for most use cases, with the additional drawback of being hard to work with manually. Retopology is the process of providing a new topology to a model such as these, while maintaining the shape of its surface. It’s a technical and time-consuming process that clashes with the rest of the artist’s workflow, which is mainly composed of creative processes. While there’s abundant research in this area focusing on polygon distribution quality based on surface shape, artists are still left with no options but to resort to manual work when it comes to deformation-optimized topology. This document exposes this disconnect, along with a proposed framework that attempts to provide a more complete retopology solution for 3D artists. This framework combines traditional mesh extraction algorithms with adapting manually-made meshes in a pipeline that tries to understand the input on a higher level, in order to solve deficiencies that are present in current retopology tools. Our results are very positive, presenting an improvement over state of the art solutions, which could possibly steer discussion and research in this area to be more in line with the needs of 3D artists.A topologia (a densidade, organização e direções tomadas pela conectividade de uma mesh 3D) limita a adequação de um modelo 3D para um leque variado de usos, entre os quais, visualização da superfície através de renders, uso em motores real-time, poses ou animações. Embora muitos destes usos não possuam requerimentos de topologia muito rigorosos, outros podem exigir número de polígonos mais baixos por questões de performance, ou até distribuição de geometria específica para acomodar direções de deformação corretamente. Muitos processos de criação de modelos 3D, como escultura, permitem que o utilizador não esteja ciente do que se passa em termos de funcionamento da geometria por debaixo da utilização. Isto é conseguido oferecendo níveis de detalhe flexíveis, alocando geometria de forma dinâmica. Os modelos resultantes têm uma topologia densa e desorganizada, que é ineficiente e pouco apropriada para a maior parte dos casos de uso, com a desvantagem adicional de ser difícil de trabalhar com a mesma manualmente. A retopologia é o processo de gerar uma nova topologia para um modelo, ao mesmo tempo que se mantém a forma da superfície. É um processo técnico e demorado, que entra em conflito com o resto do fluxo de trabalho do artista, que é composto maioritariamente por processos artísticos. Apesar de haver investigação abundante nesta área focada na qualidade da distribuição de polígonos baseada na forma da superfície, os artistas continuam a ter de recorrer ao trabalho manual quando se trata de topologia otimizada para deformações. Este documento expõe esta divergência, propondo, em conjunto, uma framework que tenta oferecer uma solução mais completa para os artistas 3D. Esta framework combina algoritmos de extração de meshes tradicionais com adaptação de meshes feitas manualmente, numa pipeline que tenta compreender o input a um nível superior, resolvendo as deficiências presentes nas ferramentas de retopologia atuais. Os nossos resultados são bastante positivos, apresentando melhorias em relação a soluções de estado da arte, facto que poderá mudar o rumo da discussão e investigação neste campo, para melhor se adequar às necessidades dos artistas 3D

Lp Centroidal Voronoi Tesselation and its applications

International audienceThis paper introduces Lp -Centroidal Voronoi Tessellation (Lp -CVT), a generalization of CVT that minimizes a higher-order moment of the coordinates on the Voronoi cells. This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy). Lp -CVT is computed by a quasi-Newton optimization framework, based on closed-form derivations of the objective function and its gradient. The derivations are given for both surface meshing (Ω is a triangulated mesh with per-facet anisotropy) and volume meshing (Ω is the interior of a closed triangulated mesh with a 3D anisotropy field). Applications to anisotropic, quad-dominant surface remeshing and to hex-dominant volume meshing are presented. Unlike previous work, Lp -CVT captures sharp features and intersections without requiring any pre-tagging

Variational Methods and Numerical Algorithms for Geometry Processing

In this work we address the problem of shape partitioning which enables the decomposition of an arbitrary topology object into smaller and more manageable pieces called partitions. Several applications in Computer Aided Design (CAD), Computer Aided Manufactury (CAM) and Finite Element Analysis (FEA) rely on object partitioning that provides a high level insight of the data useful for further processing. In particular, we are interested in 2-manifold partitioning, since the boundaries of tangible physical objects can be mathematically defined by two-dimensional manifolds embedded into three-dimensional Euclidean space. To that aim, a preliminary shape analysis is performed based on shape characterizing scalar/vector functions defined on a closed Riemannian 2-manifold. The detected shape features are used to drive the partitioning process into two directions – a human-based partitioning and a thickness-based partitioning. In particular, we focus on the Shape Diameter Function that recovers volumetric information from the surface thus providing a natural link between the object’s volume and its boundary, we consider the spectral decomposition of suitably-defined affinity matrices which provides multi-dimensional spectral coordinates of the object’s vertices, and we introduce a novel basis of sparse and localized quasi-eigenfunctions of the Laplace-Beltrami operator called Lp Compressed Manifold Modes. The partitioning problem, which can be considered as a particular inverse problem, is formulated as a variational regularization problem whose solution provides the so-called piecewise constant/smooth partitioning function. The functional to be minimized consists of a fidelity term to a given data set and a regularization term which promotes sparsity, such as for example, Lp norm with p ∈ (0, 1) and other parameterized, non-convex penalty functions with positive parameter, which controls the degree of non-convexity. The proposed partitioning variational models, inspired on the well-known Mumford Shah models for recovering piecewise smooth/constant functions, incorporate a non-convex regularizer for minimizing the boundary lengths. The derived non-convex non-smooth optimization problems are solved by efficient numerical algorithms based on Proximal Forward-Backward Splitting and Alternating Directions Method of Multipliers strategies, also employing Convex Non-Convex approaches. Finally, we investigate the application of surface partitioning to patch-based surface quadrangulation. To that aim the 2-manifold is first partitioned into zero-genus patches that capture the object’s arbitrary topology, then for each patch a quad-based minimal surface is created and evolved by a Lagrangian-based PDE evolution model to the original shape to obtain the final semi-regular quad mesh. The evolution is supervised by asymptotically area-uniform tangential redistribution for the quads