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

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

What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG. To augment reader accessibility, a dedicated IMG project page is available at \url{https://github.com/xzb030/IMG_Survey}

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