A wave-based anisotropic quadrangulation method

Zhang, Muyang; Huang, Jin; Liu, Xinguo; Bao, Hujun

doi:10.1145/1833351.1778855

Cited by 17 publications

(22 citation statements)

References 17 publications

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“…Most recent approaches use a precomputed quadrilateral feature aligned quadrilateral mesh, either directly modeled by a human, or computed with methods such as Quadcover [Klberer et al 2007], PGP [Ray et al 2006], Mixed Integer [Bommes et al 2009], or Standing Wave [Zhang et al 2010], as a base to gather a simplified parametric domain. Meshes generated automatically have a high quality, but they usually contain far too many quads to be used as parametrization domains for practical applications.…”

Section: Related Workmentioning

confidence: 99%

Simple quad domains for field aligned mesh parametrization

et al. 2011

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Section: Related Workmentioning

confidence: 99%

Simple quad domains for field aligned mesh parametrization

et al. 2011

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“…In [Ray et al 2006], the curl is minimized isotropically on a 4direction field, to form a 4-vector field with potentially less curl, leading to a more conformal than isometric parametrization. This is extended to different scaling in each axis to get an orthogonal and anisotropic, 2 2 -vector field in [Zhang et al 2010].…”

Section: Fairnessmentioning

confidence: 99%

Directional field synthesis, design, and processing

Vaxman

Campen

Diamanti

et al. 2017

ACM SIGGRAPH 2017 Courses

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SummaryDirection fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector-set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This course provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges. PrerequisitesThe audience should have some prior experience with triangle mesh representation of geometric models, and a working knowledge of vector calculus, linear algebra, and general computer graphics fundamentals. Some familiarity with the basics of differential geometry and numerical optimization are helpful, but not required. Intended AudienceThe course targets researchers and developers who seek to understand the concepts and technologies used in direction field and vector field synthesis, learn about the most recent developments, and discern how this powerful tool, which has had impact in a variety of research and application areas, might benefit their area of work. Participants will get a broad overview, and obtain the knowledge on how to choose the proper combination of techniques for many relevant tasks. SourcesThese notes are largely based on the following state-of-the-art report by the lecturers. It has been extended to include updates on the most recent developments. • The course was subsequently given at SIGGRAPH Asia 2016, including demos and real-time coding sessions. The entire course, including the notes, the presentation slides, and the demos, is provided in the following open-source GitHub repository: https://github.com/avaxman/DirectionalFieldSynthesis Further ReadingBeing a relatively young and developing topic, no textbooks covering the various aspects of directional field synthesis in the context of computer graphics and geometry processing are available. The notes of a recent course on vector field processing offer another perspective on parts of the topic, with a focus on the discrete differential geometry aspects:• F. Her current interests are in geometry processing and modeling, specifically on vector field design, surface parametrizations, and inter-surface mappings. David Bommes RWTH Aachen University, GermanyDavid Bommes is an assistant professor in the Computer Science ...

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“…Two recent quadrangulation methods focus on anisotropy: [KMZ10]: This method for computing anisotropic quadrangulations adapts quad aspect ratios to local curvature to obtain a good surface approximation with fewer quads. This method can be effectively applied to improve the visual quality of a rendering, as illustrated in Figure 11 [ZHLB10]: As in Periodic Global Parameterisation [RLL*06], the method uses the periodicity of the sine and cosine functions to represent seamless coordinates, combined with the Morse-Smale complex used in Spectral Surface Quadrangulation [DBG*06]. More control is provided to the user.…”

Section: Allowing Anisotropymentioning

confidence: 99%

Quad‐Mesh Generation and Processing: A Survey

Bommes

Lévy

Pietroni

et al. 2013

Computer Graphics Forum

286

165

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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 survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrisation and remeshing

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A wave-based anisotropic quadrangulation method

Cited by 17 publications

References 17 publications

Simple quad domains for field aligned mesh parametrization

Simple quad domains for field aligned mesh parametrization

Directional field synthesis, design, and processing

Quad‐Mesh Generation and Processing: A Survey

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