Simultaneous interior and boundary optimization of volumetric domain parameterizations for IGA

Líu, Hao; Yang, Yang; Liu, Yuan; Fu, Xiao‐Ming

doi:10.1016/j.cagd.2020.101853

Cited by 20 publications

(2 citation statements)

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“…Solid texturing is also used in advanced manufacturing to map atomic elements of periodic microstructures inside objects [PZM*15,SBR*15,ABC*19], obtaining lightweight pieces with a controlled physical response. Furthermore, cube mappings are also relevant in CAD, where IGA methods exploit them to fit tensor product splines for the numerical resolution of PDEs [ZC21,YLSF21,LYLF20].…”

Section: Field Overviewmentioning

confidence: 99%

VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base Domains

Cherchi

Livesu

2023

Computer Graphics Forum

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Correspondences between geometric domains (mappings) are ubiquitous in computer graphics and engineering, both for a variety of downstream applications and as core building blocks for higher level algorithms. In particular, mapping a shape to a convex or star‐shaped domain with simple geometry is a fundamental module in existing pipelines for mesh generation, solid texturing, generation of shape correspondences, advanced manufacturing etc. For the case of surfaces, computing such a mapping with guarantees of injectivity is a solved problem. Conversely, robust algorithms for the generation of injective volume mappings to simple polytopes are yet to be found, making this a fundamental open problem in volume mesh processing. VOLMAP is a large scale benchmark aimed to support ongoing research in volume mapping algorithms. The dataset contains 4.7K tetrahedral meshes, whose boundary vertices are mapped to a variety of simple domains, either convex or star‐shaped. This data constitutes the input for candidate algorithms, which are then required to position interior vertices in the domain to obtain a volume map. Overall, this yields more than 22K alternative test cases. VOLMAP also comprises tools to process this data, analyze the resulting maps, and extend the dataset with new meshes, boundary maps and base domains. This article provides a brief overview of the field, discussing its importance and the lack of effective techniques. We then introduce both the dataset and its major features. An example of comparative analysis between two existing methods is also present.

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Section: Field Overviewmentioning

confidence: 99%

VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base Domains

Cherchi

Livesu

2023

Computer Graphics Forum

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“…Inversion-free parameterizations are required to improve the subsequent accuracy and computational robustness for solving partial differential equations. However, the initial parameterizations often contain inverted regions, so the challenges are to eliminate them [21,22].…”

Section: Mapping Representationmentioning

confidence: 99%

Inversion-free geometric mapping construction: A survey

Zhao

et al. 2021

Comp. Visual Media

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A geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

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