ABF++: fast and robust angle based flattening

Sheffer, Alla; Lévy, Bruno; Mogilnitsky, Maxim; Bogomyakov, Alexander

doi:10.1145/1061347.1061354

Cited by 304 publications

(200 citation statements)

References 30 publications

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“…Iterative? Shape-preserving [6] Fixed Yes No MIPS [16] Free Yes Yes ABF/ABF++ [33,34] Free Local (no flips) Yes LSCM/DNCP [4,23] Free No No Holomorphic 1-form [12] Fixed No No Mean-value [7] Fixed Yes No Yamabe Riemann map [26] Fixed Yes Yes Circle patterns [22] Free Local (no flips) Yes Genus-0 surface conformal map [19] Free No Yes Discrete Ricci flow [20] Fixed Yes Yes Spectral conformal [27] Free No No Generalized Ricci flow [36] Fixed Yes Yes Two-step iteration [3] Fixed Yes Yes [13] and an iterative scheme for genus-0 surface conformal mapping in [12] to obtain a planar conformal parameterization. In [27], Mullen et al reported a spectral approach to discrete conformal parameterizations, which involves solving a sparse symmetric generalized eigenvalue problem.…”

Section: Methodsmentioning

confidence: 99%

A linear formulation for disk conformal parameterization of simply-connected open surfaces

Choi

Lui

2017

Adv Comput Math

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Surface parameterization is widely used in computer graphics and geometry processing. It simplifies challenging tasks such as surface registrations, morphing, remeshing and texture mapping. In this paper, we present an efficient algorithm for computing the disk conformal parameterization of simply-connected open surfaces. A double covering technique is used to turn a simply-connected open surface into a genus-0 closed surface, and then a fast algorithm for parameterization of genus-0 closed surfaces can be applied. The symmetry of the double covered surface preserves the efficiency of the computation. A planar parameterization can then be obtained with the aid of a Möbius transformation and the stereographic projection. After that, a normalization step is applied to guarantee the circular boundary. Finally, we achieve a bijective disk conformal parameterization by a composition of quasi-conformal mappings. Experimental results demonstrate a significant improvement in the computational time by over 60%. At the same time, our proposed method retains comparable accuracy, bijectivity and robustness when compared with the state-of-the-art approaches. Applications to texture mapping are presented for illustrating the effectiveness of our proposed algorithm.

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Section: Methodsmentioning

confidence: 99%

A linear formulation for disk conformal parameterization of simply-connected open surfaces

Choi

Lui

2017

Adv Comput Math

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“…There are many different unwrapping methods to map a 3D mesh to a 2D plane to produce a parameterization [2], [6], [11], [19]- [22]. To a great extent, they all are able to produce an initial parameterization.…”

Section: B Bar-net Based Initial Parameterizationmentioning

confidence: 99%

Constrained Texture Mapping and Foldover-Free Condition

Yu¹,

Yang²,

Zhang³

2013

IJCTE

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Abstract-Texture mapping has been widely used in image processing and graphics to enhance the realism of CG scenes. However to perfectly match the feature points of a 3D model with the corresponding pixels in texture images, the parameterisation which maps a 3D mesh to the texture space must satisfy the positional constraints. Despite numerous research efforts, the construction of a mathematically robust foldover-free parameterisation subject to internal constraints is still a remaining issue. In this paper, we address this challenge by developing a two-step parameterisation method. First, we produce an initial parameterisation with a method traditionally used to solve structural engineering problems, called the bar-network. We then derive a mathematical foldover-free condition, which is incorporated into a Radial Basis Function based scheme. This method is therefore able to guarantee that the resulting parameterization meets the hard constraints without foldovers.Index Terms-Foldover, constrained texture mapping, parameterization. I. INTRODUCTIONTexture mapping is an effective means in image processing and graphics to achieve improved visual realism. Existing research has largely concentrated on the production of planar parameterization [1]- [7] in order to map a 3D mesh to the planar domain. Most recent works are concerned with texture distortion reduction when mapping a planar image (texture) to a curved surface. Although this is an important issue, in practice the animator is also challenged with other problems in texture mapping. One of them is to register a texture map accurately with the features of a 3D model. For example, if one is to texture map a human face, in addition to reducing texture distortion, one has to ensure the important feature points and lines on the 3D model match those on the texture plane during the mapping process, such as the eyes, nose, eyebrows and lips. In another word, one needs to accurately register the 3D features with their 2D counterparts.With the current production practice, this registration operation is almost completely manual. Once a texture map is generated by animation software, the animator has to painstakingly tweak the unwrapped mesh on the texture plane to align the key feature points on the texture image with the 3D features. He/she has to manually move many vertices around each feature in order to avoid texture distortion being concentrated and visible. This is a timeconsuming task. Manuscript received September 18, 2012; revised December 7, 2012. The authors are with the National Center for Computer Animation, Bournemouth University, Poole, UK. (email:cnyuhc@yahoo.com, xyang@bournemouth.ac.uk, jzhang@bournemouth.ac.uk).Attempts have been made to formulate it as a constrained optimization problem [3]- [5], [7] where the important features in the texture images are to be located correctly on the 3D surface. Despite varying degree of success, a key issue yet to be solved is there is currently no robust solution to controlling the spread of the mesh points such th...

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“…Bump mapping stores small deviations of the pointwise normal from that of the smooth underlying surface and uses the perturbed version during shading [13]. Normal mapping [118,130] is a similar technique that replaces the normals directly rather than storing a perturbation. As the light direction changes, the shading variations produced by the normal perturbations simulate the shadows caused by small pits and dimples in the surface.…”

Section: 1)mentioning

confidence: 99%

“…For such applications the bijectivity requirement can be weakened, requiring only local rather than global bijectivity. Local bijectivity [118] requires a map of any sufficiently small region of the mesh to be bijective. This condition is violated when the mappings of adjacent mesh triangles intersect, in this case the parameterization is said to "fold over" or contain "triangle flips" (Figure 2.1(b)).…”

Section: Terminologymentioning

confidence: 99%

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Mesh Parameterization Methods and Their Applications

Sheffer

Praun

Rose

2006

FNT in Computer Graphics and Vision

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382

118

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We present a survey of recent methods for creating piecewise linear mappings between triangulations in 3D and simpler domains such as planar regions, simplicial complexes, and spheres. We also discuss emerging tools such as global parameterization, inter-surface mapping, and parameterization with constraints. We start by describing the wide range of applications where parameterization tools have been used in recent years. We then briefly review the pertinent mathematical background and terminology, before proceeding to survey the existing parameterization techniques. Our survey summarizes the main ideas of each technique and discusses its main properties, comparing it to other methods available. Thus it aims to provide guidance to researchers and developers when assessing the suitability of different methods for various applications. This survey focuses on the practical aspects of the methods available, such as time complexity and robustness and shows multiple examples of parameterizations generated using different methods, allowing the reader to visually evaluate and compare the results.

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ABF++: fast and robust angle based flattening

Cited by 304 publications

References 30 publications

A linear formulation for disk conformal parameterization of simply-connected open surfaces

A linear formulation for disk conformal parameterization of simply-connected open surfaces

Constrained Texture Mapping and Foldover-Free Condition

Mesh Parameterization Methods and Their Applications

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