Sphere-based cut construction for planar parameterizations

Chai, Shuangming; Fu, Xiao‐Ming; Hu, Xin; Yang, Yang; Liu, Ligang

doi:10.1016/j.cag.2018.05.007

Cited by 16 publications

(38 citation statements)

References 26 publications

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“…detect a set of vertices as candidates. To consistently seek candidates with strong practical robustness, we customize an effective clustering strategy, shown in [10], which uses a parameter to control the balance between the number of distortion points and the final parameterization distortion. Note that the generated candidates may include some vertices near boundaries, but they are usually detected only once since the random cut paths have almost no intersections.…”

Section: Planar Parameterizationmentioning

confidence: 99%

“…to avoid early termination due to the maximum distortion vertex's location on the boundary. To overcome this issue, spherical parameterizations are used [10]; however, efficiently computing bijective spherical parameterizations for complex objects is a non-trivial task (see the comparison in Fig. 17).…”

Section: Related Workmentioning

confidence: 99%

“…Instead of spherical parameterizations [10], we use distortion measures on planar parameterizations to detect distortion points. Thus, we first cut M as a disk topology mesh M c (Section 3.2.1), then parameterize M c onto the plane (Section 3.2.2), and finally find the distortion points (Section 3.2.3).…”

Section: Candidate Distortion Pointsmentioning

confidence: 99%

“…Clustering Method. Since the clustering method proposed in [10] is practically robust for detecting distortion points V d , we first review it and then modify it for our ACAP planar parameterizations.…”

Section: Detecting Distortion Pointsmentioning

confidence: 99%

“…In Section 4.1, we first evaluate the results and components of our algorithm and then demonstrate the practical robustness of our algorithm on different tessellations and complex models. We select the Seamster [9], Geometry Images method [7], and a sphere-based clustering method [10] as the competitors (Section 4.2). The experiments were performed on a desktop PC with an Intel Core i7-4790 processor and 8GB memory.…”

Section: Experiments and Evaluationsmentioning

confidence: 99%

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Voting for Distortion Points in Geometric Processing

Chai

Liu

2021

IEEE Trans. Visual. Comput. Graphics

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Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of these vertices is non-trivial. We call these vertices distortion points. We present a novel and automatic method to detect distortion points using a voting strategy. Our method integrates two components: candidate generation and candidate voting. Given a closed triangular mesh, we generate candidate distortion points by executing a three-step procedure repeatedly: (1) randomly cut an input to a disk topology; (2) compute a low conformal distortion parameterization; and (3) detect the distortion points. Finally, we count the candidate points and generate the final distortion points by voting. We demonstrate that our algorithm succeeds when employed on various closed meshes with a genus of zero or higher. The distortion points generated by our method are utilized in three applications, including planar parameterization, semi-automatic landmark correspondence, and isotropic remeshing. Compared to other state-of-the-art methods, our method demonstrates stronger practical robustness in distortion point detection.

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Section: Planar Parameterizationmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Candidate Distortion Pointsmentioning

confidence: 99%

Section: Detecting Distortion Pointsmentioning

confidence: 99%

Section: Experiments and Evaluationsmentioning

confidence: 99%

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Voting for Distortion Points in Geometric Processing

Chai

Liu

2021

IEEE Trans. Visual. Comput. Graphics

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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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