A Family of Barycentric Coordinates for Co‐Dimension 1 Manifolds with Simplicial Facets

Yan, Zhipei; Schaefer, Scott

doi:10.1111/cgf.13790

Cited by 10 publications

(6 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One inherent limitation of MLC is that they are only continuous across the boundary of the polygon and not defined outside the convex hull of the polygon. While this is sufficient for cage-based deformation, it rules out skeleton-based deformation as in [YS19]. Another limitation is the lack of smoothness at interior points, and it remains future work to find generalized barycentric coordinates that are at least C 1 at interior points.…”

Section: Discussionmentioning

confidence: 99%

“…This family also includes mean value coordinates [Flo03, HF06], which come with the advantage of being well‐defined for non‐convex polygons and polyhedra, too [FKR05, JSW05]. Whole families of barycentric coordinates for non‐convex polygons and polyhedra were constructed by [BLTD16] and [YS19], but just like metric [MLD05], Poisson [LH13], and Gordon–Wixom coordinates [Bel06], they may take on negative values at certain v ∈ Ω. Some constructions guarantee the non‐negativity of the coordinates, but at the price of not depending smoothly on either v ∈ Ω [LKCOL07,MLS11] or the vertices v i [APH17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Maximum Likelihood Coordinates

Chang

Deng

Hormann

2023

Computer Graphics Forum

View full text Add to dashboard Cite

Any point inside a d‐dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n > d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non‐negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non‐negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non‐convex shapes is different and based instead on the project‐and‐smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Coordinates

Chang

Deng

Hormann

2023

Computer Graphics Forum

View full text Add to dashboard Cite

show abstract

“…In 2D plane, the barycentric coordinates can represent the relative coordinate of a node with respect to three other nodes that are not on the same line [8]. The coordinates of the four nodes i , a , b , c are respectively represented by {} Conv  is denoted as the convex hull of a set  of nodes which is the smallest convex set containing  .…”

Section: Barycentric Coordinate Representationmentioning

confidence: 99%

Distributed localization algorithm for wireless sensor networks under minuscule bias injection attacks

Chen,

Wang,

Shi

et al. 2024

Ninth International Symposium on Sensors, Mechatronics, and Automation System (ISSMAS 2023)

View full text Add to dashboard Cite

In this paper, the distributed localization problem of wireless sensor networks under minuscule bias injection attacks is studied. It is assumed that the attacker launches minuscule bias injection attacks on the distance measurement between sensors during the localization process of wireless sensor network, and the accumulated bias value has a great impact on the localization accuracy. To solve the above problems, a distributed localization algorithm based on adjacent detection and numerical fitting is proposed in this paper. The proposed algorithm realizes the detection of minuscule bias injection attacks by adjacent detection and improves the localization accuracy of the algorithm by numerical fitting. Finally, the correctness and superiority of the proposed distributed localization algorithm are verified by simulation experiment.

show abstract

“…In order to provide a generalized construction of GBC, F loater et al [FHK06] show that MVC belong to a unifying family of 2D GBC for convex polygons. Y an and S chaefer [YS19] present a modification of this family, which leads to GBC that support arbitrary dimensions and non‐manifold simplicial control structures, but neither allow for quad cages nor guarantee to be positive inside non‐convex shapes. Consequently, this STAR focuses on the evolution of MVC that overcome these limitations.…”

Section: Barycentric Coordinates With Explicit Formulasmentioning

confidence: 99%

A Survey on Cage‐based Deformation of 3D Models

Ströter,

Thiery,

Hormann

et al. 2024

Computer Graphics Forum

View full text Add to dashboard Cite

Interactive deformation via control handles is essential in computer graphics for the modeling of 3D geometry. Deformation control structures include lattices for free‐form deformation and skeletons for character articulation, but this report focuses on cage‐based deformation. Cages for deformation control are coarse polygonal meshes that encase the to‐be‐deformed geometry, enabling high‐resolution deformation. Cage‐based deformation enables users to quickly manipulate 3D geometry by deforming the cage. Due to their utility, cage‐based deformation techniques increasingly appear in many geometry modeling applications. For this reason, the computer graphics community has invested a great deal of effort in the past decade and beyond into improving automatic cage generation and cage‐based deformation. Recent advances have significantly extended the practical capabilities of cage‐based deformation methods. As a result, there is a large body of research on cage‐based deformation. In this report, we provide a comprehensive overview of the current state of the art in cage‐based deformation of 3D geometry. We discuss current methods in terms of deformation quality, practicality, and precomputation demands. In addition, we highlight potential future research directions that overcome current issues and extend the set of practical applications. In conjunction with this survey, we publish an application to unify the most relevant deformation methods. Our report is intended for computer graphics researchers, developers of interactive geometry modeling applications, and 3D modeling and character animation artists.

show abstract

A Family of Barycentric Coordinates for Co‐Dimension 1 Manifolds with Simplicial Facets

Cited by 10 publications

References 39 publications

Maximum Likelihood Coordinates

Maximum Likelihood Coordinates

Distributed localization algorithm for wireless sensor networks under minuscule bias injection attacks

A Survey on Cage‐based Deformation of 3D Models

Contact Info

Product

Resources

About