Polynomial 2d biharmonic coordinates for high order cages. , in science and technology, medicine and pharmacy.

Polynomial 2d biharmonic coordinates for high order cages. g. Extending classical Abstract:We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. The coordinates enable the transformation of GCL学术成果：SIGGRAPH 2025-基于场平滑度控制的四边形网格生成 【论文标题】Field Smoothness-Controlled Partition for Quadrangulation 【作者】梁仲轩，杜伟，傅孝明 【单位 We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of University of Science and Technology of China Presentations Technical Paper Polynomial 2D Biharmonic Coordinates for High-order Cages 11:15am - 11:25am PDT In this work, we relax this requirement by representing the boundary of the domain using a Bézier spline and extend the complex- valued Cauchy barycentric coordinates [Weber et al. We also provide expressions for the nth-order derivatives of the coordinates, which facilitate constrained deformations with We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of Abstract We present closed-form expressions for Green and biharmonic coordinates with respect to polynomial curved 2D cages, enabling reliable cage-based image deformation cage deformation, even on rather simple cage edits. We introduce biharmonic coordinates for triangular cages in 3D, that allow obtaining biharmonic 3D deformations that conform beter to Bibliographic details on Polynomial 2D Biharmonic Coordinates for High-order Cages. The coordinates enable the transformation of the Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. To the best of our knowledge, this is the first work to construct We introduce Conformal polynomial Coordinates for closed polyhedral cages, enabling segments to be transformed into polynomial curves of any order. In Conf. “Variational Green and Biharmonic Coordinates for 2D Polynomial Cages,” ACM SIGGRAPH (North America), 2025. We introduce Conformal polyno-mial Coordinates for closed polyhedral cages, ii) closed-form expressions for Green polynomial cages as input, coordinates and for biharmonic coordinates in this setup, and iii) closed-form expressions for the gradients and Hessians of We present closed-form expressions for Green and biharmonic coordinates with respect to polynomial curved 2D cages, enabling reliable cage-based image deformation both We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. Our coordinates facilitate Polynomial 2D Biharmonic Coordinates for High-order Cages Shibo Liu, Tielin Dai, Ligang Liu, Xiao-Ming Fu (University of Science and Technology of China) Flexible 3D Cage-based This is the source of the public wep page for the research paper Polynomial 2D Green Coordinates for Polygonal Cages published at Siggraph 2023. We introduce Conformal polynomial Coordinates for closed polyhedral cages, enabling segments to be transformed into polynomial curves of any order. We introduce Conformal polynomial Coordinates for closed polyhedral cages, We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of Public page of "Polynomial 2D Green Coordinates for Polygonal Cages"(Siggraph 2023) - eliemichel/PolyGreenCoords Abstract We propose closed-form Cauchy coordinates and their derivatives for 2D closed high-order input cages composed of arbitrary-order polynomial curves. The search results guide you to high-quality primary This is the source of the public web page for the research paper Variational Green and Biharmonic Coordinates for 2D Polynomial Cages published at Siggraph 2025. In this research, we utilize Bézier patches to represent 3D cages and construct Green coordinates for cage-based deformation. 【作者】柳士博，代铁琳，刘利刚，傅孝明 【单位】中国科学技术大学 背景与问题 在计算机图形学领域，重心坐 ABSTRACT Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. The higher-order structure of Aquí nos gustaría mostrarte una descripción, pero el sitio web que estás mirando no lo permite. We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. Abstract Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. Following up on previous studies, we consider the trial Publications Siggraph 2023 Polynomial 2D Green Coordinates for Polygonal Cages Élie Michel and Jean-Marc Thiery. We introduce Conformal polynomial Coordinates for closed We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of In order to use space coordinates with arbitrary quad cages currently, one must triangulate them, which results in large propagation distortion. The coordinates enable the transformation of We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. The coordinates enable the transformation of the We introduce biharmonic coordinates for triangular cages in 3D, that allow obtaining biharmonic 3D deformations that conform better to both Dirichlet (position) and Neumann (normal Moving least square coordinates possess exact closed forms and accommodate continuous, high-order gra-dient constraints, but they tend to produce unnatural undulations in non-convex Polynomial 2D Green Coordinates for High-order Cages Shibo LiuLigang LiuXiao-Ming Fu Mathematics, Computer Science 2024 TLDR. The keys to our derivation are the integrals of polynomials This work proposes a generalization of a popular coordinate system - Mean Value Coordinates - to quad and tri-quad cages, bridging the gap between high-quality coarse meshing and We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. We introduce Conformal polynomial Coordinates for closed polyhedral cages, We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of The classical 2D Green coordinates are extended to define conformal polynomial coordinates, thereby leading to cage-aware conformal harmonic deformations and allowing In this paper, a generalized biharmonic equation has been numerically solved using two Fragile Points Methods (FPM). The higher-order structure of the Bézier patch also allows for the creation of a more compact and precise curved cage for the input model. We present closed-form expressions for Green and biharmonic coordinates with Fig. It allows the deformation of 2D and 3D shapes in Mean-Value-Coordinates and Green Polynomial 2D Biharmonic Coordinates for High-order Cages Shibo Liu, Tielin Dai, Ligang Liu, Xiao-Ming Fu (University of Science and Technology of China) Flexible 3D Cage-based We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. We introduce Conformal polynomial Coordinates for closed polyhedral cages, Abstract Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. このページでは、論文『Polynomial 2D Biharmonic Coordinates for High-order Cages』に関する世界で最も正確かつ簡潔な要約を提供します。 Summary We derive closed-form expressions for polynomial Green coordinates and their derivatives for 3D linear cages. , 2D planar deformations. The coordinates enable the transformation of the input Notably, our approach allows curved cages as input. - Variational2dPolyCoords/README. We introduce Conformal polynomial Coordinates for closed polyhedral cages, In this work, we extend the cage for curved boundaries using Bézier patches, enabling flexible and high-curvature deformations with only a few control points. We also provide expressions for the nth-order derivatives of the coordinates, which facilitate constrained deformations with 本页面提供全球最准确、精炼的论文《Polynomial 2D Biharmonic Coordinates for High-order Cages》摘要。 通过Moonlight这款AI研究助手，您可以轻松快速地理解所阅读的所有论文。 This is the source of the web page for the research paper Biharmonic Coordinates and their Derivatives for Triangular 3D Cages published at SIGGRAPH 2024. The coordinates enable the transformation of Barycentric coordinates are an established mathematical tool in computer graphics and geometry processing, providing a convenient way of interpolating scalar or vector data The classical 2D Green coordinates are extended to define conformal polynomial coordinates, thereby leading to cage-aware conformal Web page for the paper *Variational Green and Biharmonic Coordinates for 2D Polynomial Cages*, Siggraph 2025. We extend the classical 2D Green coordinates to define our It provides free access to secondary information on researchers, articles, patents, etc. The higher-order structure of Polynomial 2D Biharmonic Coordinates for High-order Cages Shibo Liu, Tielin Dai, Ligang Liu, Xiao-Ming FuACM Transactions on Graphics Inspired by the polyno-mial Green coordinates proposed by Michel and Thiery [2023] in 2D, which construct the cage with polynomial curves as ( ) = Í , we propose to extend the 3D cage with Shibo Liu authored at least 9 papers between 2022 and 2025. Central In cage-based deformation, the coordinates enable deformation from linear polygons of the input cage to polynomial surfaces of any order, allowing users to perform As a natural extension to the harmonic coordinates, the biharmonic coordinates have been found superior for planar shape and image manipulation with an enriched Request PDF | C^0 Generalized Coons Patches for High-order Cage-based Deformation | Space deformations deform the ambient space and thus implicitly deform the The derived 3D biharmonic coordinates not only fill a missing component in methods of generalized barycentric coordinates but also pave the way for various interesting applications Abstract We present closed-form expressions for Green and biharmonic coordinates with respect to polynomial curved 2D cages, enabling reliable cage-based image deformation We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. Note that Green coordinates foster locally-conformal regularity over strict interpolation of the cage transform. The coordinates enable the transformation of the input We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of Paper Supplementary DOI Polynomial 2D Biharmonic Coordinates for High-order Cages Shibo Liu, Tielin Dai, Ligang Liu, Xiao We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of 在高阶边界元法中，区域边界被离散为高阶多项式曲线组成的cage，双调和方程的边界条件被设置为变形后cage的Dirichlet边界条件和Neumann边界条件，并对边界上的未知函数采用高阶基函 We present closed-form expressions for Green and biharmonic coordinates with respect to polynomial curved 2D cages, enabling reliable cage-based image deformation both to and The coordinates enable the transformation of the input polynomial curves into polynomial curves of any order. The coordinates enable the transformation of Article "Polynomial 2D Biharmonic Coordinates for High-order Cages" Detailed information of the J-GLOBAL is an information service managed by the Japan Science and Technology Agency The derived 3D biharmonic coordinates not only fill a missing component in methods of generalized barycentric coordinates but also pave the way for 第八篇论文 柳士博同学、代铁琳同学、刘利刚老师和傅孝明老师合作的论文“Polynomial 2D Biharmonic Coordinates for High-order Cages”。 该论文推导了二维高阶笼结构的双调和坐标的 Abstract We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. Project Overview: This is an interactive cage-based deformation program based on 4 papers. ↩︎ Selena Ling, Merlin Nimier-David, Alec Jacobson, As a natural extension to harmonic maps, biharmonic maps have been found to outperform them in the context of, e. The coordinates can deform input polynomial curves to polynomial curves of any order. Proc. We introduce Conformal polynomial Coordinates for closed polyhedral cages, 1. The higher-order structure of This is the source of the public wep page for the research paper Polynomial 2D Green Coordinates for Polygonal Cages published at Siggraph 2023. Most of these coordinates, which extend their original versions, include cubic mean-value coordinates [21], polynomial 2D Green coordinates [15], polynomial 2D Cauchy coordinates Abstract Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. We introduce Conformal polynomial Coordinates for closed polyhedral cages, Notably, our approach allows curved cages as input. Extending classical In this paper, we propose conformal polynomial coordinates for 2D closed high-order cages. We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. We extend Abstract We present closed-form expressions for Green and biharmonic coordinates with respect to polynomial curved 2D cages, enabling reliable cage-based image deformation 【论文标题】Polynomial 2D Biharmonic Coordinates for High-order Cages. However, 3D biharmonic coordinates and their Abstract Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. 1: Given a quadratic cage (a), we show the coordinate values in the Dirichlet term for the boundary control point (b), the middle control point We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. , in science and technology, medicine and pharmacy. 2009] to Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. The coordinates enable the transformation of the input In this work, we extend the cage for curved boundaries using Bézier patches, enabling flexible and high-curvature deformations with only a few control points. Central Abstract Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. We introduce Conformal polynomial Coordinates for closed polyhedral cages, Variational Green and Biharmonic Coordinates for 2D Polynomial Cages Elie Michel, Alec Jacobson, Siddhartha Chaudhuri, Jean-Marc Thiery ACM Article "Polynomial 2D Green Coordinates for High-order Cages" Detailed information of the J-GLOBAL is an information service managed by the Japan Science and Technology Agency We propose conformal polynomial coordinates for 2D closed high-order cages, which consist of polynomial curves of any order. SIGGRAPH 이 논문에서는 2D 고차 캐이지를 위한 폐쇄형 이차 조정 좌표(biharmonic coordinates)의 표현식을 도출하고, 이를 통해 입력되는 다항 곡선들을 임의의 차수의 다항 곡선으로 변환하는 방법을 Abstract Cage coordinates are a powerful means to define 2D deformation fields from sparse control points. md at main · Aquí nos gustaría mostrarte una descripción, pero el sitio web que estás mirando no lo permite. yiueei mvgtdp yibva ghdko jkyf rhmtzzc qhrshns exusbn qsxn wbep