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Related papers: Barycentric Coordinates as Interpolants

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This paper presents a method for enhancing the gray level images. This method takes part from the category of point transforms and it is based on interpolation functions. The latter have a graphic represented by polygonal lines. The…

Computer Vision and Pattern Recognition · Computer Science 2014-12-19 Vasile Patrascu

In this paper, the concept of the metric matrix is introduced to establish a concise and unified formulation for the inner product in barycentric coordinates. Building on this framework, we explore the intrinsic algebraic identities of…

General Mathematics · Mathematics 2025-05-13 Xi Feng

We give a formula for scalar product and distance in generalized barycentric coordinates for Euclidean and Pseudo-Euclidean spaces.

Metric Geometry · Mathematics 2023-01-02 Vladimir Zolotov

Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with…

Computational Geometry · Computer Science 2023-03-24 Benjamin Kenwright

The aim of this paper is a construction of quartic parametric polynomial interpolants of a circular arc, where two boundary points of a circular arc are interpolated. For every unit circular arc of inner angle not greater than $\pi$ we find…

Numerical Analysis · Mathematics 2020-06-22 Aleš Vavpetič

Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we…

Computational Geometry · Computer Science 2026-04-03 Michal Zamboj , Jakub Řada

Homographies -- a mathematical formalism for relating image points across different camera viewpoints -- are at the foundations of geometric methods in computer vision and are used in geometric camera calibration, image registration, and…

Computer Vision and Pattern Recognition · Computer Science 2016-08-02 Graham D. Finlayson , Han Gong , Robert B. Fisher

Encoding 3D points is one of the primary steps in learning-based implicit scene representation. Using features that gather information from neighbors with multi-resolution grids has proven to be the best geometric encoder for this task.…

Computer Vision and Pattern Recognition · Computer Science 2024-02-13 Arihant Gaur , G. Dias Pais , Pedro Miraldo

The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional…

Optics · Physics 2018-02-14 Anthony Vella , Miguel A. Alonso

In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations…

Spectral Theory · Mathematics 2009-03-05 W. M. Greenlee , L. Hermi

Bar charts are among the most frequently used visualizations, in part because their position encoding leads them to convey data values precisely. Yet reproductions of single bars or groups of bars within a graph can be biased. Curiously,…

Human-Computer Interaction · Computer Science 2021-08-20 Cristina R. Ceja , Caitlyn M. McColeman , Cindy Xiong , Steven L. Franconeri

Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…

Mathematical Physics · Physics 2014-09-25 Gennady V. Kovalev

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that…

Functional Analysis · Mathematics 2017-10-11 Daniel Schmitter , Julien Fageot , Anaïs Badoual , Pablo Garcia-Amorena , Michael Unser

We define barycentric coordinates on a Riemannian manifold using Karcher's center of mass technique applied to point masses for n+1 sufficiently close points, determining an n-dimensional Riemannian simplex defined as a "Karcher simplex."…

Numerical Analysis · Mathematics 2016-10-06 Stefan W. von Deylen , David Glickenstein , Max Wardetzky

Each convex combination of extreme points of a compact convex set represents a certain point of the convex set. Barycentric coordinates provide solutions to the inverse problem of expressing an element of a compact convex set as a convex…

Metric Geometry · Mathematics 2026-03-10 A. B. Romanowska , J. D. H. Smith , A. Zamojska-Dzienio

Penner coordinates are extended to the Teichm\"uller spaces of oriented closed surfaces.

Geometric Topology · Mathematics 2014-03-04 Rinat Kashaev

This paper presents a method for enhancing the gray level images. This presented method takes part from the category of point operations and it is based on piecewise linear functions. The interpolation nodes of these functions are…

Computer Vision and Pattern Recognition · Computer Science 2014-12-19 Vasile Patrascu

This work presents a simple alternative technique to observe the polarization of the skylight on Earth. Using a birefringent material and a polarizer to look at the polarized light from the blue sky, it is possible to see a colored pattern…

Physics Education · Physics 2024-08-20 Diogo Soga , Daniel M. Faes , Mikiya Muramatsu

The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special…

Algebraic Topology · Mathematics 2022-07-14 Emile Jacquard , Vidit Nanda , Ulrike Tillmann

The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…

Combinatorics · Mathematics 2021-04-01 László Németh