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A novel static algorithm is proposed for numerical reparametrization of periodic planar curves. The method identifies a monitor function of the arclength variable with the true curvature of an open planar curve and considers a simple…

Numerical Analysis · Mathematics 2022-03-21 Kazuki Koga

In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…

Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface…

Differential Geometry · Mathematics 2015-02-16 Fatma Güler , Gülnur Şaffak Atalay , Ergin Bayram , Emin Kasap

In this paper we establish a framework for planar geometric interpolation with exact area preservation using cubic B\'ezier polynomials. We show there exists a family of such curves which are $5^{th}$ order accurate, one order higher than…

Numerical Analysis · Mathematics 2019-03-21 Geoffrey McGregor , Jean-Christophe Nave

The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered. The proposed method is based on the periodicity properties…

Numerical Analysis · Mathematics 2021-10-12 V. P. Denysiuk

We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…

Computational Engineering, Finance, and Science · Computer Science 2022-11-30 Albert Jiménez-Ramos , Abel Gargallo-Peiró , Xevi Roca

In this paper, we present a new Hermite type curve piecewise polynomial of C1 continuity on nonuniform grids. Depending on the location of the knots of the grid (uniform and nonuniform), the curve is quadratic or cubic. The approximation…

Numerical Analysis · Mathematics 2020-11-26 Oleg Stelia , Leonid Potapenko , Igor Stelia

Interpolating between points is a problem connected simultaneously with finding geodesics and study of generative models. In the case of geodesics, we search for the curves with the shortest length, while in the case of generative models we…

Machine Learning · Computer Science 2023-03-14 Łukasz Struski , Michał Sadowski , Tomasz Danel , Jacek Tabor , Igor T. Podolak

In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize…

Exactly Solvable and Integrable Systems · Physics 2021-07-08 Jun-ichi Inoguchi , Yoshiki Jikumaru , Kenji Kajiwara , Kenjiro T. Miura , Wolfgang K. Schief

A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each…

Numerical Analysis · Mathematics 2021-09-08 Zeyuan Zhou , Mei-Yuan Zhen , Kun Qu , Jin-Sheng Cai

We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape…

Graphics · Computer Science 2015-06-25 Dongsung Huh

Rapid satellite-to-site visibility determination is of great significance to coverage analysis of satellite constellations as well as onboard mission planning of autonomous spacecraft. This paper presents a novel self-adaptive Hermite…

Instrumentation and Methods for Astrophysics · Physics 2017-02-08 Chao Han , Xiaojie Gao , Xiucong Sun

We propose a multi-moment method for one-dimensional hyperbolic equations with smooth coefficient and piecewise constant coefficient. The method is entirely based on the backward characteristic method and uses the solution and its…

Numerical Analysis · Mathematics 2020-01-14 Kazufumi Ito , Tomoya Takeuchi

In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in $\mathbb{R}^{2}$. The main idea is to smooth the parametrization of the curve by…

Numerical Analysis · Mathematics 2023-05-25 Mohan Zhao , Kirill Serkh

In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…

Numerical Analysis · Mathematics 2016-01-08 Michele Antonelli , Carolina Vittoria Beccari , Giulio Casciola

Facial Image inpainting aim is to restore the missing or corrupted regions in face images while preserving identity, structural consistency and photorealistic image quality, a task specifically created for photo restoration. Though there…

Computer Vision and Pattern Recognition · Computer Science 2026-02-17 Abhigyan Bhattacharya , Hiranmoy Roy , Debotosh Bhattacharjee

For the classic aesthetic interpolation problem, we propose an entirely new thought: apply the golden section. For how to apply the golden section to interpolation methods, we present three examples: the golden step interpolation, the…

Graphics · Computer Science 2018-09-13 Ying He , Jincai Chang

We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision…

Numerical Analysis · Mathematics 2020-04-17 Ulrich Reif , Andreas Weinmann

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…

Numerical Analysis · Mathematics 2014-11-18 Costanza Conti , Lucia Romani , Michael Unser

This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…

Numerical Analysis · Mathematics 2022-09-02 Shuhao Cao , Long Chen , Ruchi Guo , Frank Lin