相关论文: Interactive $G^1$ and $G^2$ Hermite Interpolation …
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…