Related papers: New Geometric Continuity Solution of Parametric Su…
In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant theoretic quotients for which semistability is not necessarily the…
The article completes the research of two-point G$^2$ Hermite interpolation problem with spirals by inversion of conics. A simple algorithm is proposed to construct a family of 4th degree rational spirals, matching given G$^2$ Hermite data.…
In this paper, we study bi-Hermitian metrics on complex surfaces with split holomorphic tangent bundle and construct 2 types of metric cones. We introduce a new type of fully non-linear geometric PDE on such surfaces and establish smooth…
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…
The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula for a parametrized surface.
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
Hermite methods, as introduced by Goodrich et al., combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite…
This paper attempts to study the continuity of the Hurwitz metric in arbitrary proper subdomains of the complex plane and to introduce a new invariant metric bi-Lipschitz equivalent to the Hurwitz metric in hyperbolic domains. The lower…
In two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the…
Recently, parametric mappings have emerged as highly effective surface representations, yielding low reconstruction error. In particular, the latest works represent the target shape as an atlas of multiple mappings, which can closely encode…
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…
This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
In this paper, we study conjugacy invariants for 2-dimensional diffeomorphisms with homoclinic cubic tangencies (two-sided tangencies of the lowest order) under certain open conditions. Ordinary arguments used in past studies of conjugacy…
We produce implicit equations for general biquadratic (order 2x2) B\'ezier triangle and quadrilateral surface patches and provide function evaluation code, using modern computing resources to exploit old algebraic construction techniques.
This paper aims to study the existence of asymmetric solutions for the two-dimensional generalized surface quasi-geostrophic (gSQG) equations of simply connected patches for $\alpha\in[1,2)$ in the whole plane, where $\alpha=1$ corresponds…