Related papers: Construction of Smooth Isogeometric Function Space…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
Given a smooth bounded planar domain, we construct a compact set on the boundary s.t. its characteristic function is not the trace of a least gradient function. This generalize the construction of Spradlin and Tamasan [ST14] on the disc.
Given values of a piecewise smooth function $f$ on a square grid within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. Standard approximation techniques achieve reduced approximation orders near the boundary of…
We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we…
We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.
In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain…
In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis-Russo type identity and a co-area formula are stated with applications to deviation inequalities…
In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and…
Geometrically continuous splines are piecewise polynomial functions defined on a collection of patches which are stitched together through transition maps. They are called $G^{r}$-splines if, after composition with the transition maps, they…
In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatness on bounded generic convex domains.…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating…
Shearlet systems have so far been only considered as a means to analyze $L^2$-functions defined on $\R^2$, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial…
Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…
In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit…
The parameterization of closed surfaces typically requires either multiple charts or a non-planar domain to achieve a seamless global mapping. In this paper, we propose a numerical framework for the seamless parameterization of genus-zero…
We study several connected problems of holomorphic function spaces on homogeneous Siegel domains. The main object of our study concerns weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II. These problems include:…