Related papers: High quality local interpolation by composite para…
We study those smooth complex hypersurfaces W in C^n having the property that all holomorphic functions of finite weighted L^p norm on W extend to entire functions with finite weighted L^p norm. Such hypersurfaces are called interpolation…
This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
Analysis-suitable $G^1$ (AS-$G^1$) multi-patch spline surfaces [4] are particular $G^1$-smooth multi-patch spline surfaces, which are needed to ensure the construction of $C^1$-smooth multi-patch spline spaces with optimal polynomial…
High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…
A mesh improvement methodology is pre- sented which aims to improve the quality of the worst elements in 3D meshes with non-planar surfaces which cannot be improved using traditional methods. A nu- merical optimisation algorithm, which…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
As a two-dimensional planar material with low depth profile, a metasurface can generate non-classical phase distributions for the transmitted and reflected electromagnetic waves at its interface. Thus, it offers more flexibility to control…
We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a nonsingular variety M `interpolates' between two other notions of characteristic classes for singular varieties, provided that the singular locus of X is smooth and…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over $\mathbb{C} ^n$ is not well-understood except for $n=1$. We present four examples of smooth affine algebraic hypersurfaces that…
Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…
High-quality quadrilateral mesh generation is a fundamental challenge in computer graphics. Traditional optimization-based methods are often constrained by the topological quality of input meshes and suffer from severe efficiency…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
We propose an end-to-end pipeline to robustly generate high-quality quadrilateral meshes for complex CAD models. An initial quad-dominant mesh is generated with frontal point insertion guided by a locally integrable cross field and a scalar…
Topology optimization is one of the engineering tools for finding efficient design. For the material interpolation scheme, it is usual to employ the SIMP (Solid Isotropic Material with Penalization) or the homogenization based interpolation…