相关论文: Analysis-suitable unstructured T-splines: Multiple…

Portrait Stylization aims to imbue portrait photos with vivid artistic effects drawn from style examples. Despite the availability of enormous training datasets and large network weights, existing methods struggle to maintain geometric…

In this paper we introduce a $C^1$ spline space over mixed meshes composed of triangles and quadrilaterals, suitable for FEM-based or isogeometric analysis. In this context, a mesh is considered to be a partition of a planar polygonal…

Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…

A triangulated piecewise-linear minimal surface in Euclidean 3-space defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial…

A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven…

Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…

Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…

Finite elements has been proven to be an useful tool to discretize the vertical coordinate in the hydrostatic forecast models allowing to define model variables in full levels so that no staggering is needed. In the non-hydrostatic case a…

We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite…

Large-scale atomistic simulations are essential to bridge computational materials and chemistry to realistic materials and drug discovery applications. In the past few years, rapid developments of machine learning interatomic potentials…

This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw…

Reachable Minimally supported (RM) B-splines have been recently introduced as a novel B-spline--like basis. They feature local linear independence and admit a fast de Boor--like evaluation algorithm. These properties make them particularly…

This paper proposes an Adaptive Isogeometric Topology Optimization framework for shell structures based on PHT-splines (PHT-AITO). In this framework, the design domain, displacement, and density are represented by PHT-splines. Leveraging…

In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The extended Tchebycheff spaces and their dimensions are allowed to…

Subspace clustering methods based on expressing each data point as a linear combination of other data points have achieved great success in computer vision applications such as motion segmentation, face and digit clustering. In face…

Thin-plate spline (TPS) is a principal warp that allows for representing elastic, nonlinear transformation with control point motions. With the increase of control points, the warp becomes increasingly flexible but usually encounters a…

B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…