Related papers: Adaptive Surface Meshes from Harmonic Maps
Recently, the mapping approach to surface hopping (MASH) was proposed as a method to simulate the non-adiabatic dynamics of two-level systems. It was shown that the method possesses many desirable qualities, both theoretically and through…
As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…
In this work, we address the limitation of surface fitting-based grasp planning algorithm, which primarily focuses on geometric alignment between the gripper and object surface while overlooking the stability of contact point distribution,…
Extracting high-fidelity mesh surfaces from Signed Distance Fields has become a fundamental operation in geometry processing. Despite significant progress over the past decades, key challenges remain namely, how to automatically capture the…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
Classically, anisotropic surface wave tomography is treated as an optimisation problem where it proceeds through a linearised two-step approach. It involves the construction of 2D group or phase velocity maps for each considered period,…
In this paper we introduce a new type of symmetrization, which preserves the anisotropic perimeter of the level sets of a suitable concave smooth function, in order to prove sharp comparison results for solutions of a class of homogeneous…
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…
We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…
In this paper, we propose a stochastic geometric iterative method to approximate the high-resolution 3D models by finite Loop subdivision surfaces. Given an input mesh as the fitting target, the initial control mesh is generated using the…
Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field…
Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…
This paper presents an alternative formulation of the ASPH algorithm for evolving anisotropic smoothing kernels, in which the geometric approach of Shapiro et al. (1996; Paper I) is replaced by an approach involving a local transformation…
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…
Image alignment by mesh warps, such as meshflow, is a fundamental task which has been widely applied in various vision applications(e.g., multi-frame HDR/denoising, video stabilization). Traditional mesh warp methods detect and match image…