Related papers: Adaptive Surface Meshes from Harmonic Maps
Mesh adaptation for finite element approximation is a procedure used in numerous applications. The use of thin and long anisotropic triangles improves the efficiency of the procedure. When piecewise linear finite elements are used, the…
Mesh reconstruction is a cornerstone process across various applications, including in-silico trials, digital twins, surgical planning, and navigation. Recent advancements in deep learning have notably enhanced mesh reconstruction speeds.…
Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity…
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…
We propose a fully automatic method for fitting a 3D morphable model to single face images in arbitrary pose and lighting. Our approach relies on geometric features (edges and landmarks) and, inspired by the iterated closest point…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation.…
The optimal traverse of irregular terrains made by ground mobile robots heavily depends on the adequacy of the cost models used to plan the path they follow. The criteria to define optimality may be based on minimizing energy consumption…
A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh…
We propose a harmonic surface mapping algorithm (HSMA) for electrostatic pairwise sums of an infinite number of image charges. The images are induced by point sources within a box due to a specific boundary condition which can be…
We present MeshODE, a scalable and robust framework for pairwise CAD model deformation without prespecified correspondences. Given a pair of shapes, our framework provides a novel shape feature-preserving mapping function that continuously…
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…
Recent advances have equipped 3D Gaussian Splatting with texture parameterizations to capture spatially varying attributes, improving the performance of both appearance modeling and downstream tasks. However, the added texture parameters…
Adaptive methods do not have a direct generalization to manifolds as the adaptive term is not invariant. Momentum methods on manifolds suffer from efficiency problems stemming from the curvature of the manifold. We introduce a framework to…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…
In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometrics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid…