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We apply state-of-the-art computational geometry methods to the problem of reconstructing a time-varying sea surface from tide gauge records. Our work builds on a recent article by Nitzke et al.~(Computers \& Geosciences, 157:104920, 2021)…
High-dimensional visual computer models are poised to revolutionize the space mission design process. The circular restricted three-body problem (CR3BP) gives rise to high-dimensional toroidal manifolds that are of immense interest to…
A weighted residual collocation methodology for simulating two-dimensional shear-driven and natural convection flows has been presented. Using a dyadic mesh refinement, the methodology generates a basis and a multiresolution scheme to…
We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an…
We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point.…
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific computing, but to date have ignored a very basic requirement: in many situations, surfaces must not pass through themselves or each…
Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…
In this work, we present a general, efficient, and provably robust representation for intrinsic triangulations. These triangulations have emerged as a powerful tool for robust geometry processing of surface meshes, taking a low-quality mesh…
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
We present a differentiable representation, DMesh, for general 3D triangular meshes. DMesh considers both the geometry and connectivity information of a mesh. In our design, we first get a set of convex tetrahedra that compactly tessellates…
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted,…
We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…
Meshes are commonly used as 3D maps since they encode the topology of the scene while being lightweight. Unfortunately, 3D meshes are mathematically difficult to handle directly because of their combinatorial and discrete nature. Therefore,…
Reconfigurable intelligent metasurfaces have been proposed as an efficient solution for improving wireless telecommunication systems in multiple scattering or reverberating media. Concurrently, topology optimization has been successfully…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that…
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…