313 citations · 473 across the 16 of their papers we have counts for
20 papers
Heat kernel asymptotics for scaling limits of isoradial graphs
Simon Schwarz, Anja Sturm, Max Wardetzky
We consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptoti…
Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics
Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl +1
The metric tensor of a Riemannian manifold can be approximated using Regge finite elements and such approximations can be used to compute approximations to the Gauss curvature and…
Weak topologies for unbounded nets in CAT() spaces
Philip Miller, Arian Berdellima, Max Wardetzky
Weak topologies that yield weak convergence for bounded sequences and nets in CAT() spaces have been studied in the past. We are here concerned with weak topologies that yield w…
Efficient Random Walks on Riemannian Manifolds
Simon Schwarz, Michael Herrmann, Anja Sturm +1
According to a version of Donsker's theorem, geodesic random walks on Riemannian manifolds converge to the respective Brownian motion. From a computational perspective, however, ev…
A mixed finite element method with piecewise linear elements for the biharmonic equation on surfaces
Oded Stein, Eitan Grinspun, Alec Jacobson +1
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of bounda…
A Smoothness Energy without Boundary Distortion for Curved Surfaces
Oded Stein, Alec Jacobson, Max Wardetzky +1
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for…
Elastic energy regularization for inverse obstacle scattering problems
Julian Eckhardt, Ralf Hiptmair, Thorsten Hohage +2
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bend…
Variational Convergence of Discrete Elasticae
Sebastian Scholtes, Henrik Schumacher, Max Wardetzky
We discuss a discretization by polygonal lines of the Euler-Bernoulli bending energy and of Euler elasticae under clamped boundary conditions. We show Hausdorff convergence of the…
Natural Boundary Conditions for Smoothing in Geometry Processing
Oded Stein, Eitan Grinspun, Max Wardetzky +1
In geometry processing, smoothness energies are commonly used to model scattered data interpolation, dense data denoising, and regularization during shape optimization. The squared…
Topology determines force distributions in one-dimensional random spring networks
Knut M. Heidemann, Andrew O. Sageman-Furnas, Abhinav Sharma +3
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technolog…
Topology counts: force distributions in circular spring networks
Knut M. Heidemann, Andrew O. Sageman-Furnas, Abhinav Sharma +3
Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous and, althou…
Distortion estimates for barycentric coordinates on Riemannian simplices
Stefan W. von Deylen, David Glickenstein, Max Wardetzky
We define barycentric coordinates on a Riemannian manifold using Karcher's center of mass technique applied to point masses for n+1 sufficiently close points, determining an n-dime…
Variational Convergence of Discrete Minimal Surfaces
Henrik Schumacher, Max Wardetzky
Building on and extending tools from variational analysis, we prove Kuratowski convergence of sets of simplicial area minimizers to minimizers of the smooth Douglas-Plateau problem…
On the incompressibility of cylindrical origami patterns
Friedrich Bös, Etienne Vouga, Omer Gottesman +1
The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the de…
A discrete parametrized surface theory in R^3
Tim Hoffmann, Andrew O. Sageman-Furnas, Max Wardetzky
We propose a discrete surface theory in that unites the most prevalent versions of discrete special parametrizations. This theory encapsulates a large class of discre…
Elasticity of 3D networks with rigid filaments and compliant crosslinks
Knut M. Heidemann, Abhinav Sharma, Florian Rehfeldt +2
Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at small strains, but stiffen dramatically at high strains. Experiments have sh…
Persistence Barcodes versus Kolmogorov Signatures: Detecting Modes of One-Dimensional Signals
Ulrich Bauer, Axel Munk, Hannes Sieling +1
We investigate the problem of estimating the number of modes (i.e., local maxima) - a well known question in statistical inference - and we show how to do so without presmoothing t…
Geodesics in Heat
Keenan Crane, Clarisse Weischedel, Max Wardetzky
We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and…
Optimal topological simplification of discrete functions on surfaces
Ulrich Bauer, Carsten Lange, Max Wardetzky
We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance δ from a given input function. The result is achieved…
Uniform convergence of discrete curvatures from nets of curvature lines
Ulrich Bauer, Konrad Polthier, Max Wardetzky
We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explici…