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Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
Surface parameterization plays an essential role in numerous computer graphics and geometry processing applications. Traditional parameterization approaches are designed for high-quality meshes laboriously created by specialized 3D…
Multi-view 3D surface reconstruction using neural implicit representations has made notable progress by modeling the geometry and view-dependent radiance fields within a unified framework. However, their effectiveness in reconstructing…
Complete control of electromagnetic fields requires particles that exhibit bianisotropic constituent parameters (i.e. permittivity, permeability, and chirality). Here, methods to analyze and synthesize two-dimensional, bianisotropic…
Speckle photography can be used to monitor deformations of solid surfaces. The measuring characteristics, such as range or lateral resolution depend heavily on the optical recording and illumination set-up. This paper shows how, by the…
It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an…
In this paper, we provide new discrete uniformization theorems for bounded, $m$-connected planar domains. To this end, we consider a planar, bounded, $m$-connected domain $\Omega$ and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$…
We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…
This note derives parametrizations for surfaces of revolution that satisfy an affine-linear relation between their respective curvature radii. Alongside, parametrizations for the uniform normal offsets of those surfaces are obtained. Those…
In this paper, we propose a topology optimization (TO) framework where the design is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry. In…
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…
Treatment of fields near domain boundaries is a long-standing problem in signal processing that has come into renewed focus following recent efforts in convolution-based multiscale coarse-graining and in machine-learned parameterizations…
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…
In this paper, we present an approach to enhance and improve the current normal map rendering technique. Our algorithm is based on semi-discrete Optimal Mass Transportation (OMT) theory and has a solid theoretical base. The key difference…
The asymptotic Dirichlet problem for harmonic maps from the hyperbolic plane into conformally compact Einstein manifolds is used to give a holographic characterization of conformal geodesics on the boundary at infinity, in a way deeply…
Optical metasurfaces are planar arrangements of subwavelength meta-atoms that implement a wide range of transformations on incident light. The design of efficient metasurfaces requires that the responses of and interactions among meta-atoms…
When two bodies get into contact, only a small portion of the apparent area is actually involved in producing contact and friction forces, because of the surface roughnesses. It is therefore crucial to accurately describe the morphology of…
Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point correspondences via the geodesic boundary value problem, solving…
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…