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Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…
As a two-dimensional planar material with low depth profile, a metasurface can generate non-classical phase distributions for the transmitted and reflected electromagnetic waves at its interface. Thus, it offers more flexibility to control…
We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise…
We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis…
An accurate method for designing transmissive metasurfaces is presented that provides perfect transmission while transforming the amplitude and phase of the wavefront. The designed metasurfaces consist of three spatially-varying, electric…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…
In this short note, we propose to extend differentiability (with respect to a multidimensional parameter) of a normalized eigenfunction associated to the simple, dominating eigenvalue of the weighted transfer operator for a uniformly…
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in…
Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is…
We study harmonic surfaces in $\mathbb{R}^3$ through the framework of harmonic Enneper immersions and prove a superposition principle for such surfaces. We prove that minimal and maximal surfaces admit a decomposition into harmonic…
In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…
We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
The Weierstrass representation for minimal surfaces in $\mathbb{R}^3$ provides a flexible method for constructing minimal surfaces of arbitrary genus. The topological limitations of minimal surfaces interfere with this providing a more…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
This work concerns a detailed review of data analysis methods used for remotely sensed images of large areas of the Earth and of other solid astronomical objects. In detail, it focuses on the problem of inferring the materials that cover…
We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can…
Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered…
We consider harmonic diffeomorphisms to a fixed hyperbolic target $Y$, from a family of domain Riemann surfaces degenerating along a Teichm\"{u}ller ray. We use the work of Minsky to show that there is a limiting harmonic map from the…