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A construction of Calabi-Yaus as quotients of products of lower-dimensional spaces in the context of weighted hypersurfaces is discussed, including desingularisation. The construction leads to Calabi-Yaus which have a fiber structure, in…
Accurately rendering the appearance of fabrics is challenging, due to their complex 3D microstructures and specialized optical properties. If we model the geometry and optics of fabrics down to the fiber level, we can achieve unprecedented…
Binary image segmentation plays an important role in computer vision and has been widely used in many applications such as image and video editing, object extraction, and photo composition. In this paper, we propose a novel interactive…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
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…
Identifying trendline visualizations with desired patterns is a common and fundamental data exploration task. Existing visual analytics tools offer limited flexibility and expressiveness for such tasks, especially when the pattern of…
Using the techniques introduced by Corvaja and Zannier we solve the non-split case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane. In this situation…
A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. Averaging over boundary conditions leads to explicit formulas for the averaged spectral measure which can…
We present our implementation of an automated VLBI data reduction pipeline dedicated to interferometric data imaging and analysis. The pipeline can handle massive VLBI data efficiently which makes it an appropriate tool to investigate…
This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA…
We construct a set of shape-finders which determine shapes of compact surfaces (iso-density surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations as done earlier. The new indicators arise from…
Interferometric scattering microscopy (iSCAT) can image the dynamics of nanometer-scale systems. The typical approach to analyzing interferometric images involves intensive processing, which discards data and limits the precision of…
The accuracy-speed-memory trade-off is always the priority to consider for several computer vision perception tasks. Previous methods mainly focus on a single or small couple of these tasks, such as creating effective data augmentation,…
We investigate the seven sphere as a soft Lie algebra i.e. an algebra with structure functions instead of structure constants. We calculate its structure functions explicitly and also discuss some relevant points such as the validity of the…
Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface.…
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain spaces carrying higher-order data associated to the variety at non-singular points. In this note we will define a higher-order Jacobian matrix…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit…