Related papers: A package for computing implicit equations of para…
Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an…
Every surface that is intrinsically polyhedral can be represented by a portalgon: a collection of polygons in the Euclidean plane with some pairs of equally long edges abstractly identified. While this representation is arguably simpler…
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to…
We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…
Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…
Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural…
Results of number of geometric operations (often used in technical practise, as e.g. the operation of blending) are in many cases surfaces described implicitly. Then it is a challenging task to recognize the type of the obtained surface,…
Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…
We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples,…
We study analytic surfaces in 3-dimensional Euclidean space containing two circular arcs through each point. The problem of finding such surfaces traces back to the works of Darboux from XIXth century. We reduce finding all such surfaces to…
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
Motivated by the interest in computing explicit formulas for resultants and discriminants initiated by B\'ezout, Cayley and Sylvester in the eighteenth and nineteenth centuries, and emphasized in the latest years due to the increase of…
Surface parameterization is widely used in computer graphics and geometry processing. It simplifies challenging tasks such as surface registrations, morphing, remeshing and texture mapping. In this paper, we present an efficient algorithm…
It is known that every real orthogonal matrix can be brought into the domain of the Cayley transform by multiplication with a suitable diagonal signature matrix. In this paper we provide a constructive and numerically efficient algorithm…
We deploy algebraic complexity theoretic techniques for constructing symmetric determinantal representations of for00504925mulas and weakly skew circuits. Our representations produce matrices of much smaller dimensions than those given in…
New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families…
Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization.…
Boundary conforming coordinates are commonly used in plasma physics to describe the geometry of toroidal domains, for example, in three-dimensional magnetohydrodynamic equilibrium solvers. The magnetohydrodynamic equilibrium configuration…