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The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We find all analytic surfaces in space R^3 such that through each point of the surface one can draw two circular arcs fully contained in the surface. The proof uses a new decomposition technique for quaternionic matrices.
In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…
This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
We use simple equations in order to compare the basins of attraction on the complex plane, corresponding to a large collection of numerical methods, of several order. Two cases are considered, regarding the total number of the roots, which…
We establish results about algebraic shifting of simplicial complexes and use them to compare different shifting operations. In particular, we show that each shifting operation does not decrease the number of facets, and that the exterior…
The solving of scientific and practical application connected with conducting of satellite experiments and measurement demand analysis of geometric and physic conditions according to different kind of models. This is forced in connect of…
This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…
Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
The impact of statistical methodologies on studying groundwater has been significant in the last several decades, due to cheaper computational abilities and presence of technologies that enable us to extract and measure more and more data.…
This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by…
We report on our project to find explicit examples of $K3$ surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for…
We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have…
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…