Related papers: Characterization of Rational Ruled Surfaces

The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the…

We construct the topological partition function of local nontoric del Pezzo surfaces using the ruled vertex formalism.

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…

We give a systematic construction of uniruled surfaces in positive characteristic. Using this construction, we find surfaces of general type with non-trivial vector fields, surfaces with arbitrarily non-reduced Picard schemes as well as…

In this paper we present a new methodology for edge detection in digital images. The first originality of the proposed method is to consider image content as a parametric surface. Then, an original parametric local model of this surface…

We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration…

In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic…

An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…

Deep implicit surfaces excel at modeling generic shapes but do not always capture the regularities present in manufactured objects, which is something simple geometric primitives are particularly good at. In this paper, we propose a…

We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational surfaces of this kind under some technical restrictions…

Rule-based explanations provide simple reasons explaining the behavior of machine learning classifiers at given points in the feature space. Several recent methods (Anchors, LORE, etc.) purport to generate rule-based explanations for…

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…

In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane curves. This problem is solved by applying the upper bound…

This paper deals with relative normalizations of skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$. In section 2 we investigate some new formulae concerning the Pick invariant, the relative curvature, the relative mean curvature…

We study degree two unirational parameterizations of geometrically rational surfaces over the real field.

We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…

This paper studies properties of certain hypersurfaces in prime characteristic: we give a sufficient and necessary conditions for some classes of such hypersurfaces to have Finite $F$-representation Type (FFRT) and we compute the…

Riemann surfaces which are set by algebraic, algebroid and inverse functions are considered. A method for describing these Riemann surfaces by graphs is proposed. Each such Riemann surface is assigned to a special type of graph - profile.…

It is proved that a smooth rational surface in projective four-space, which is ruled by cubics or quartics has degree at most 12. It is also proved that a smooth rational surface in projective four-space which is the image of Fn by a linear…

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…