相关论文: Simple Methods For Drawing Rational Surfaces as Fo…
A rational elliptic surface with section is a smooth, rational, complex, projective surface $\mathcal{X}$ that admits a relatively minimal fibration $f: \mathcal{X}\longrightarrow \bbP^1$ such that its general fibre is a smooth irreducible…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
Welschinger invariants enumerate real nodal rational curves in the plane or in another real rational surface. We analyze the existence of similar enumerative invariants that count real rational plane curves having prescribed non-nodal…
We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general…
We present an approach to finding the implicit equation of a planar rational parametric cubic curve, by defining a new basis for the representation. The basis, which contains only four cubic bivariate polynomials, is defined in terms of the…
Let S be a smooth cubic surface defined over a field K. As observed by Segre and Manin, there is a secant and tangent process on S that generates new K-rational points from old. It is natural to ask for the size of a minimal generating set…
Orthogonal graph drawing has many applications, e.g., for laying out UML diagrams or cableplans. In this paper, we present a new pipeline that draws multigraphs orthogonally, using few bends, few crossings, and small area. Our pipeline…
In this paper we compute upper bounds for the number of ordinary triple points on a hypersurface in $P^3$ and give a complete classification for degree six (degree four or less is trivial, and five is elementary). But the real purpose is to…
We design and analyze an algorithm for computing rational points of hypersurfaces defined over a finite field based on searches on "vertical strips", namely searches on parallel lines in a given direction. Our results show that, on average,…
Control architectures are often implemented in a layered fashion, combining independently designed blocks to achieve complex tasks. Providing guarantees for such hierarchical frameworks requires considering the capabilities and limitations…
Given two planar graphs that are defined on the same set of vertices, a RAC simultaneous drawing is one in which each graph is drawn planar, there are no edge overlaps and the crossings between the two graphs form right angles. The…
In this paper, we prove a general result computing the number of rational points of bounded height on a projective variety $V$ which is covered by lines. The main technical result used to achieve this is an upper bound on the number of…
Shape abstraction is an important task for simplifying complex geometric structures while retaining essential features. Sweep surfaces, commonly found in human-made objects, aid in this process by effectively capturing and representing…
We give an algorithm that, for a given value of the geometric genus $p_g,$ computes all regular product-quotient surfaces with abelian group that have at most canonical singularities and have canonical system with at most isolated base…
Octilinear graph drawings are a standard paradigm extending the orthogonal graph drawing style by two additional slopes (+1 and -1). We are interested in two constrained drawing problems where the input specifies a so-called representation,…
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
We present a novel and effective method for detecting 3D primitives in cluttered, unorganized point clouds, without axillary segmentation or type specification. We consider the quadric surfaces for encapsulating the basic building blocks of…
We determine the Cox rings of the minimal resolutions of cubic surfaces with at most rational double points, of blow ups of the projective plane at non-general configurations of six points and of three dimensional smooth Fano varieties of…
We prove the sharp bound of at most 64 lines on complex projective quartic surfaces (resp. affine quartics) that are not ruled by lines. We study configurations of lines on certain non-K3 surfaces of degree four and give various examples of…
When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is…