28 citations · 95 across the 23 of their papers we have counts for
23 papers
Bivariate quaternionic factorizations and surfaces that decompose into two circles
Johanna Frischauf, Niels Lubbes, Hans-Peter Schröcker
We present an algebraic and geometric condition for bivariate quaternionic polynomials of arbitrary bidegree to have a univariate linear left or right factor. We apply this quatern…
Self-intersections of surfaces that contain two circles through each point
Niels Lubbes
We classify the singular loci of real surfaces in three-space that contain two circles through each point. We characterize how a circle in such a surface meets this loci as it move…
Irreducible components of sets of points in the plane that satisfy distance conditions
Niels Lubbes, Mehdi Makhul, Josef Schicho +1
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between th…
Calibrating Figures
Niels Lubbes, Josef Schicho
It is known that a camera can be calibrated using three pictures of either squares, spheres, or surfaces of revolution. We give a new method to calibrate a camera with the picture…
Calligraphs and sphere realizations
Matteo Gallet, Georg Grasegger, Niels Lubbes +1
We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredient…
Shapes of surfaces that contain a great and a small circle through each point
Niels Lubbes
We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are ho…
Coupler curves of moving graphs and counting realizations of rigid graphs
Georg Grasegger, Boulos El Hilany, Niels Lubbes
A calligraph is a graph that for almost all edge length assignments moves with one degree of freedom in the plane, if we fix an edge and consider the vertices as revolute joints. T…
Projective isomorphisms between rational surfaces
Bert Jüttler, Niels Lubbes, Josef Schicho
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of…
Reconstruction of rational ruled surfaces from their silhouettes
Matteo Gallet, Niels Lubbes, Josef Schicho +1
We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We de…
Möbius automorphisms of surfaces with many circles
Niels Lubbes
We classify real two-dimensional orbits of conformal subgroups such that the orbits contain two circular arcs through a point. Such surfaces must be toric and admit a Möbius automo…
Reconstruction of surfaces with ordinary singularities from their silhouettes
Matteo Gallet, Niels Lubbes, Josef Schicho +1
We present algorithms for reconstructing, up to unavoidable projective automorphisms, surfaces with ordinary singularities in three dimensional space starting from their silhouette…
Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces
Niels Lubbes
We classify webs of minimal degree rational curves on surfaces and give a criterion for webs being hexagonal. In addition, we classify Neron-Severi lattices of real weak del Pezzo…
Minimal degree rational curves on real surfaces
Niels Lubbes
We classify real families of minimal degree rational curves that cover an embedded rational surface. A corollary is that if the projective closure of a smooth surface is not biregu…
Kinematic generation of Darboux cyclides
Niels Lubbes, Josef Schicho
We state a relation between two families of lines that cover a quadric surface in the Study quadric and two families of circles that cover a Darboux cyclide.
Computing curves on real rational surfaces
Niels Lubbes
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
Computing basepoints of linear series in the plane
Niels Lubbes
We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for…
The number of realizations of a Laman graph
Jose Capco, Matteo Gallet, Georg Grasegger +3
Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph…
A degree bound for families of rational curves on surfaces
Niels Lubbes
We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the deg…
Translational and great Darboux cyclides
Niels Lubbes
A surface that is the pointwise sum of circles in Euclidean space is either coplanar or contains no more than 2 circles through a general point. A surface that is the pointwise pro…
Surfaces that are covered by two pencils of circles
Niels Lubbes
We list up to Möbius equivalence all possible degrees and embedding dimensions of real surfaces that are covered by at least two pencils of circles, together with the number of suc…
Families of bitangent planes of space curves and minimal non-fibration families
Niels Lubbes
We define a cone curve to be a reduced sextic space curve which lies on a quadric cone and does not go through the vertex. We classify families of bitangent planes of cone curves.…
Algorithms for singularities and real structures of weak Del Pezzo surfaces
Niels Lubbes
In this paper we consider the classification of singularities (Du Val) and real structures (Wall) of weak Del Pezzo surfaces from an algorithmic point of view. It is well known tha…
Lattice polygons and families of curves on rational surfaces
Niels Lubbes, Josef Schicho
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more ge…