Conventional methods for solving intersections between two offset parametric surfaces often include iteratively using computationally expensive SSI (surface/surface intersections) algorithm. In addition, these methods ignore the relations between the intersection curves of parametric surfaces with different offset distances. The algorithm presented in this paper, makes full use of the topologic...

We consider a restricted version of the general Set Covering problem in which each set in the given set system intersects with any other set in at most 1 element. We show that the Set Covering problem with intersection 1 cannot be approximated within a o(log n) factor in random polynomial time unless N P ZT IM E(n O(log log n)). We also observe that the main challenge in derandomizing this redu...

In the literature of graph recognition algorithms, two of the most extensively covered graphs are interval graphs and permutation graphs [6, 2]. One way of generalizing both interval graphs and permutation graphs is the intersection graph of a collection of trapezoids with corner points lying on two parallel lines. Such a graph is called the trapezoid graph [3, 4]; Ma and Spinrad [8] show that ...

In this paper, we present a generic 3-D modeling for analyzing court-net sports videos, which enables to map points in the real-world coordinates to the image coordinates. To this end, we propose a two-step algorithm to extract the feature lines and points from two perpendicular planes (ground and net plane) for determining the camera calibration parameters. In the first step, we bridge the gap...

We investigate and visualize the manifold M of planes that intersect six straight lines of real projective three space in points of a conic section. It is dual to the apex-locus of the cones of second order that have six given tangents. In general M is algebraic of dimension two and class eight. It has 30 single and six double lines. We consider special cases, derive an algebraic equation of th...

In central catadioptric systems 3D lines are projected into conics. In this paper we present a new approach to extract conics in the raw catadioptric image, which correspond to projected straight lines in the scene. Using the internal calibration and two image points we are able to compute analytically these conics which we name hypercatadioptric line images. We obtain the error propagation fro...

We consider special critical points in multicomponent fluid mixtures, where critical phenomena occur between three phases simultaneously. We show that although such points may be the intersection of three lines of critical points, they are not in general analogous to the tricritical points originally proposed by Gr iffiths. Rather the three lines are part of a single surface of critical points ...

This paper presents a marching method for computing intersection curves between two solids represented by subdivision surfaces of Catmull-Clark or Loop type. It can be used in trimming and boolean operations for subdivision surfaces. The main idea is to apply a marching method with geometric interpretation to trace the intersection curves. We first determine all intersecting regions, then find ...

We first recall results on the boundary of the so-called admissible set for state and input constrained nonlinear systems, namely that the boundary is made up of two parts: one included in the state constraints and its complement called the barrier, made of integral curves that satisfy a minimum-like principle. Then we define the notions of barrier stopping points by intersection and by self-in...