A VLSI chip for ray tracing bicubic patches in Bezier form is explored. The purpose of the chip is to calculate the intersection point of a ray with the bicubic patch to a specified level of accuracy, returning the location of the intersection on the patch and on the ray. This is done by computing the intersection of the ray with a bounding volume of the patch and repeatedly subdividing the pat...

Recently, Pawlik et al. have shown that triangle-free intersection graphs of line segments in the plane can have arbitrarily large chromatic number. Specifically, they construct triangle-free segment intersection graphs with chromatic number Θ(log log n). Essentially the same construction produces Θ(log log n)-chromatic triangle-free intersection graphs of a variety of other geometric shapes—th...

Uncontrolled intersections are the intersections where there are no external signs or signals to control the movement of vehicles. In mixed traffic conditions priority rules are often violated by the road users. In All-way-stop-controlled intersections (AWSC), the vehicle should stop themselves before they enter the intersection and should check whether any vehicles are present in the other app...

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G there corresponds a circle. If two vertices are connected by an edge in G then the corresponding circles intersect with an intersection angle in (0, π) and these intersection points can be associated to the dual graph G. Two sequences of circle patterns are ...

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of social networks including common-interest networks, collaboration networks, and actor networks. Simply put, a random intersection graph is constructed by assi...

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for graphs with small intersection number and random intersection graphs (a model in which each one of m labels is chosen independently with probability p by each ...

Given a system S of simple continuous curves (``strings'') in the plane, we can define a graph GS as follows. Assign a vertex to each curve, and connect two vertices by an edge if and only if the corresponding two curves intersect. GS is called the intersection graph of S. Not every graph is an intersection graph of a system of curves [EET76] (see Fig. 1 for a simple example). This implies that...

In this paper we use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that are nonlinear convolutions that can be expressed as supremum (resp. infimum) of fuzzy intersection (resp. union) norms. Our emphasis and differences with many previous works is the construction of pairs of fuzzy dilation (sup of fuzzy intersec...

‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...