Let S be a finite set of points in the plane and let T (S) be the set of intersection points between pairs of lines passing through any two points in S. We characterize all configurations of points S such that iteration of the above operation produces a dense set. We also discuss partial results on the characterization of those finite point-sets with rational coordinates that generate all of Q ...

Principal lattices are distributions of points in the plane obtained from a triangle by drawing equidistant parallel lines to the sides and taking the intersection points as nodes. Interpolation on principal lattices leads to particularly simple formulae. These sets were generalized by Lee and Phillips considering three-pencil lattices, generated by three linear pencils. Inspired by the additio...

Many photographs are taken in perspective. Techniques for rectifying resulting perspective distortions typically rely on the existence of parallel lines in the scene. In scenarios where such parallel lines are hard to automatically extract or manually annotate, the unwarping process remains a challenge. In this paper, we introduce an automatic algorithm to rectifying images containing textures ...

Given S1, a starting set of points in the plane, not all on a line, we define a sequence of planar point sets {Si}∞i=1 as follows. With Si already determined, let Li be the set of all the lines determined by pairs of points from Si , and let Si+1 be the set of all the intersection points of lines in Li . We show that with the exception of some very particular starting configurations, the limiti...

Refined topological relations play an important role in spatial database quality control. Currently, there is no unified and reasonable method to represent refined line/region line/line two-dimensional (2D) space. In addition, the existing independent models have some drawbacks such as incomplete type discrimination too many invariants. this paper, a are represented uniformly by sequence, dimen...

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are d...