A restricted-orientation convex set is a set of points whose intersection with lines from some fixed set is empty or connected. This notion generalizes both standard convexity and orthogonal convexity. We explore basic properties of restricted-orientation convex sets in three dimensions. In particular, we establish analogs of the following properties of standard convex sets: The intersection of...

A restricted-orientation convex set is a set of points whose intersection with lines from some fixed set is empty or connected. This notion generalizes both standard convexity and orthogonal convexity. We explore basic properties of restricted-orientation convex sets in three dimensions. In particular, we establish analogs of the following properties of standard convex sets: The intersection of...

In conventional methods for detecting vanishing points and vanishing lines, the observed feature points are clustered into collections that represent different lines. The multiple lines are then detected and the vanishing points are detected as points of intersection of the lines. The vanishing line is then detected based on the points of intersection. However, for the purpose of optimization, ...

We propose a method of improving the reconstruction of edges and corners in surface meshes of sparsely populated point clouds by exploiting the presence of planes in the scene, the calculated geometry of the cameras and the images themselves. By robustly identifying co-planar points in the point cloud, isolating suitable plane-pairs for intersection, identifying the regions-of-interest along th...

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (2003) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi-Trotter Theorem ...

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (2003) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi-Trotter Theorem ...

In analytic geometry, Bézout’s theorem stated the number of intersection points two algebraic curves and Fulton introduced multiplicity at some point in local case. It is meaningful to give exact expression point. this paper, we mainly express R 2 id="M2"...

When using the original slope-intercept parameter-isation for the Hough transform, the resulting parameter space actually corresponds to the dual space. Indeed , lines are transformed into points, and for every point there is also a corresponding line. This paper presents a way of exploiting this special property, by the introduction of the Cascaded Hough Transform, or CHT for short. This allow...

Principal lattices in the plane are distributions of points particularly simple to use Lagrange, Newton or Aitken-Neville interpolation formulas. Principal lattices were generalized by Lee and Phillips, introducing three-pencil lattices, that is, points which are the intersection of three lines, each one belonging to a different pencil. In this contribution, a semicubical parabola is used to co...