Reconstructing Generalized Staircase Polygons with Uniform Step Length

Reconstructing Generalized Staircase Polygons with Uniform Step Length

Visibility graph reconstruction, which asks us to construct a polygon that has a given visibility graph, is a fundamental problem with unknown complexity (although visibility graph recognition is known to be in PSPACE). We show that two classes of uniform step length polygons can be reconstructed efficiently by finding and removing rectangles formed between consecutive convex boundary vertices ...

A Staircase Illumination Theorem for Orthogonal Polygons

Let S be a simply connected orthogonal polygon in the plane, and let T be a horizontal (or vertical) segment such that T ′ ∩ S is connected for every translate T ′ of T . If every two points of S see via staircase paths a common translate of T , then there is a translate of T seen via staircase paths by every point of S. That is, some translate of T is a staircase illuminator for S. Clearly the...

Reconstructing Polygons from Scanner Data

Range scanners are used in many configurations: looking in to capture objects on a platform or in-situ, looking down to capture terrain or urban environments, or looking out to capture rooms or factory floors. In addition to point coordinates, different scanners may be able to provide surface labels, normals, or unobstructed segments of scanned rays. The problem of reconstructing a surface from...

Reconstructing polygons from moments with connections to array processing

Absstract-In this paper, we establish a set of results showing that the vertices of any simply connected planar polyg~nd region can be reconstructed from a finite number of its complex moments. These results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory, where in the Former, it is of iaterest to estimate the shape of an...

Visibility: Finding the Staircase Kernel in Orthogonal Polygons