The importance of digital geometry in image processing is well documented. To understand global properties of digital spaces and manifolds we need a solid understanding of local pr...
This paper presents a formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assi...
The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid gr...
We show that (A), 14 points on the boundary of a Jordan curve, and (B), 16 points in convex position encircled by a Jordan curve, cannot be shattered by interior visibility domains...
Consider a closed curve in the plane that does not intersect itself; by the Jordan-Schoenflies Theorem, it bounds a distorted disk. Now consider a closed curve that intersects its...