On the Area of Overlap of Translated Polygons (1994)
| Citations: | 11 - 0 self |
BibTeX
@MISC{Mount94onthe,
author = {David M. Mount and Ruth Silverman and Angela Y. Wu},
title = {On the Area of Overlap of Translated Polygons},
year = {1994}
}
Years of Citing Articles
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Given two simple polygons P and Q in the plane and a translation vector t 2 R 2 , the area-of-overlap function of P and Q is the function Ar(t) = Area(P " (t +Q)), where t +Q denotes Q translated by t. This function has a number of applications in areas such as motion planning and object recognition. We present a number of mathematical results regarding this function. We also provide efficient algorithms for computing a representation of this function, and for tracing contour curves of constant area of overlap. The support of the National Science Foundation under grant CCR 93-10705 is gratefully acknowledged, as is the help of Sandy German in preparing this paper. A preliminary version of this paper appeared in Vision Geometry II , R.A. Melter and A.Y. Wu, Editors, Proc. SPIE 2060, 1993, 254--264. 1 Introduction An important geometric problem involving planar shapes is whether two simple polygons intersect one another. If the polygons do intersect it is often useful to acquire mo...
