Abstract

In this paper we define a new linearity measure for closed curves. We start with simple closed curves which represent the boundaries of bounded planar regions. It turns out that the method can be extended to closed curves which self-intersect and also to certain configurations consisting of several curves, including open curve segments. In all cases, the measured linearities range over the interval (0,1], and do not change under translation, rotation and scaling transformations of the considered curve. In addition, the highest possible linearity (which is 1) is reached if and only if the measured curve consists of two overlapping (i.e. coincident) straight line segments. The new linearity measure is theoretically well founded and all related statements are supported with rigorous mathematical proofs.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.