Signed Chord Length Distribution. I

Understand

In this paper is discussed an application of signed measures (charges) to description of segment and chord length distributions in nonconvex bodies.

• The signed distribution may naturally appears due to definition via derivatives of nonnegative autocorrelation function simply related with distances distribution between pairs of points in the body.
• In the work is suggested constructive geometrical interpretation of such derivatives and illustrated appearance of "positive" and "negative" elements similar with usual Hanh-Jordan decomposition in measure theory.
• The construction is also close related with applications of Dirac method of chords.