Chord length distributions of infinitely long geometric figures

A transformation method for establishing chord length distributions for infinitely long “rods” of various cross-sections is presented. Here, the information on the two-dimensional cross section of the object is used to define the chord length distribution of the three-dimensional “rod”. r) be the chord length distribution density of a plane convex two-dimensional geometric figure X, for example of a circle. Let Y be the corresponding three-dimensional infinitely long geometric figure with the same cross-section X, for example, a right infinitely long circular cylinder. Then, the chord length distribution density A(r) of figure Y is completely defined in terms of P(r). An integral transform, which solves the problem for each convex X, Y, is evaluated and tested. This is useful for an effective characterization of long-stretched microparticles in micropowders via their chord length distribution. The spectrum of available A(r) functions is increased for a large class of geometric figures. ample, the new transformation allows the evaluation of A(r,a,b) of an infinitely long elliptical cylinder with semiaxes a, b based on P(r,a,b) of an ellipse X.