| Abstract: | Elements of surfaces that bound a phase (β) in a two phase mixture (α+β) may be classified as: (a) convex (++) if both principal curvatures are positive; (b) concave (? ?) if both are negative; and (c) saddle (+ ?) if one is positive and the other negative. This classification excludes the limiting cases for which one or both of the principal curvatures is zero. The traces of these surfaces that form the boundaries of the β areas on a representative two dimensional section may also be: (a) convex (+) if the local curvature is positive; or (b) concave (?) if it is negative. Line intercepts may be tabulated separately for intersections with convex (+) and concave (?) segments of boundary. This paper presents a derivation of fundamental stereological formulae that relate these counting measurements to three-dimensional geometric properties of the structure they sample. |
