Motivated by the work of Gert K. Pedersen on a geometric function, which is defined on the unit ball of a C*-algebra and called the λ_u-function, the present author recently initiated a study of the λ_u-function in the more general setting of JB*-algebras. He used his earlier results on the geometry of the unit ball to investigate certain convex combinations of elements in a JB*-algebra and to obtain analogues of some related C*-algebra results, including a formula to compute λ_u-function on invertible elements in a JB*-algebra. The main purpose in this article is to investigate the computation of the λ_u-function on noninvertible elements in the unit ball of a JB*-algebra. Additional results that relate the λ_u-function to convex combinations, unitary rank, and distance to the invertibles in the C*-algebra setting are generalized to the JB*-algebra context. Results of G. K. Pedersen and M. Rordam are generalized. An open problem is presented.