  In the recent paper "On a formula for sets of constant width in 2D", Comm.
Pure Appl. Anal. 18 (2019), 2117-2131, we gave a constructive formula for all
2d sets of constant width. Based on this result we derive here a formula for
the parametrization of the boundary of bodies of constant width in 3
dimensions, depending on one function defined on S^2. Each such function gives
a minimal value r_0 and for all r \ge r_0 one finds a body of constant width
2r. Moreover, we show that all bodies of constant width in 3d have such a
parametrization. The last result needs a tool that we describe as 'shadow
domain' and that is explained in an appendix. The construction is explicit and
and offers a parametrization different from the one given by T. Bayen, T.
Lachand-Robert and \'E. Oudet, "Analytic parametrization of three-dimensional
bodies of constant width" in Arch. Ration. Mech. Anal., 186 (2007), 225-249.
