  We extend previous work on Schwarz-Chrsitoffel mappings, including the
special cases when the image is a convex polygon or its complement. We center
our analysis on the relationship between the pre-Schwrazian of such mappings
and Blaschke products. For arbitrary Schwarz-Christoffel mappings, we resolve
an open question in \cite{ChDO2} that relates the degrees of the associated
Blaschke products with the number of convex and concave vertices of the
polygon. In addition, we obtain a sharp sufficient condition in terms of the
exterior angles for the injectivity of a mapping given by the
Schwarz-Christoffel formula, and study the geometric interplay between the
location of the zeros of the Blaschke products and the separation of the
pre-vertices.
