  The plane case of central configurations with four different masses is
analyzed theoretically and is computed numerically. We follow Dziobek's
approach to four body central configurations with a direct implicit method of
our own in which the fundamental quantities are the quotient of the directed
area divided by the corresponding mass and a new simple numerical algorithm is
developed to construct general four body central configurations. This tool is
applied to obtain new properties of the symmetric and non-symmetric central
configurations. The explicit continuous connection between three body and four
body central configurations where one of the four masses approaches zero is
clarified. Some cases of coorbital 1+3 problems are also considered.
