  A comprehensive study is performed of general massive, scalar, two-loop
Feynman diagrams with three external legs. Algorithms for their numerical
evaluation are introduced and discussed, numerical results are shown for all
different topologies, and comparisons with analytical results, whenever
available, are performed. An internal cross-check, based on alternative
procedures, is also applied. The analysis of infrared divergent configurations,
as well as the treatment of tensor integrals, will be discussed in two
forthcoming papers.
