The main problems in the computerization of discrete goods production
lie in the sheer complexity of developing scientific principles for fo
rmalizing their design and manufacture. This paper first summarizes a
broad framework for understanding the current state of technology usin
g a (function, form, fabrication) triad. Geometric modeling of form pl
ays a central role within this framework, and recent research results
are presented in five related topics: 1) virtual design and manufactur
ing, 2) massively parallel processing, 3) multi-representation free-fo
rm modeling, 4) Numerical Control (NC) machining simulation and verifi
cation, and 5) enterprise-wide integration. The paper concludes with e
volving trends in network-centric computing, and its impact on manufac
turing in the 21st century.