Communication of quantized information is frequently followed by a
computation.  In this case the distortion of the result of the
computation is of interest, yielding a functional source coding
problem.  We consider situations of distributed functional
quantization: distributed quantization of (possibly correlated)
sources followed by centralized computation of a function.  Under
smoothness conditions on the sources and function,
asymptotically-optimal regular scalar quantizer designs are
developed.  As extensions to the basic analysis, we characterize
a large class of functions for which regular quantization suffices
for optimality and we allow limited collaboration between source
encoders.  In the entropy-constrained setting, a single bit
communicated between encoders can have an arbitrarily-large effect
on functional distortion. In contrast, such communication has very
little effect in the fixed-rate setting.