  We present the analysis of the phase space geometry of 2 $\rightarrow$ 3
reaction for the general case of nonzero and unequal particle masses. Its
purpose is to elaborate an alternative approach to the problem of integration
over phase space which does not exploit the Monte Carlo principle. The fast and
effective algorithm of integration based on Gauss method is developed for
treating 1--dimensional distributions in two--particle invariant variables. The
algorithm is characterized by significantly improved accuracy and it can meet
requirements of interactive processing.
