The Scaling of Digital Differential Analyzers

A method for computing the scales needed for programming a digital differential analyzer (DDA) is developed. DDA program (interconnection) maps containing integrators and servos are considered. The scales must satisfy ``equilibrium,´´ ``topological,´´ and ``boundary´´ constraints. These constraints are shown to be equivalent to a set of linear inequalities. Linear programming techniques are used to find both feasible and ``optimal´´ scales. The use of linear programming eliminates the need for the usual trial-and-error scaling techniques and makes the scheme amenable to programming on a general-purpose digital computer.