Early constraint solvers used propagation techniques that were inadequate for solving simultaneous constraint problems. Simultaneous problems, also called variational problems, require solving systems of nonlinear equations and can be approached using a variety of numerical techniques such as Newton iteration or relaxation. DCM was the first commercial system to allow algebraic solutions to constraint problems, thereby achieving robustness previously not possible in variational solvers.

The ideal geometric constraint solver should exhibit the fundamental properties of persistence and of stability. By persistence is meant that, after a change to the dimensional constraint values, returning to the prior values always means returning to the original configuration. D-Cubed calls the persistence property a lack of hysteresis, a term familiar from physics, DCM excels here by paying close attention to the chirality (see below) of a solution. Stability means that small changes in constraint values do not...

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