Underdefined Constraint Systems

The item above (see Item Overdefined Consistent And Inconsistent Constraint Systems) discussed the overdefined state, when the constraint system has more constraints than needed. This item is dedicated to other situation natural to drawing process: in the sketch there are geometric objects not completely defined by constraints. In the beginning of the drawing process, the sketch may have no constraints at all, and all geometric objects may have full degrees of freedom. The more logical constraints and dimensions are added to the sketch, the less degrees of freedom remains for the objects. Completely defined sketch has no degrees of freedom at all. We should note that both situations can coexist in one drawing; some part of the sketch can be overdefined, the rest can be underdefined and at the same time some part of geometry may be completely defined.

Most solution methods available in C3D Solver were designed specifically for underdefined constraint systems. Besides that C3D Solver uses some benefits of underdefined cases to split the whole constraint system into a sequence of subsystems of smaller size calculated one after another. In these or other underdefined cases, the solver selects one of the optimal solutions based on the following principles:

• The number of geometric objects changed to satisfy the constraints should be as low as possible.

• Offset distances of the geometric objects modified by the solution from their initial approximation should be minimal (see Item Initial Approximation).