Optimization Criterion

To optimize one or more outputs, there is the target criterion Smoothness that limits the variation of the stiffness (see Consideration of the Roughness) of a map or a curve. This factor is a weighted penalty term,

Equ. 8: Smoothness factor S_i

where S is the Smoothness factor and M the number of support points of the map or curve.

Different Smoothing Factors in X/Y Direction

For maps, Cube-3D and Cube-4D, the smoothing factor S is used per input direction. If only one value is given, the factor works for all directions. If a vector is given, each element corresponds to one input direction. In case of a map, e.g., one may set smoothness in X direction to 0.1 and in Y direction to 0.001 by specifying a vector [0.1 0.001].

The smoothing factor has to be a real number ≥ 0 and can be defined in the Optimization Step either via the Optimization Criteria button or by directly editing the column "Smoothness" in the parameter table.

Optimization Criteria Selection

For curves, maps, Cube-3D and Cube-4D, the gradients in each respective input direction can be constrained by defining a limit for the maximal and/or the minimal gradient. The gradient constraints can be defined in the Optimization Step via the Optimization Criteria button. All gradient constraints are handled as weak constraint by the optimizer.

You can also assign a weight to each set of gradient limits. This weight sets the priority of the gradient limits in relation to the primary optimization criteria. A higher weight makes the gradient limits more important.