class AppDef_TheVariational (in fact it is AppParCurves_Variational) provides approximation according minimization of complex criterion:
J = w0*J0 + wq*Jq, where J0 is usual least square criterion and Jq is quality criterion. Jq is : Jq = w1*J1 + w2*J2 + w3*J3, where J1, J2 and J3 represent correspondently linear tension, linear flexion and linear jerk. w1+w2+w3 = 1 and can be set by SetCriteriumWeigth(...) If WithMinMax = true (case max error criterion) algorithm will try to minimize max error (max distance between given multipoint and obtained curve) too and try to make it less then given tolerance. In other case (WithMinMax = false) tolerance is used to define wq.
Best regards, Commenter-1