We took up the challenge by implementing the modeling of top-quality curves and surfaces. Our geometric modeling system offers the C3D FairCurveModeler component, which is designed to model so-called Class F curves that meet the following requirements:
- the minimal number of reference points of a modeled spline trajectory and a high, not lower than the 4th, order of smoothness;
- smooth torsion of a spatial curve;
- limiting the maximal value of the curvature and the rate of its change;
- Minimization of the potential energy functional.
Class F curves are modeled with methods provided by our C3D FairCurveModeler. The methods generate high-quality curves that meet exacting smoothness criteria, and so offer the following advantages:
- sustainable shape generation (isogeometricity);
- invariance to affine transformations and projections;
- the possibility of isogeometric approximation of analytical curves that preserves their basic features;
- flexible and various API.