Automatic inference of parametric equations in geometric modeling using dual kriging

This paper presents a novel application of dual kriging for the automatic inference of analytical equations of geometric entities. It is based on the combination of interpolation profiles representing generally classical shapes. These profiles are deduced from designer intuition of the shape of the curve, surface or solid. Dual kriging was successfully used for curve/surface modeling. It is a general method which incorporates several interpolation techniques such as piecewise interpolation, cubic splines, Bezier and NURBS curves/surfaces and solids in a single formulation. Elementary shapes such as conics, cylinders are represented exactly. Detailed examples of curve, surface and solid equations inference are presented