Surfaces filling polygonal holes with G 1 quasi G 2 continuity

Two constructions of surfaces filling polygonal holes in piecewise B-spline bicubic surfaces with tangent plane continuity are described. The filling surfaces are obtained by minimization of functionals which impose penalty on curvature discontinuities. One of the functionals is a quadratic form, while the other functional is defined with a parameterization-independent formula. The resulting surfaces may be used instead of class G2 surfaces in practical applications; the penalty approach enables simplification of the construction, and reduction in the degree of patches filling the hole from (9,9) to (5,5) without any visible quality degradation. The notion of class Gn quasi Gm surfaces, i.e. class Gn surfaces optimized to approximate class Gm surfaces, is proposed.