G interpolation of free form curve networks by biquintic Gregory patches

The problem of interpolating a free form curve network with irregular topology is investigated in order to create a curvature continuous surface. The spanning curve segments are parametric quintic polynomials, the interpolating surface elements are biquintic Gregory patches. A necessary compatibility condition is formulated and proved which need to be satisfied at each node of the curve network. Constraints are derived for assuring G² continuity between biquintic Gregory patches, which share a common side or a common corner point. The above conditions still leave certain geometric freedom for defining the entire G² surface, so following some analysis a particular construction is presented, by which after computing the principle curvatures at each node the free parameters are locally set for each interpolating Gregory patch.