G2 interpolation of free form curve networks by biquintic Gregory patches Original Research Article

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.