Curve networks compatible with G2G2 surfacing

Prescribing a network of curves to be interpolated by a surface model is a standard approach in geometric design. Where n   curves meet, even when they afford a common normal direction, they need to satisfy an algebraic condition, called the vertex enclosure constraint, to allow for an interpolating piecewise polynomial C1C1 surface. Here we prove the existence of an additional, more subtle constraint that governs the admissibility of curve networks for G2G2 interpolation. Additionally, analogous to the first-order case but using the Monge representation of surfaces, we give a sufficient geometric, G2G2 Euler condition on the curve network. When satisfied, this condition guarantees existence of an interpolating surface.

► The paper proves the existence of a second-order vertex enclosure constraint.
► This constraint governs the admissibility of curve networks for G2G2 interpolation.
► The paper also gives a sufficient geometric, G2G2 Euler condition on the curve network.
► When satisfied, the constraint guarantees existence of an interpolating surface.