Curve networks compatible with G2 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 C surface. Here we prove the existence of an additional, more subtle constraint that governs the admissibility of curve networks for G interpolation. Additionally, analogous to the first-order case but using the Monge representation of surfaces, we give a sufficient geometric, G Euler condition on the curve network. When satisfied, this condition guarantees existence of an interpolating surface.