Curve networks compatible with image surfacing Original Research Article

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