Constraints on Curve Networks Suitable for G 2 Interpolation [chapter]

Thomas Hermann, Jorg Peters, Tim Strotman
2010 Lecture Notes in Computer Science  
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 1 surface. Here we prove the existence of an additional, more subtle constraint that governs the admissibility of curve networks for G 2 interpolation. Additionally, analogous
more » ... the first-order case but using the Monge representation of surfaces, we give a sufficient geometric, G 2 Euler condition on the curve network. When satisfied, this condition guarantees existence of an interpolating surface.
doi:10.1007/978-3-642-13411-1_6 fatcat:7n32xwj2yvgiteqq7fgd5qsdsa