A shell space constrained approach for curve design on surface meshes

Abstract

Curve design on surface meshes has wide applications in computer graphics and computer aided design. The key challenge of the problem is to efficiently and robustly handle the manifold constraint which forces the curve to exactly lie on the surface meshes. Popular approaches, such as projection-based and smoothing-based methods, solve it by either totally relaxing or strictly holding the above constraint, which have their own merits. We propose a shell space method which combines the advantages of both approaches. First, a shell space surrounding the mesh with a distance-like scalar field is constructed. Then the manifold constraint is relaxed to the shell space and a global optimization with the interior point method is conducted. Mimicking the behavior of the both methods, it gradually shrinks the shell space and increases the weight of the manifold energy during the iterations. The adaptive scheme sufficiently relaxes the curve to gain its geometric property (e.g., smoothness) easily (like projection-based method) but converges stably and robustly (like smoothing-based method). Finally, the curve is snapped to the surface with a robust projection. Experiments exhibit that our method outperforms existing work on various aspects, including efficiency, robustness, and controllability.