A variational approach for feature-aware B-spline curve design on surface meshes

Robust curve design on surface meshes with flexible controls is useful in a wide range of applications but remains challenging. Most existing methods fall into one the two strategies: to discretize polyline, which then optimized, and other directly smooth splines meshes. While former approach usually needs sufficiently dense sampling points, computational costly, latter relaxes requirement suffers from lack user control. To tackle these problems, we proposed variational method for designing feature-aware B-spline curves Given recent advances shell space construction methods, could relax inside simplified mesh evaluate its distance using equipped bijective mapping. effectively minimize between surface, additional form both internal external constraints, applied interior point adaptively inserted knots spline increase freedom adjust weighting during iterations. When close enough it can be efficiently sampled at any resolution robustly projected surface. Experiments show that our more robust, has higher flexibility, generates smoother results than methods.