Discrete Spline Curve Design on Surface Mesh via Cascaded Optimization

To meet the requirements of robustness,high efficiency and wide applicability,this paper proposes a discrete spline curve design method on mesh domain based on global optimization.The method relaxes the strict manifold constraint,i.e.the curve is located on the surface by constraining discrete points of the curve.With the idea of interior point method,it adopts block coordinate descent method to solve the global optimization equation,and then maps the curve to the mesh surface through local parameterization.In addition,a multi-scales coarse-to-fine strategy is proposed to accelerate computation,which can not only estimate the discretization of the differential operator more accurately,but also decreases the computation of the sample point locations to improve the performance.Experiments on convergence analysis show that the cascaded optimization method converges quickly,obtaining smoother results with multi-scales strategy.In contrast to existing projection-based and smoothness-based methods,the proposed method has advantages in controllability,generality and robustness.