Curve smoothing is an important topic for surface processing. While putting effort on the smoothness of the curve, existing methods cannot preserve the closeness to the initial curve on the triangle mesh. In this paper, a novel method is presented for curve smoothing to make the smoothed curve remain close to its initial location based on a local reduction of the geodesic curvature while simultaneously controlling the deviation from the initial contour.

The authors present the curve-smoothing algorithm covering the initialization, during which it uses a user-specified parameter for the desired geodesic curvature, the curve smoothing and splitting step, and the proof of the convergence of the algorithm. Experiments on artificial and real-world datasets including geometric and parametric noise models verify its robustness and convergence. Comparison to the spline approximation shows that the proposed method is the right choice for their applications. Furthermore, the authors conducted an informal interview with a domain expert who rated the results positively.

The main contribution of this paper is the presentation of a novel method for curve smoothing. The beauty of the method is that the user can employ a single parameter to balance the closeness versus the smoothness with respect to the geodesic curvature. The proposed method will help those who need to adjust the closeness as well as the smoothness for curve smoothing in surface processing applications.