面向模型切割的网格闭合光滑曲线设计

Model-Cutting Oriented Closed Curve Design on Surface Mesh

摘要: 在网格上鲁棒地设计光滑曲线在计算机辅助设计领域中有广泛的应用。针对网格表面模型切割问题，本文提出一种网格表面离散闭合光滑曲线的设计方法。该方法将离散采样点限制在网格的边或者顶点上，以减少切割算法的计算量。输入一组位于网格上的插值点，本文首先生成一条经过所有插值点的初始曲线，随后本文利用高斯赛德尔迭代优化一个离散曲线曲率能量来保证曲线的光滑性。实验结果表明本文算法可以满足实时交互需求，且具有很高的鲁棒性。

Abstract: Robust curve design on surface meshes with flexible controls is useful across applications but remains challenging. Aiming at hole cutting on the mesh surface, this paper proposes an approach for designing discrete closed smooth curves on the mesh surface. We restrict the discrete sampling points to the edges or vertices of the mesh to reduce the computational complexity of the cutting algorithm. Inputting a set of interpolation points on the mesh, we first generate an initial curve that passes through all the interpolation points, and then we use Gauss-Seidel iterative optimization to optimize the curvature energy of a discrete curve to ensure the smoothness of the curve. The experimental results show that the proposed algorithm can meet the real-time interaction requirements and has high robustness.