网格模型PDE曲面重建中的边界曲线构造

Constructing boundary curves from complex mesh models for PDE-based shape reconstruction

利用偏微分方程(PDE)进行曲面拟合是计算机图形学研究领域中的常用方法,该类方法通过选取适当的边界条件来构造PDE,用PDE的解来表示几何曲面.基于网格简化方法和离散曲面测地线计算等技术,提出一种从网格模型提取PDE曲面片边界条件曲线的方法.首先,对复杂模型进行简化并分片处理;通过计算离散曲面的测地线为每个分片定义相应的PDE边界条件曲线,进而构造复杂模型的PDE拟合表面.最后,通过细分方法建立原模型的多分辨率表示.实验表明,该方法可以对具有不同几何复杂度的网格模型进行处理,产生具有细分连通性的多分辨网格模型.

Partial differential equations（PDE）have been used in computer graphics for concise representation of geometric shape.These equations for PDE surfaces are reconstructed subject to suitable boundary conditions.In this paper,we propose an efficient algorithm to automatically derive these boundary curves on the surface of the original polygon mesh.Our method first decimates a given complex model into a simplified version called base mesh,leading to a segmentation of the complex model into a group of patches.The algorithm then derives the boundary curves for each patch by abstracting geodesic curves from the original model.Parametric patch can finally be obtained as the solution of the PDE equation.Experiment results show that our method can deal with various complex mesh models with different topologies.