基于平方距离函数的曲面分片参数化重构

Surface Reconstruction with Parametric Patches Based on Squared Distance Function

提出了基于平方距离函数的曲面分片参数化重构方法,实现了任意拓扑结构模型表面的参数化重构.在四边形网格模型基础上,得到各表面片及其边界线初始参数化模型,以平方距离函数作为误差的度量,采用逐步迭代的方法,使初始参数化模型逼近目标表面.首先,重构出表面片的边界线网格,然后再进行表面片的重构,使重构过程中各参数化表面片始终保持位置连续,因此有效地避免了三维数据点云的参数化问题.其中,影响重构质量的关键因素———四边形网格划分问题,可以通过惩罚项的引入得到改进.实验表明,该方法对复杂模型表面可以得到满意的参数化曲面重构结果.

A new approach for the surface reconstruction with arbitrary topology by parametric patches fitting is presented, where the surface is divided into patches and each is reconstructed by a parametric surface. The quadrilateral meshes are generated from point cloud, and each patch with the boundary is parameterized as the initial model based on the quadrilateral meshes. The reconstruction method is an iterative procedure regarding squared distance function （SDF） as measurement of the error to approach the initial parametric models to the target. The patch boundaries, then the patches themselves, are reconstructed respectively, and the position connectivity among the patches are ensured during the reconstruction. This approach enables to avoid the parametrization of the point cloud. The reconstructed surface is primarily affected by the quadrilateral meshes and can be improved by introducing penalty function. A case study shows the effectiveness of this approach for complex model reconstruction