裁剪B样条曲面重建算法研究

Research on Trimmed B-spline Surface Reconstruction

提出了具有不规则边界的裁剪B样条曲面重建方法。采用基准平面对数据点进行参数化,并建立以B样条曲面控制顶点为未知量的超定方程组;提出了基于有效点判别条件的孔洞识别算法,通过对孔洞区域的控制顶点施加顶点形状保持约束,确保方程组最小二乘解的存在;基于误差控制重构B样条曲面整体覆盖数据区域,通过边界线提取或曲面求交剪裁来重构裁剪曲面的边界。该方法具有符合设计意图、曲面在孔洞区域具有良好的形状一致性、曲面重构精度高等特点。

An approach was proposed to reconstruct trimmed B-spline surface with irregular boundaries. A base plane was firstly rebuilt to parameterize the data points, and the over-determinant equations were derived taking the control points of B-spline surface as variables. A hole detection algorithm based on valid point identification was proposed to mark holes with no or less data points, and then the CNSP（control network shape preservation） constraints were selectively imposed on control points relevant to holes to guarantee the existence of equations＇ least square solution. Finally＇, an error-controllable algorithm was utilized to reconstruct B-spline surface covering the data points, grid then irregular boundaries of trimmed surface could be rebuilt via boundary curves extraction or surface intersection. The proposed approach accordant with design intent is characterized by good shape consistence around holes and high precision of resulted surfaces.