基于边界网格模型的T样条实体重建

Reconstruction of T-Spline Solid from Boundary Mesh

为解决零亏格边界网格模型的T样条实体重建问题,提出一种基于八叉树细分和渐进迭代最小二乘拟合算法的T样条实体构建算法.首先给出一种基于体-面-边-点4层几何拓扑的T样条实体数据结构和节点矢量计算算法;接着对边界网格进行参数化,在单位参数立方体和网格模型之间建立参数映射关系,并且采用MVC方法保证参数化结果的单射无自交性;最后实现T样条实体的渐进迭代最小二乘拟合.对sphere模型, head模型和bunny模型进行测试,实现了基于边界网格模型的T样条实体重建,提高了T样条实体构建的效率。

A T-spline solid reconstruction algorithm based on octree subdivision and least square progressive iterative approximation(LSPIA)is proposed to solve the problem of reconstruction of T-spline solid from genus-zero boundary mesh.Firstly,this paper presents a cube-face-edge-vertex based four-layer geometry topology T-spline solid data structure and its knot vector calculation algorithm.Then,the parameterization of boundary mesh is realized to build the parametric mapping between the unit cube and the boundary mesh.The MVC parameterization method is also implemented to guarantee the injective mapping and no self-intersection property of the parameterization results.Later,the least square progressive iterative approximation of T-spline solid is implemented.The algorithm presented in this paper has been tested in the case study,which realizes the reconstruction of T-spline solid from boundary mesh.The proposed algorithm improves the efficiency of the reconstruction of T-spline solid and has the advantage in handling large amount of data.