保持参数分布状态的有限元变形网格B样条曲面重建算法

摘要

According to the information of original surfaces,original meshes and deformed me-shes,a method for reconstructing B-spline surfaces with consistent parametric distribution was pres-ented.In trimmed regions,initial fitting surfaces were constructed by some operations on original surfaces such as translation,extension,segment and reparametrization,etc.In untrimmed regions, bidirectional skinning method was adopted for the production of initial surfaces after inserting section lines across the highly curved boundaries and revising their parameterization.Then a loop of reparam-eterizing the nodes and refitting the surfaces proceeded until some ending rules were satisfied.During the process of iteration,a more precise method was presented for determining under-constrained re-gions by calculating extreme points of basis functions;fairness of the fitting surfaces was improved evidently by splitting coarse meshes to provide enough constraints with interpolatory quad/triangle subdivision scheme.Fitting precision is improved for trimmed surfaces by dint of boundaries and in-ternal nodes interpolation constraints together with shape preservation constraints of under-constrain-ed regions.Test results indicate effectivity of the proposed method.%针对变形前后的有限元网格模型及原始曲面模型，提出一种保持参数分布状态的B样条曲面重建算法。在裁剪区域，通过对原始曲面进行平移、延伸、截取及重新参数化等操作，构造初始拟合曲面；在非裁剪区域，在垂直于大曲率边界的参数方向上插入截面线并重新参数化两条大曲率边界，用双向蒙皮的方法重建拟合曲面。然后进入重新参数化网格点和重新拟合曲面的迭代过程，直至满足终止准则。在曲面迭代修改过程中，通过计算基函数的极值点给出一种更精确的欠约束区域判定方法；利用插值四边/三角细分算法细化粗糙网格模型，补充约束条件，提高拟合曲面的光顺性；借助拟合曲面补充边界约束条件，结合网格点插值和形状保持约束，改进裁剪曲面的拟合精度。实验结果验证了算法的有效性。