摘要
为了计算对于任意复杂拓扑拟合域的低扭曲、满足拟合误差阈值和较少控制点的非结构T样条拟合曲面,提出了一种逐步求解的方法。首先,生成与拟合域具有相同拓扑的多立方体作为参数域,通过多次重参数化过程优化待拟合表面和参数域之间的对应关系,得到一个适用于获得低拟合误差样条曲面的低扭曲映射。与此同时,利用非结构T样条局部细分的性质对不满足拟合误差阈值的区域进行自适应局部细分,得到满足拟合误差阈值的低扭曲样条曲面。接下来,提出一种删除冗余控制顶点的拟合曲面简化策略,在满足拟合误差阈值和低扭曲的基础上删除冗余的控制顶点,得到控制顶点数量较少的误差有界的低扭曲非结构T样条拟合曲面。在各种复杂模型上证明了此方法的有效性。与最新的方法相比,该方法以更少的控制顶点实现了更低的参数化扭曲。
In order to calculate the unstructured T-spline fitting surface with low distortion and meet the fitting error threshold and fewer control points for any complex topology fitting domain, we presented a step-by-step solution method. First, a polycube structure with the same topology as the fitting domain was generated as the parameter domain, and the corresponding relationship between the surface to be fitted and the parameter domain was optimized through multiple re-parameterization processes, thus obtaining a low distortion mapping suitable for the generation of low fitting error spline surfaces. At the same time, with the local subdivision property of the unstructured T-spline, the region, which did not meet the fitting error threshold, was adaptively subdivided, and the low distortion spline surface meeting the fitting error threshold was obtained. Next, a simplification strategy of fitting surface was presented to delete redundant control vertices. On the basis of meeting the fitting error threshold and low distortion, redundant control vertices were deleted, and a low distortion unstructured T-spline fitting surface was obtained with less control vertices and bounded error. The effectiveness of this method was verified on various complex models. Compared with the latest methods, this method could attain lower parametric distortion with fewer control vertices.
作者
关启超
刘浩
王远成
傅孝明
GUAN Qi-chao;LIU Hao;WANG Yuan-cheng;FU Xiao-ming(School of Mathematical Sciences,University of Science and Technology of China,Hefei Anhui 230000,China)
出处
《图学学报》
CSCD
北大核心
2022年第6期1104-1113,共10页
Journal of Graphics
基金
国家自然科学基金(61802359)。
关键词
低扭曲
非结构T样条
曲面拟合
多立方体参数域
局部细分
low distortion
unstructured T-spline
surface fitting
polycube structures
local subdivision
