Implicit surfaces from polygon soup with compactly supported radial basis functions
Implicit surfaces from polygon soup with compactly supported radial basis functions
复制标题
具有紧凑支持的径向基函数的多边形汤的隐式曲面
DOI：
10.1007/s00371-018-1529-3
复制
发表时间：
2018
期刊：
影响因子：
3.5
通讯作者：
Liu Xinru
中科院分区：
文献类型：
--
作者：
Liu Shengjun;Xiao Jintao;Hu Ling;Liu Xinru
提出了一种基于紧支撑径向基函数的多边形曲面隐式曲面生成方法。曲面表示为隐函数的零水平集，该隐函数用多边形数据的外法线约束进行插值。通过指定支撑尺寸和形状参数两个参数，用户可以灵活地控制重建表面的精度。对于rbf系数的确定，我们的方法采用了准插值框架，避免了求解大型线性系统，从而可以高效、鲁棒地处理大型网格。在此基础上，给出了形状参数与支撑半径之间的关系，并通过严格的理论分析推导出了近似于原模型的重构曲面的误差界。
This paper presents a method for generating implicit surfaces from polygon soups based on compactly supported radial basis functions (CSRBFs). The surface is represented as the zero level set of an implicit function which interpolates the polygonal data with their outward normal constraints. By specifying two parameters, the support size and the shape parameter, users can flexibly control the accuracy of the reconstructed surfaces. For determining coefficients of RBFs, our method uses a quasi-interpolation framework to avoid solving a large linear system, which allows processing large meshes efficiently and robustly. Moreover, a relationship between the shape parameter and the support radius is provided for the quasi-solution validity, and an error bound of the reconstructed surfaces approximating the original models is deduced through the rigorous theoretical analysis.