TY - JOUR
T1 - Fitting $C^1$ Surfaces to Scattered Data with $S^1_2(∆^{(2)}_{m,n})$
AU - Kai Qu, Renhong Wang & Chungang Zhu
JO - Journal of Computational Mathematics
VL - 4
SP - 396
EP - 414
PY - 2011
DA - 2011/08
SN - 29
DO - http://doi.org/10.4208/jcm.1101-m3203
UR - https://global-sci.org/intro/article_detail/jcm/10385.html
KW - Bivariate spline, Scattered data, Surface fitting, Energy minimization, Type-2
triangulation, $C^1$-continuous.
AB - <p style="text-align: justify;">This paper presents a fast algorithm (BS2 Algorithm) for fitting $C^1$ surfaces to scattered data points. By using energy minimization, the bivariate spline space $S^1_2(∆^{(2)}_{m,n})$ is introduced to construct a $C^1$-continuous piecewise quadratic surface through a set of irregularly 3D points. Moreover, a multilevel method is also presented. Some experimental results show that the accuracy is satisfactory. Furthermore, the BS2 Algorithm is more suitable for fitting surfaces if the given data points have some measurement errors.</p>