@Article{NMTMA-9-383,
author = {},
title = {Spline Surfaces over Arbitrary Topological Meshes: Theoretical Analysis and Application},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2016},
volume = {9},
number = {3},
pages = {383--415},
abstract = {<p style="text-align: justify;">Based on polyhedral splines, some multivariate splines of different orders
with given supports over arbitrary topological meshes are developed. Schemes for
choosing suitable families of multivariate splines based on pre-given meshes are
discussed. Those multivariate splines with inner knots and boundary knots from
the related meshes are used to generate rational spline shapes with related control
points. Steps for up to $C^2$-surfaces over the meshes are designed. The relationship
among the meshes and their knots, the splines and control points is analyzed. To
avoid any unexpected discontinuities and get higher smoothness, a heart-repairing
technique to adjust inner knots in the multivariate splines is designed.<br/>With the theory above, bivariate $C^1$-quadratic splines over rectangular meshes are
developed. Those bivariate splines are used to generate rational $C^1$-quadratic surfaces over the meshes with related control points and weights. The properties of
the surfaces are analyzed. The boundary curves and the corner points and tangent
planes, and smooth connecting conditions of different patches are presented. The $C^1$−continuous connection schemes between two patches of the surfaces are presented.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2016.y14020},
url = {http://global-sci.org/intro/article_detail/nmtma/12382.html}
}