TY - JOUR
T1 - On linear independence of linear and bilinear point-based splines
AU - Cho, Durkbin
N1 - Publisher Copyright:
© 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
PY - 2021/6
Y1 - 2021/6
N2 - The basis of T-splines are the point-based splines (PB splines) that are unstructured meshless splines. In this paper, we study associated PB splines with local knot vectors that are arbitrarily distributed in ([0 , 1] ∩ Q) d, d= 1 , 2 , where Q is the set of rational numbers. We prove the linear independence of linear PB splines under a mild assumption that their central knots are all distinct. The linearly independent property is one of important prerequisites for isogeometric analysis. Moreover, we illustrate that the same assumption can not be extended to two-dimensional case, by giving a set of linearly dependent bilinear PB splines.
AB - The basis of T-splines are the point-based splines (PB splines) that are unstructured meshless splines. In this paper, we study associated PB splines with local knot vectors that are arbitrarily distributed in ([0 , 1] ∩ Q) d, d= 1 , 2 , where Q is the set of rational numbers. We prove the linear independence of linear PB splines under a mild assumption that their central knots are all distinct. The linearly independent property is one of important prerequisites for isogeometric analysis. Moreover, we illustrate that the same assumption can not be extended to two-dimensional case, by giving a set of linearly dependent bilinear PB splines.
KW - CAD
KW - Isogeometric analysis
KW - Linear independence
KW - PB splines
UR - http://www.scopus.com/inward/record.url?scp=85106682041&partnerID=8YFLogxK
U2 - 10.1007/s40314-021-01533-3
DO - 10.1007/s40314-021-01533-3
M3 - Article
AN - SCOPUS:85106682041
SN - 2238-3603
VL - 40
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 4
M1 - 152
ER -