TY - JOUR
T1 - A shape preserving C2 non-linear, non-uniform, subdivision scheme with fourth-order accuracy
AU - Yang, Hyoseon
AU - Yoon, Jungho
N1 - Funding Information:
J. Yoon was supported in part by the National Research Foundation of Korea under grant NRF-2020R1A2C1A01005894 .
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/9
Y1 - 2022/9
N2 - The objective of this study is to present a shape-preserving non-linear subdivision scheme generalizing the exponential B-spline of degree 3, which is a piecewise exponential polynomial with the same support as the cubic B-spline. The subdivision of the exponential B-spline has a crucial limitation in that it can reproduce at most two exponential polynomials, yielding the approximation order two. Also, finding a best-fitting shape parameter in the exponential B-spline is a challenging and important problem. In this regard, we present a method for selecting an optimal shape parameter and then formulate it in the construction of new refinement rules. As a result, the new scheme provides an improved approximation order four while maintaining the same C2 smoothness as the (exponential) B-spline of degree 3. Moreover, we show that the proposed method preserves geometrically important characteristics such as monotonicity and convexity, under some suitable conditions. Some numerical examples are provided to demonstrate the ability of the new subdivision scheme.
AB - The objective of this study is to present a shape-preserving non-linear subdivision scheme generalizing the exponential B-spline of degree 3, which is a piecewise exponential polynomial with the same support as the cubic B-spline. The subdivision of the exponential B-spline has a crucial limitation in that it can reproduce at most two exponential polynomials, yielding the approximation order two. Also, finding a best-fitting shape parameter in the exponential B-spline is a challenging and important problem. In this regard, we present a method for selecting an optimal shape parameter and then formulate it in the construction of new refinement rules. As a result, the new scheme provides an improved approximation order four while maintaining the same C2 smoothness as the (exponential) B-spline of degree 3. Moreover, we show that the proposed method preserves geometrically important characteristics such as monotonicity and convexity, under some suitable conditions. Some numerical examples are provided to demonstrate the ability of the new subdivision scheme.
KW - Approximation order
KW - Asymptotical equivalence
KW - Convexity preserving
KW - Exponential B-spline
KW - Exponential polynomial reproducing property
KW - Monotonicity preserving
KW - Non-linear, non-uniform, non-stationary subdivision
UR - http://www.scopus.com/inward/record.url?scp=85127345237&partnerID=8YFLogxK
U2 - 10.1016/j.acha.2022.03.006
DO - 10.1016/j.acha.2022.03.006
M3 - Article
AN - SCOPUS:85127345237
SN - 1063-5203
VL - 60
SP - 267
EP - 292
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
ER -