TY - JOUR
T1 - Convexity preservation of the four-point interpolatory subdivision scheme
AU - Dyn, Nira
AU - Kuijt, Frans
AU - Levin, David
AU - Van Damme, Ruud
N1 - Funding Information:
∗Corresponding author. E-mail: [email protected]. 1Much of this work has been done during a visit of the second author to Tel-Aviv University in March 1998, which was financially supported by Tel-Aviv University and the Dutch Technology Foundation STW.
PY - 1999/9
Y1 - 1999/9
N2 - In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension parameter bounded from above by a bound smaller than 1/16. Thus the scheme generates C1 limit functions and has approximation order two.
AB - In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension parameter bounded from above by a bound smaller than 1/16. Thus the scheme generates C1 limit functions and has approximation order two.
UR - http://www.scopus.com/inward/record.url?scp=0033189258&partnerID=8YFLogxK
U2 - 10.1016/S0167-8396(99)00019-9
DO - 10.1016/S0167-8396(99)00019-9
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AN - SCOPUS:0033189258
SN - 0167-8396
VL - 16
SP - 789
EP - 792
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
IS - 8
ER -