Dyadic C² Hermite interpolation on a square mesh

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• 作者：Serge Dubuc ; Bin Han ; Jean-Louis Merrien and Qun Mo
• 关键词：Hermite interpolation ; Subdivision ; Surfaces ; Hö ; lder condition
• 刊名：Computer Aided Geometric Design
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：22
• 期：8
• 页码：727-752
• 全文大小：1049 K

文摘

For prescribed values of a function and its partial derivatives of orders 1 and 2 at the vertices of a square, we fit an interpolating surface. We investigate two families of solutions provided by two Hermite subdivision schemes, denoted S4SW-1&_mathId=mml2&_user=10&_cdi=5623&_rdoc=2&_handle=V-WA-A-W-Z-MsSAYZW-UUA-U-AABZBZWDDU-AABBEVBCDU-CAYZDYWBY-Z-U&_acct=C000050221&_version=1&_userid=10&md5=b742ed8b614ec72c1cdf282ca203b0a2"" title=""Click to view the MathML source"">HD² and HR². Both schemes depend on 2 matrix parameters, a square matrix of order 2 and a square matrix of order 3. We exhibit the masks of both schemes. We compute the Sobolev smoothness exponent of the general solution of the Hermite problem for the most interesting schemes 0a42a1c845e581b72bd7503c9962"" title=""Click to view the MathML source"">HD² and HR² and we get a lower bound for the Hölder smoothness exponent. We generate a 0ad5dc164d74b"" title=""Click to view the MathML source"">C² interpolant on any semiregular rectangular mesh with Hermite data of degree 2.