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- W2000331079 abstract "We present an explicit formula for the mask of odd points<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>-ary, for any odd<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>n</mml:mi><mml:mo>⩾</mml:mo><mml:mn>3</mml:mn></mml:math>, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-point<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:math>-ary schemes introduced by Lian, 2008, and (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mn>2</mml:mn><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>)-point<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:math>-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd point<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>-ary schemes including the schemes introduced by Zheng et al., 2009, can easily be generated by our formula. In addition, error bounds between subdivision curves and control polygons of schemes are computed. It has been noticed that error bounds decrease when the complexity of the scheme decreases and vice versa. Also, as we increase arity of the schemes the error bounds decrease. Furthermore, we present brief comparison of total absolute curvature of subdivision schemes having different arity with different complexity. Convexity preservation property of scheme is also presented." @default.
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- W2000331079 date "2012-01-01" @default.
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- W2000331079 title "The Mask of Odd Pointsn-Ary Interpolating Subdivision Scheme" @default.
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- W2000331079 doi "https://doi.org/10.1155/2012/205863" @default.
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