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- W3164403314 abstract "Abstract In this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of $(m+1)$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:math> -point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The $C^{0}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> , $C^{1}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> and $C^{2}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes." @default.
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- W3164403314 date "2021-03-22" @default.
- W3164403314 modified "2023-10-17" @default.
- W3164403314 title "A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes" @default.
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- W3164403314 doi "https://doi.org/10.1186/s13662-021-03336-6" @default.
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