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• W3017195528 endingPage "112937" @default.
• W3017195528 startingPage "112937" @default.
• W3017195528 abstract "An integration of fractional calculus, data interpolation, and Lie group leads to new treatments of interpolation problems. A local and centered fractional derivative is introduced, which enables the fractional interpolant to create a Cα-smooth (α∈R+) curve by extending integer order cost functions to fractional ones. The fractional interpolant fills the gaps between the traditional linear interpolating segments, cubic splines, and higher-order splines. Interpolating rigid body transformations has enormous applications in mechanics, computer graphics, and robotics. Previous approaches have provided the re-parametrization methods, the recursive methods (e.g., de Casteljau’s algorithm), and the gradient methods. To approximate the correct interpolating curve on SO(3), a closed-form model that merges the tangent spaces of knots is proposed. The model first constructs a family of candidate curves and then combines them into an improved approximation. Applications in modeling functionally graded materials and rigid body transformations are discussed." @default.
• W3017195528 created "2020-04-24" @default.
• W3017195528 creator A5011688144 @default.
• W3017195528 creator A5028364253 @default.
• W3017195528 creator A5091692262 @default.
• W3017195528 date "2020-11-01" @default.
• W3017195528 modified "2023-10-15" @default.
• W3017195528 title "Fractional derivative for interpolation in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e320 altimg=si6.svg><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>and SO(n) applications in functionally graded materials and rigid body transformations" @default.
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• W3017195528 doi "https://doi.org/10.1016/j.cam.2020.112937" @default.
• W3017195528 hasPublicationYear "2020" @default.
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