CINAPACT-Splines: A Family of Infinitely Smooth, Accurate and Compactly Supported Splines

  • Bita Akram
  • Usman R. AlimEmail author
  • Faramarz F. Samavati
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9474)


We introduce CINAPACT-splines, a class of \(C^\infty \), accurate and compactly supported splines. The integer translates of a CINAPACT-spline form a reconstruction space that can be tuned to achieve any order of accuracy. CINAPACT-splines resemble traditional B-splines in that higher orders of accuracy are achieved by successive convolutions with a B-spline of degree zero. Unlike B-splines however, the starting point for CINAPACT-splines is an infinitely smooth and compactly supported bump function that has been properly normalized so that it fulfills the partition of unity criterion. We use our construction to design two CINAPACT-splines, and explore their properties in the context of rendering volumetric data sampled on Cartesian grids. Our results show that CINAPACT-splines, while being infinitely smooth, are capable of providing similar reconstruction accuracy compared to some well-established filters of similar cost.


Approximation Order Volume Rendering Reconstruction Scheme Support Size Bump Function 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Bita Akram
    • 1
  • Usman R. Alim
    • 1
    Email author
  • Faramarz F. Samavati
    • 1
  1. 1.Department of Computer ScienceUniversity of CalgaryCalgary ABCanada

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