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Smooth Stream Surfaces of Fourth Order Precision
Author(s) -
Schneider Dominic,
Wiebel Alexander,
Scheuermann Gerik
Publication year - 2009
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01462.x
Subject(s) - streamlines, streaklines, and pathlines , interpolation (computer graphics) , rendering (computer graphics) , computer science , hermite interpolation , algorithm , surface (topology) , mathematics , mathematical optimization , computer graphics (images) , hermite polynomials , geometry , mathematical analysis , animation , physics , thermodynamics
We introduce a novel technique for the construction of smooth stream surfaces of 4th order precision. While common stream surface techniques use linear interpolation for generating seed points for new streamlines in the refinement phase, we use Hermite interpolation. The derivatives needed for Hermite interpolation are obtained by integration along the streamlines. This yields stream surfaces of4th order precision. Additionally, we analyse the accuracy ofthe well known Hultquist approach and our new algorithm and proof that Hultquist's method is exact for linear vector fields. We compare both methods using the well known distance based and a novel error based refinement strategy. Our resulting surface is C 1 ‐continuous, enabling improved rendering among other benefits.