A Quartic Clough-Tocher Interpolant

Xiang Fang; Stephen Mann

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Paper

A Quartic Clough-Tocher Interpolant

Topics: Modeling and Algorithms; Surface Modeling

In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: VISIGRAPP, 199-206, 2018 , Funchal, Madeira, Portugal

Authors: Xiang Fang and Stephen Mann

Affiliation: University of Waterloo, Canada

Keyword(s): Triangular Bézier Patches, Clough-Tocher Interpolation, Least Squares.

Related Ontology Subjects/Areas/Topics: Computer Vision, Visualization and Computer Graphics ; Geometry and Modeling ; Modeling and Algorithms ; Surface Modeling

Abstract: In this paper we present a quartic version of the Clough-Tocher scheme for Hermite interpolation of functional data. This variation uses least squares to minimize discontinuities across the macro-patch boundaries, as well as adjusting one of the macro-boundary control points. The resulting surfaces have significantly better shape than a cubic version of Clough-Tocher that also used least squares to minimize discontinuities across patch boundaries. We compare our method to this cubic version of Clough-Tocher using shaded images and Gaussian curvature plots.

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Paper citation in several formats:

Fang, X. and Mann, S. (2018). A Quartic Clough-Tocher Interpolant. In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - GRAPP; ISBN 978-989-758-287-5; ISSN 2184-4321, SciTePress, pages 199-206. DOI: 10.5220/0006547201990206

@conference{grapp18,
author={Xiang Fang. and Stephen Mann.},
title={A Quartic Clough-Tocher Interpolant},
booktitle={Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - GRAPP},
year={2018},
pages={199-206},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006547201990206},
isbn={978-989-758-287-5},
issn={2184-4321},
}

TY - CONF

JO - Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - GRAPP
TI - A Quartic Clough-Tocher Interpolant
SN - 978-989-758-287-5
IS - 2184-4321
AU - Fang, X.
AU - Mann, S.
PY - 2018
SP - 199
EP - 206
DO - 10.5220/0006547201990206
PB - SciTePress