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Authors: Curtis Luk and Stephen Mann

Affiliation: University of Waterloo, Canada

ISBN: 978-989-8111-67-8

Keyword(s): Algebraic surfaces, A-patches, Tesselation.

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

Abstract: This work approaches the problem of triangulating algebraic curves and surfaces with a subdivision-style algorithm using A-patches. An algebraic curve or surface is converted from the monomial basis to the Bernstein-Bezier basis over a simplex. If the coefficients are all positive or all negative, then the curve or surface does not pass through the domain simplex. If the scalar Bernstein coefficients are of mixed sign and have a layer separating the positive from the negative, then the patch is in A-patch format and can be efficiently tessellated. Cases of mixed sign without a separating layer are resolved by subdividing the structure into a set of smaller patches and repeating the algorithm. Using A-patches to generate a tessellation of the surface has the advantage of reducing the amount of subdivision required. And because of the A-patch properties, we are guaranteed that features within the designated region will not be missed.

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Paper citation in several formats:
Luk C.; Mann S. and (2009). TESSELLATING ALGEBRAIC CURVES AND SURFACES USING A-PATCHES.In Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009) ISBN 978-989-8111-67-8, pages 82-89. DOI: 10.5220/0001790400820089

@conference{grapp09,
author={Curtis Luk and Stephen Mann},
title={TESSELLATING ALGEBRAIC CURVES AND SURFACES USING A-PATCHES},
booktitle={Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)},
year={2009},
pages={82-89},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001790400820089},
isbn={978-989-8111-67-8},
}

TY - CONF

JO - Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)
TI - TESSELLATING ALGEBRAIC CURVES AND SURFACES USING A-PATCHES
SN - 978-989-8111-67-8
AU - Luk, C.
AU - Mann, S.
PY - 2009
SP - 82
EP - 89
DO - 10.5220/0001790400820089

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