# TESSELLATING ALGEBRAIC CURVES AND SURFACES USING A-PATCHES

### Curtis Luk, Stephen Mann

#### 2009

#### 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.

#### References

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#### Paper Citation

#### in Harvard Style

Luk C. and Mann S. (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

#### in Bibtex Style

@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},

}

#### in EndNote Style

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