# A NEW POTENTIAL FUNCTION FOR SELF INTERSECTING GIELIS CURVES WITH RATIONAL SYMMETRIES

### Yohan D. Fougerolle, Frédéric Truchetet, Johan Gielis

#### Abstract

We present a new potential field equation for self-intersecting Gielis curves with rational rotational symmetries. In the literature, potential field equations for these curves, and their extensions to surfaces, impose the rotational symmetries to be integers in order to guarantee the unicity of the intersection between the curve/surface and any ray starting from its center. Although the representation with natural symmetries has been applied to mechanical parts modeling and reconstruction, the lack of a potential function for Rational symmetry Gielis Curves (RGC) remains a major problem for natural object representation, such as flowers and phyllotaxis. We overcome this problem by combining the potential values associated with the multiple intersections using R-functions. With this technique, several differentiable potential fields can be defined for RGCs. Especially, by performing N-ary R-conjunction or R-disjunction, two specific potential fields can be generated: one corresponding to the inner curve, that is the curve inscribed within the whole curve, and the outer -or envelope- that is the curve from which self intersections have been removed.

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#### Paper Citation

#### in Harvard Style

D. Fougerolle Y., Truchetet F. and Gielis J. (2009). **A NEW POTENTIAL FUNCTION FOR SELF INTERSECTING GIELIS CURVES WITH RATIONAL SYMMETRIES** . 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 90-95. DOI: 10.5220/0001798200900095

#### in Bibtex Style

@conference{grapp09,

author={Yohan D. Fougerolle and Frédéric Truchetet and Johan Gielis},

title={A NEW POTENTIAL FUNCTION FOR SELF INTERSECTING GIELIS CURVES WITH RATIONAL SYMMETRIES},

booktitle={Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)},

year={2009},

pages={90-95},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001798200900095},

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 - A NEW POTENTIAL FUNCTION FOR SELF INTERSECTING GIELIS CURVES WITH RATIONAL SYMMETRIES

SN - 978-989-8111-67-8

AU - D. Fougerolle Y.

AU - Truchetet F.

AU - Gielis J.

PY - 2009

SP - 90

EP - 95

DO - 10.5220/0001798200900095