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# Formulae for the convolution of $\mathcal{G}^1$ skeleton curves into smooth surfaces

1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
Abstract : We develop closed form formulae for the computation of the defining fields of convolutions surfaces. The formulae are obtained for power inverse kernels with skeletons made of line segments or arcs of circle. We apply the new formulae to obtain convolutions surfaces around $\mathcal{G}^1$ skeletons, some of them closed curves. We showcase how the use of arcs of circles greatly improves the visualization of the surface around a general curve compared with a segment based approach.
Keywords :
Document type :
Preprints, Working Papers, ...

Cited literature [23 references]

https://hal.archives-ouvertes.fr/hal-01534159
Contributor : Alvaro Javier Fuentes Suárez Connect in order to contact the contributor
Submitted on : Wednesday, June 7, 2017 - 12:07:42 PM
Last modification on : Thursday, November 26, 2020 - 3:50:03 PM
Long-term archiving on: : Friday, September 8, 2017 - 12:39:42 PM

### File

FuentesHubert17.pdf
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### Identifiers

• HAL Id : hal-01534159, version 1

### Citation

Alvaro Javier Fuentes Suárez, Evelyne Hubert. Formulae for the convolution of $\mathcal{G}^1$ skeleton curves into smooth surfaces. 2017. ⟨hal-01534159v1⟩

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