Convolution surfaces with varying radius: Formulae for skeletons made of arcs of circles and line segments - Archive ouverte HAL Access content directly
Book Sections Year : 2018

## Convolution surfaces with varying radius: Formulae for skeletons made of arcs of circles and line segments

Evelyne Hubert

#### 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. To obtain the formulae we use Creative Telescoping and describe how this technique can be used for other families of kernels and skeleton primitives. We apply the new formulae to obtain convolution 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.

#### Domains

Mathematics [math] General Mathematics [math.GM]
Loading...

### Dates and versions

hal-01534159 , version 1 (07-06-2017)
hal-01534159 , version 2 (04-01-2018)

### Identifiers

• HAL Id : hal-01534159 , version 2
• DOI :

### Cite

Alvaro Javier Fuentes Suárez, Evelyne Hubert. Convolution surfaces with varying radius: Formulae for skeletons made of arcs of circles and line segments. Asli Genctav; Kathryn Leonard; Sibel Tari; Evelyne Hubert; Geraldine Morin; Noha El-Zehiry; Erin Chambers. Research in Shape Analysis, 12, Springer, 2018, Association for Women in Mathematics Series, 978-3-319-77065-9. ⟨10.1007/978-3-319-77066-6_3⟩. ⟨hal-01534159v2⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

617 View
581 Download

### Share

Gmail Facebook Twitter LinkedIn More