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Conference Papers Year : 2007

## Visualisation of implicit algebraic curves

(1, 2) , (1)
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Lionel Alberti
• Function : Author
• PersonId : 842419
Bernard Mourrain

#### Abstract

We describe a new algorithm for the visualisation of implicit algebraic curves, which isolates the singular points, compute the topological degree around these points in order to check that the topology of the curve can be deduced from the points on the boundary of these singular regions. The other regions are divided into $x$ or $y$ regular regions, in which the branches of the curve are also determined from information on the boundary. Combined with enveloping techniques of the polynomial represented in the Bernstein basis, it is shown on examples that this algorithm is able to render curves defined by high degree polynomials with large coefficients, to identify regions of interest and to zoom safely on these regions.

#### Domains

Mathematics [math] Algebraic Geometry [math.AG]

### Dates and versions

inria-00175062 , version 1 (26-09-2007)

### Identifiers

• HAL Id : inria-00175062 , version 1

### Cite

Lionel Alberti, Bernard Mourrain. Visualisation of implicit algebraic curves. Pacific Conference on Computer Graphics and Applications 2007, Ron Goldman, Oct 2007, Lahaina, Maui, Hawaii, United States. pp.303-312. ⟨inria-00175062⟩

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