GENERATION ET ANIMATION D'ENTRELACS,

EFFETS LARSEN

Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées), Ecole Polytechnique, CNRS
91128 Palaiseau Cedex
France

tel = +33.(0)1.69.33.46.45
jean-francois.colonna@polytechnique.edu

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

[Site Map, Help and Search [Plan du Sîte, Aide et Recherche]]

[The Y2K bug [Le bug de l'an 2000]]
[Croyez-vous que les Nombres Réels existent dans un ordinateur et que les calculs flottants sont sûrs ?]
[N'oubliez pas de visiter Une Machine Virtuelle à Explorer l'Espace-Temps où vous trouverez plus de 3230 images à la frontière de l'Art et de la Science]

(cette page a été créée le 30/09/2008)
(la dernière mise à jour de cette page -appartenant au sîte CMAP28- a eu lieu le 01/03/2010 19:10:13 -CET-)

[in english]

Resume : Comment construire et animer des entrelacs ? Comment générer des effets Larsen ?

Mots-Clefs : Picture Synthesis, Entrelacs, Intertwinings.

Plan de ce document :

1-UNE LIBRAIRIE DE MOTIFS ELEMENTAIRES :
2-DEFINITION DE TRANSFORMATIONS :
3-ENTRELACS "BIDIMENSIONNELS" :
4-ENTRELACS "TRIDIMENSIONNELS" :
5-ENTRELACS "BIDIMENSIONNELS" DYNAMIQUES :
6-ENTRELACS "TRIDIMENSIONNELS" DYNAMIQUES :
7-EFFETS LARSEN "BIDIMENSIONNELS" :
8-EFFETS DIVERS :

1-UNE LIBRAIRIE DE MOTIFS ELEMENTAIRES :

2-DEFINITION DE TRANSFORMATIONS :

PR[x,y] = PA[FX[x,y],FY[x,y]]

```
FX[x,y] = PX[x,y]
```
```
FY[x,y] = PY[x,y]
```

FX[x,y] = A11.PX[x,y] + A12.PY[x,y] + A13.PZ[x,y]

FY[x,y] = A21.PX[x,y] + A22.PY[x,y] + A23.PZ[x,y]

```
PX[PX[x,y],PY[x,y]]
```
```
PY[PX[x,y],PY[x,y]]
```

3-ENTRELACS "BIDIMENSIONNELS" :

```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

4-ENTRELACS "TRIDIMENSIONNELS" :

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

5-ENTRELACS "BIDIMENSIONNELS" DYNAMIQUES :

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```

6-ENTRELACS "TRIDIMENSIONNELS" DYNAMIQUES :

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

7-EFFETS LARSEN "BIDIMENSIONNELS" :

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

8-EFFETS DIVERS :

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=)(PA=)
```
```
(PR=) = (PX=,PY=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

```
(PR=) = (PX=,PY=,PZ=)(PA=)
```
```
(PR=) = (PX=,PY=,PZ=)(PA=)
```

Copyright (c) Jean-François Colonna, 2008-2010.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2008-2010.