Johan Gielis, a Belgian biologist, has modified and extended the formula of a superellipse, which was found 1818 by the French Mathematician Gabriel Lamé.

It discribes in one simple formula a large group of different organic forms. From a square about a circle up to very complex amorph looking objects.

Gielis has founded a company to develop and market software, based on this formula.

Because the formula results 2 dimensional coordinates by an iteration process it is predestined to convert it in a GDL-object. I've done this and you can download the object from below.

How the parameters work:

width/hight:

The widht and hight of the object are the parameters a and b of the formula.

Rotations:

The shape will be calculated by the formula using polar coordinates. Beginning from center to the right (0°) the object coordinates are produced counterclockwise. To get a closed shape, you hat to rotate once (=1 =360°). But some shapes change in the 2nd, 3rd or i'th round, so you can adjust here the complexity. Filling this more than once rotated shapes is producing irregular polys in GDL, so pay attention.

Number of iterations:

Sets the number of coordinates, which are taken to produce the poly.

n1, n2, n3, m

This are the parameters, which describe the shape. Theres much finetuning to get a decided form. You have to try. Don't play too much, I think you have to work something else too. Some general settings you can take from one of the links below.

There are two checkboxes to lock the n-parameters, which is helpful in some cases.

fill:

the shape can be filled. Use the settings of the section-attributes of the object.

area:

You can automatic calculate the area, if you use a closed shape and rotation set to 1. Just use a fontsize larger than 0 and it will be printed with the object. (unit as the general settings of your actual project)

Related Links:

Where I found the formula and got inspired - attention, german. :

http://www.heise.de/newsticker/meldung/45863

Explanation and coding base of the formula - who else - Paul Bourke:

http://astronomy.swin.edu.au/~pbourke/c ... upershape/

Some further articel on math sides:

http://mathworld.wolfram.com/Superellipse.html

http://www.nature.com/nsu/030331/030331-3.html

http://www.sciencenews.org/articles/200 ... thtrek.asp

Johan Gielis and its company:

http://www.genicap.com/

http://www.geniaal.be/

It discribes in one simple formula a large group of different organic forms. From a square about a circle up to very complex amorph looking objects.

Gielis has founded a company to develop and market software, based on this formula.

Because the formula results 2 dimensional coordinates by an iteration process it is predestined to convert it in a GDL-object. I've done this and you can download the object from below.

How the parameters work:

width/hight:

The widht and hight of the object are the parameters a and b of the formula.

Rotations:

The shape will be calculated by the formula using polar coordinates. Beginning from center to the right (0°) the object coordinates are produced counterclockwise. To get a closed shape, you hat to rotate once (=1 =360°). But some shapes change in the 2nd, 3rd or i'th round, so you can adjust here the complexity. Filling this more than once rotated shapes is producing irregular polys in GDL, so pay attention.

Number of iterations:

Sets the number of coordinates, which are taken to produce the poly.

n1, n2, n3, m

This are the parameters, which describe the shape. Theres much finetuning to get a decided form. You have to try. Don't play too much, I think you have to work something else too. Some general settings you can take from one of the links below.

There are two checkboxes to lock the n-parameters, which is helpful in some cases.

fill:

the shape can be filled. Use the settings of the section-attributes of the object.

area:

You can automatic calculate the area, if you use a closed shape and rotation set to 1. Just use a fontsize larger than 0 and it will be printed with the object. (unit as the general settings of your actual project)

Related Links:

Where I found the formula and got inspired - attention, german. :

http://www.heise.de/newsticker/meldung/45863

Explanation and coding base of the formula - who else - Paul Bourke:

http://astronomy.swin.edu.au/~pbourke/c ... upershape/

Some further articel on math sides:

http://mathworld.wolfram.com/Superellipse.html

http://www.nature.com/nsu/030331/030331-3.html

http://www.sciencenews.org/articles/200 ... thtrek.asp

Johan Gielis and its company:

http://www.genicap.com/

http://www.geniaal.be/

##### Attachments

GSM-Object and UI-bitmap in PLA for AC6.5+

(36.38 KiB) Downloaded 1113 times

(36.38 KiB) Downloaded 1113 times

Last edited by F. Beister on Wed Mar 24, 2004 3:22 pm, edited 1 time in total.