The Shape of Birds Eggs

Hello friends, we need your help in building the forms of eggs. If possible please help.

D'Arcy Thomson in his "On Growth and Form" (1917)developed his method of transformed coordinates to study the geometric relationship between similar structures in different species.

Applying his ideas to the shape of birds eggs (viewed from the side), we start with a circle drawn on a square grid and deform it by deforming the grid

Different species of birds have different egg shapes. Drag the named grid points to change the shape of the birds egg.http://saltire.com/egg1.html

The formula for the egg shape is taken from the paper:

"The Shape of Birds' Eggs" by P.H. Todd & I.H.M. Smart, J. Theoretical Biology, (1984) vol 106, pp 239 - 243

Attachments:

The Shape of Birds' Eggs.bmp, 664 KB

Replies to This Discussion

Permalink Reply by Danny Boyes on July 10, 2012 at 2:54pm

As the majority of this post is cut and paste from the link I cannot work out what the question is.

All I can add is possible the work I did last moth on eggs which you can find here: http://www.grasshopper3d.com/forum/topics/draw-egg-curves-from-an-e...

Permalink Reply by Alex on July 10, 2012 at 3:21pm

Thank you Danny Boyes. I met with your decision, it is a bit does not fit. The form must form by changing the parameters of the grid.

Permalink Reply by David Rutten on July 10, 2012 at 3:52pm

What parameters are these? If you have a 2D 4x4 grid and you allow every single grid node to be freely adjusted you end up with 50 individual parameters. If you only allow the grid to be deformed as per the applet on that site, then you end up with 10 parameters.

I attached a file which only allows symmetric deformation along the y-axis, i.e. 5 parameters. It uses Surface to Surface mapping.