# Generative Design Variations M.3.2.4 Drawing a mesh using u-v-coördinates

This is the fourth example of the ‘Formulated bodies’ chapter. The Generative Design book describes this example as follows: ‘Obtaining the values of x and y becomes much simpler if they are calculated using a formula rather than taken directly. The shapes that can be generated use the same formulas and are also rotated the same way in space. The different value ranges for u and v make sure that a different part of the formula’s entire surface is drawn.’ Here is the original code:
M_3_2_04

I have prepared a Flickr Album which contains all the images I have made during this assignment. You can find that clicking this url:
GDV_M_3_2_4

And because these programs do not work in JavaScript I have prepared the code on my loftmatic page. When you click on the previews you get to see the Processing code only:
Loftmatic

I was so impolite to remove the arrow left / right: uMin, uMax – / + and replace the arrow down / up with: Zoom – / +. They were used twofold (you can find the same functionality under the keys 1-8). I did this because I needed those keys for my zoom in and out functionality. It seems that you can make pretty abstract objects with this program. Let’s see where we are going this time.
M_3_2_04_GDV_01

I tried to reconstruct the examples of M.3.2.4  from the Generative Design book. But the settings from the book gave me totally different objects than the printed examples. And because that did not work out I started working on more than one object. Using a for loop I have repeated the object 9 times. Horizontal and vertical. This gives me the possibility to make complex patterns with 81 3-dimensional objects.
M_3_2_04_GDV_02

I am trying to get the total number of 81 higher. Of course this is a tradeoff between the amount of objects and the image quality / H & V GridDefinition. I have now 18 objects horizontal and vertical = 324 objects in total. And they are still listening to my keystrokes of 1 – 8.
M_3_2_04_GDV_03

Made some variations by adjusting the horizontal and vertical min-max value range.
M_3_2_04_GDV_04

Used a small modification on line 128 and 135. Changed that setting from 0.75 to 1.01.
M_3_2_04_GDV_05

What if I decrease the H & V GridDefinition to 1? Than I can increase the complexity again. But 1 gives me a dull flat object. 2 Makes a difference. Doubled the amount of objects.
M_3_2_04_GDV_06

Introduced a second field with meshes. And this makes the program terribly slow. Rotated one field 45 degrees. Because this is not working I decreased the H & V GridDefinition to 10.
M_3_2_04_GDV_07

The same two objects but now one of them is rotated on the x-angle.
M_3_2_04_GDV_08

Increased the amount of objects to 100 (-50, 50). Kept the H & V GridDefinition to a very low 4. This gives me plenty of room to use more objects. And because I will not be close with the camera I am able to do this without losing image quality. Used 1 * 1.5, 2.0, 2.5, 3.0 and 3.5 for bending the object. Now I can use the original objects to put a structure on the model. After a while I found out that it was no problem to go up closer with the camera into the object. The image quality is good enough.
M_3_2_04_GDV_09

Introduced a copy of the first object. Rotated it on the y. And mostly made screendumps on the inside of the object. I think the object itself is too complicated for showing it totally. But the separate parts close-up are fine.
M_3_2_04_GDV_10