Phyllotaxis on any surface of revolution?

grasshopper
unhandled
math

#1

Hello all,
Currently I am trying be able to input any profile curve into the definition, make a surface of revolution and populate it with points with a phyllotaxis pattern.
After extensive research on papers, gh forums and wolfram, I think I found what I needed.

http://blog.wolfram.com/2011/07/28/how-i-made-wine-glasses-from-sunflowers/

This blog thoroughly explains how any surface of revolution can be populated with this kind of pattern.Showing the math and explaining the logic behind it. It first populated a half a sphere (Thing I have achieve in GH with same results) and then goes on into populating any surface of revolution. Problem is it is coded in Mathematica.

I was able to interpret it with some help, and populated half a sphere correctly. Then I tried the rest, with a result, but not exactly the same. (If I input an arc to have half a sphre as a surface of revolution, the population varies, with many points stacked and superpositioning on top) this is not ok.

Both hemishpheres are supposed to be the same.
The first one in right.
The second one is not.

If someone could help me with finding errors in the translation, making a translation of his own, or coming up with a total different method it would be really helpful.

Phyllotaxis Surface Revolution 1.0.gh (11.0 KB)


#2


Phyllotaxis Surface Revolution 1.0.gh (23.0 KB)
This is what the PhylloSurface component does in PhylloMachine.


#3

Thanks Daniel, will look into it, but I was really hoping to achieve it with what I already had.


#4

Daniel, I saw the corrections you made to the first equation that populated a hemisphere with the pi/180.
What I don’t is why this equation gives a much organized population and the other two a much more packed one. (using approximately the same number of points).

Which one is right?

First Equation:

Second Equation:

Your example (practically the same as my second equation, love your solution btw)

I think both the second equation I arrived to and your example show an overpopulation in the center, but maybe this is the way it is in nature and the first equation is simply wrong?


#5

I don’t think it’s that simple. We can use mathematics to approximate or simulate natural solutions, so one method is more correct than another following aesthetic criteria of similarity, and that depends on the specific natural object you are trying to simulate.
The phyllotaxis is a pattern characterized by radially rotating the golden angle, how you treat the rest of the parameters, in any coordinate system (Cartesian, cylindrical (second way, and mine) or polar (first way)) is completely indifferent from my point of view, there is no one better than the other, just ways to express what you want to do, the nature works differently.


#6

I understand, I wrongly assumed that as two methods gave the same solution then the odd one must be wrong. But its just a variation.

I guess my question would be then, how do you control this parameter? So that the example you provided can also generate the organization of the first equation. Maybe its just a factor of addition or multiplication?


#7

Plug in a GraphMapper between the second Series and the Point Cylindrical and use a Bezier graph, or if you want to use the equations you’ll have to fiddle with operations.