# Project curves to asymmetric surface

Hi there

In a research activity in the field of plastic surgery, I face a problem in modeling. I want to fill the outer surface of the breast with the curves that follow the Fibonacci sequence, I create these curves in plan view but when I want to project them into the breast surface it takes on a strange shape due to the asymmetric of breast shape.

I read many posts here and some articles about how to create breasts by differential equation but I can’t find the right way.

my goal is these Fibonacci curves when coming down to the breast have the same shape and distance to the plan view. if give me some think and suggest to go in right way i will be thankful so much.

grasshopper file:
Fibo projection.gh (815.4 KB)

Then I ignored your approach and took a different tack. The bright colored curves are planar sections, sorted and flipped (white group). I tried Relative Item to get spiral curves from them (in ‘Tree/List Viewer’, blue and yellow) but that didn’t work vey well?

Fibo projection_2022Jan16a.gh (850.7 KB)

P.S. Planar sections are aligned better using the axis between the bottom and top of the “cone” shape. Diagonal curves aren’t working too well.

Fibo projection_2022Jan16b.gh (852.3 KB)

P.P.S. This method adjusts seams on divided “horizontal” curves to get well behaved diagonals.
UPDATED to add ‘Count’ slider’, then updated again to add ‘Target’ slider (version ‘17a’)

Later… Too bad Pull Curve fails in this case, missing segments of the curves.

P.S. I forgot to add a Remap ‘T’ (Target) slider (0 to 1, cyan group) after the Graph Mapper, which controls the degree of twist that results from adjusting seams.

Fibo projection_2022Jan17a.gh (860.6 KB)

1 Like

@Joseph_Oster Thank you very much for your comprehensive description and process. as you say you ignore my approach but the way you described it helped me a lot in moving towards the optimal answer. In the coming days, I will work more on your solution and the goal I was pursuing, and if progress is made, I will share my findings here.

I think instead of Graph Mapper, if I implement some equation I can close to my target and create Fibonacci curves. something by this concept: Phyllotaxis: The Fibonacci Sequence in Nature - The Myth of the Golden Ratio

I first tried applying your Fibonacci numbers when adjusting seams (and just tried again now) but found no satisfactory result or advantage, though maybe I did it wrong.

the previous method produces curves that do not follow a Fibonacci sequence, I use half of the process and complete it in my way. I start at the point that divides the breast by some concentric plane:

after that, I use a method that unrolls these curves have the same length as the original curves:

after I project Fibonacci spiral to these planar curves:

to fill the surface with these spirals I rotate this spiral around the start point (center of the nipple):

after that, I extract the intersection of the Fibo spirals and planar curves:

now because the planar curves have the same length ( and domain) as the original curve ( that divide the breast) we can orient the position of the points from planar curves to originals:

because I preserve the order of the points in this orientation now I can connect these points to create a Fibo spiral on breast shape:

I think I reach it as I can to my target and thank you @Joseph_Oster without your help I can not proceed with it.

file:
Fibo projection 220125.gh (828.9 KB)