2
$\begingroup$

I wanted to find an equation which would result in a given type of pasta (e.g. Farfalle) when plotted. I looked into George Legendre's book Pasta by Design which gives some interesting equations to plot dozens of different pasta types. However, the plots in the book are only many discrete points that together look like pasta. I would prefer a continous function that gives the right surface. I tried using the points that I obtained from one of the formulas in the book to create a response surface via a second degree taylor approximation. However, this resulted in a not-so-nice approximation which was total rubbish on the pasta boundaries (which is not surprising when using response surfaces).

Does anyone have an idea how to obtain a surface plot of a Farfalle noodle? I know that other kinds of pasta like spaghetti are easier to plot but I am interested in creating a Farfalle plot. Any hints and help would be much appreciated.

Edit: as was pointed out, the teeth of the Farfalle might be hard to design. If it makes the problem significantly easier, these could be left out.

  • 0
    [cross=cap][1] portions of cross cap may be adjusted as also the Whitney umbrella. [1]: https://www.google.co.in/search?q=whitney%20cap&espv=2&biw=1236&bih=563&source=lnms&tbm=isch&sa=X&ved=0ahUKEwja8fur4eXRAhVIN48KHZkrC4wQ_AUIBigB#tbm=isch&q=cross%20cap%20surface&imgrc=RGa7Vw_b8UwApM%3A – 2017-01-28

1 Answers 1

2

Due to the presence of "teeth" at the boundary of the pasta, I would suggest to forget the search for an equation and rather consider using CSG (contructive solid geometry ... In case you don't know what it is about, look here)

EDIT :

Here is a try, with Maple ...

enter image description here

plot3d([.2*t*(.2+s^2-(1/2)*s^4), s, .3*cos(t)], s = -1 .. 1, t = -2*Pi .. 2*Pi, grid = [20, 60], scaling = constrained)

Or maybe better :

enter image description here

plot3d([.2*t*(.1+s^2-(1/2)*s^4), s, .2*cos(t)*exp(-3*s^2)], s = -1 .. 1, t = -2*Pi .. 2*Pi, grid = [30, 50], scaling = constrained, style = patchnogrid)

To be compared with :

enter image description here

  • 0
    Why do you think the teeth cannot be given by an equation? – 2017-01-28
  • 0
    I have the intuition that it would be possible only by considering some parametric surface with the parameters varying in some ugly set. If we forget the teeth, I think it's not so difficult to get a neat set of parametric equations (I mean something like $x=f(u,v)$, $y=g(u,v)$ and $z=h(u,v)$). – 2017-01-28
  • 0
    I guess the teeth can be dropped, if it makes the problem significantly easier. – 2017-01-28