parametric pasta

With the help of George L. Legendre’s mathematical equations defining the shape of Italian pasta - conchiglie rigate, I created their 3D models.

Using the Python programming language inside the Grasshopper plug-in for Rhino 3D modeling software I added additional parameters to the form, like the intensity of grooving, what completely changes the appearance and creates fresh, unique and surprising shapes. Those can be easily adjusted playing with sliders for different parameters.

equations of conchiglie rigate by george l. legendre

the code behind it

import rhinoscriptsyntax as rs
from math​ import pi, cos, sin, pow

point_list = []
polygon_list = []

for i in range(0, spiral + 1):
  for j in range(0, vertical + 1):
    alfa = grooves * 0.25 * sin(j * pi / 250) * cos((6 * j + 25) * pi / 25)
    beta = ((40 - i) / 40) * (0.3 + sin(j * pi / 250)) * pi
    gamma = bend * 2.5 * cos(j / 125 * pi) + 2 * pow(sin((40 - i) / 80 * pi), 10) * pow(sin(j / 250 * pi), 10) * sin(j / 125 * pi + 1.5 * pi)
    x = scale_xy * (alfa + cos(j / 125 * pi) + (5 + 30 * sin(j / 250 * pi)) * sin(beta) * sin(i / 40 * (0.1 * (1.1 + pow(sin(j / 250 * pi), 5))) * pi))
    y = scale_xy * (alfa + (5 + 30 * sin(j / 250 * pi)) * cos(beta) * sin(i / 40 * (0.1 * (1.1 + pow(sin(j / 250 * pi), 5))) * pi) + gamma)
    z = scale_z * 25 * cos((j / 250) * pi)
    point_list.append([x, y, z])

for i in range(0, spiral):
  for j in range(0, vertical):
    p0 = i * (vertical + 1) + j
    p1 = i * (vertical + 1) + j + 1
    p2 = (i + 1) * (vertical + 1) + j + 1
    p3 = (i + 1) * (vertical + 1) + j
    polygon_list.append([p0, p1, p2, p3])

rs.AddMesh(point_list, polygon_list)
conchiglie = ghdoc.Objects.Geometries