How to make shamrock image

Question

I am trying to make a shamrock crystal for later fabrication, and am using nazca design tool for doing it.

How can I place the trapezoid so that the sides of the trapezoid are parallel to the cyrcles and are always at the end of the sharp corners.

import nazca as nd
import numpy as np
# Define parameters
a = 500
semib = 0.255 * a
semia = semib * 0.75
shift = 0.22 * a
thickness = 0.65 * a
f = 2 * semia / np.sqrt(3)
r = semia

with nd.Cell(name="shamrock") as sham:
    # Create circles for the shamrock pattern
    circ1 = nd.geometries.circle(radius=semia, N=100)
    circ2 = nd.geometries.circle(radius=semia, N=100)
    circ3 = nd.geometries.circle(radius=semia, N=100)

    # Create Polygon objects for circles
    circ1_polygon = nd.Polygon(layer=56, points=circ1)
    circ2_polygon = nd.Polygon(layer=56, points=circ2)
    circ3_polygon = nd.Polygon(layer=56, points=circ3)

    # Place circles for the shamrock pattern using put
    circ1_polygon.put(0, shift)
    circ2_polygon.put(-shift * 0.5 * np.sqrt(3), -shift * 0.5)
    circ3_polygon.put(shift * 0.5 * np.sqrt(3), -shift * 0.5)

    # Identify sharp corners
    sharp_corner1 = ((-shift * 0.5 * np.sqrt(3)) / 2, (shift + (-shift * 0.5)) / 2)
    sharp_corner2 = ((0 + (shift * 0.5 * np.sqrt(3))) / 2, (shift + (-shift * 0.5)) / 2)
    sharp_corner3 = ((-shift * 0.5 * np.sqrt(3) + (shift * 0.5 * np.sqrt(3))) / 2, (-shift * 0.5 + (-shift * 0.5)) / 2)
    semicircle_radius  =  f-r
    # Create trapezoid using the trapezoid function
    
    trapezoid_shape = nd.geometries.trapezoid(length=50, height=160, angle1=132, angle2=132, position=1)

    # Create Polygon object for trapezoid
    trapezoid_polygon = nd.Polygon(layer=56, points=trapezoid_shape)

    # Place trapezoid at the sharp corners
    trapezoid_polygon.put(25,75,180)


nd.export_plt(sham)

And here is the picture.

Ideally would be nice to have something like this with the smoothen corners. But I was thinking to put a trapezoid on top to have smoothen the sharper corners.

Answer 1

This can be done by growing and shrinking the polygons in Nazca:

import nazca as nd
import numpy as np

# Define parameters
a = 500
semib = 0.255 * a
semia = semib * 0.75
shift = 0.22 * a
thickness = 0.65 * a
f = 2 * semia / np.sqrt(3)
r = semia

with nd.Cell(name="shamrock") as sham:
    # Create circles for the shamrock pattern
    circ1 = nd.geometries.circle(radius=semia, N=100)
    circ2 = [(x - semia, y - np.sqrt(3) * semia) for x, y in circ1]
    circ3 = [(x + semia, y - np.sqrt(3) * semia) for x, y in circ1]

    # grow and shrink 20%
    pols = nd.grow_polygons([circ1, circ2, circ3], 0.2 * semia)
    pols = nd.grow_polygons(pols, -0.2 * semia)

    for p in pols:
        nd.Polygon(layer=56, points=p).put()

nd.export_plt(sham)