Crocheted sphere pattern generator

crocheted_sphere.py

#!/usr/bin/env python3

''' Crocheted sphere pattern generator.

    Calculate the number of stitches per row in a crocheted sphere
    of a given number of rows, and thence print a crochet pattern.

    Original patterns from http://www.craftster.org/forum/index.php?topic=341241.0

    Written by PM 2Ring 2011.10.20
    Updated to Python 3.6 2018.10.03

Key:
Ch = chain
Sc = single crochet
inc = 2 single crochet in next stitch.
dec = single crochet decrease.
These are worked in spiral rounds.

'''

import sys
from math import sin, pi
from itertools import chain

intro = """
An ideal Crocheted Sphere pattern.

All stitches are single crochet, apart from the initial chain.

Ch = chain
Sc = single crochet
inc = 2 single crochet in next stitch.
dec = single crochet decrease.

These are worked in spiral rounds.
"""

def main(n):
    """ Print an ideal crocheted sphere pattern """
    print(intro)

    #Account for null "rows" at the poles.
    nn = n + 1
    #Polar angle between each row
    ang = pi / nn
    #1st row is always == 6
    equator = 6.0 / sin(ang)

    head = 'Ch 2. 6 Sc in second Ch from hook.'
    foot = (
        '[dec] * 4. Fasten off. (4)\n'
        'Weave loose end through each stitch '
        'in the opening. Pull tightly to close.'
    )

    rowlengths = [int(0.55 + equator * sin(i * ang)) for i in range(nn)]
    deltas = [0] + [j - k for j, k in zip(rowlengths[1:], rowlengths)] 

    print("Total number of rows =", n)
    print("Total number of stitches =", sum(rowlengths[1:]) - 2)
    print(f"Equator = {equator:.3f}\n")

    for i in range(1, nn):
        rowlen = rowlengths[i]
        #First and last rows
        if i == 1:
            print(f"Row {i:2}: {head} ({rowlen})")
            continue
        elif i == n:
            print(f"Row {i:2}: {foot}")
            return

        delta = deltas[i]
        if delta > 0:
            # Northern hemisphere, increasing
            ch = 'inc'
            k = rowlen - 2 * delta
        elif delta < 0:
            # Southern hemisphere, decreasing
            ch = 'dec'
            k = rowlen + delta
        else:
            # Equatorial band
            print(f"Row {i:2}: even ({rowlen})")
            continue

        delta = abs(delta)
        f = k / delta
        # Fill the stitches buffer with the delta pattern
        buff = [int(f * u) for u in range(delta + 1)]
        buff = [u - v for u, v in zip(buff[1:], buff)]
        # Rotate the end section to the front
        buff = [buff[-1]] + buff[:-1]

        # Halve the front section, and save the other
        # half so it can be rotated back to the end
        u = buff[0]
        buff[0] = u // 2
        sa = u - buff[0]

        # Insert the 'inc' or 'dec' tokens. A token replaces a zero delta,
        # and a token is inserted after a non-zero delta.
        buff = list(chain.from_iterable((u, ch) if u else (ch,) for u in buff))
        if sa:
            # Append the the rotated half from the front section
            buff.append(sa)

        #Condense the pattern, if it repeats exactly
        u = len(buff)
        for k in range(1, u // 2):
            if u % k == 0:
                start = buff[:k]
                m = u // k
                if buff == start * m:
                    buff = start
                    break
        else:
            m = 1

        buff = ', '.join([f"{u:2}" for u in buff])
        if m > 1:
            buff = f"[{buff}] * {m}"

        print(f"Row {i:2}: {buff} ({rowlen})")

if __name__ == '__main__':
    n = int(sys.argv[1]) if len(sys.argv) > 1 else 20
    main(n)