a Python bit that creates the shape of the spline for a 'standard' Shimano freehub cassette body

shimano9spline280.py

from math import cos,sin,atan,radians
import os

class Pt():
	def __init__(self,x=0,y=0):
		self.x = x
		self.y = y
	def rotate(self,about,a,returnInts=False):
		ax = about.x
		ay = about.y
		rads = radians(a)
		cosa = cos(rads)
		sina = sin(rads)
		rx = ax + cosa * (self.x - ax) - sina * (self.y - ay)
		ry = ay + sina * (self.x - ax) + cosa * (self.y - ay)
		return(self.returnPt(rx,ry,returnInts))
	def trans(self,transPt,returnInts=False):
		tx = self.x + transPt.x
		ty = self.y + transPt.y
		return(self.returnPt(tx,ty,returnInts))
	def rect(self,len,a,returnInts=False):
		dx = self.x + len * cos(radians(a))
		dy = self.y - len * sin(radians(a))
		return(self.returnPt(dx,-dy,returnInts))
	def cs(self,b,c):
		f = cos(atan(b/c))
		x = self.x + round(f * c)
		y = self.y + b
		return Pt(x,y)
	def couplet(self):
		return(f'{round(self.x,2)},{round(self.y,2)}')
	@staticmethod
	def returnPt(x,y,returnInts):
		if returnInts:
			return(Pt(round(x),round(y)))
		else:
			return(Pt(x,y))

a = 40.0
r = 280
s = 18
a1 = 22
a2 = 182

pz = Pt(r,0)
p1 = pz.rotate(Pt(),-20)
#p2 = p1.rect(s,a1)
p2 = Pt(p1.x-17,p1.y+11)
p4 = pz
#p3 = p4.rect(s,a2)
p3 = Pt(p4.x-19,p4.y-3)
p5 = p4.rotate(Pt(),20)
path = ""

for t in range(9):
	if t == 0:
		cmd = 'M'
	else:
		cmd = 'L'
	p1r = p1.rotate(Pt(),a*t)
	p2r = p2.rotate(Pt(),a*t)
	p3r = p3.rotate(Pt(),a*t)
	p4r = p4.rotate(Pt(),a*t)
	p5r = p5.rotate(Pt(),a*t)
	path = path + f'{cmd}{round(p1r.x)},{round(p1r.y*-1)} '
	path = path + f'L{round(p2r.x)},{round(p2r.y*-1)} '
	path = path + f'L{round(p3r.x)},{round(p3r.y*-1)} '
	path = path + f'L{round(p4r.x)},{round(p4r.y*-1)} '
	path = path + f'A 280,280 0 0 0 {round(p5r.x)},{round(p5r.y*-1)} '
	path = path + '\n'

svg = f'''
<svg width="800" height="800">

	<rect width="800" height="800" style="fill:#ccc; "/>

	<g transform="translate(400,400)">

		<path
			style= "fill:rgb(33,33,33); stroke-width:0px; stroke:#f00;"
			d="{path} Z"/>
	</g>

</svg>
'''
print(svg)
fp = open('thurs.svg','w')
fp.write(svg)
fp.close