reuleaux_triangle.py

# https://en.wikipedia.org/wiki/Reuleaux_triangle
import math
import cairo

def pos_on_circle(cx, cy, radius, angle):
    # Convert polar to cartesian, Author: Matthew Schweiss

    x = math.cos(angle) * radius + cx
    y = math.sin(angle) * radius + cy
    return x, y

filename = "reuleaux_triangle.svg"

center_radius = 100
arc_radius = center_radius * math.sin(math.pi / 3) / math.sin(math.pi / 6)

with cairo.SVGSurface(filename, arc_radius, center_radius * 2) as surface:
    # Draw a Reuleaux triangle
    ctx = cairo.Context(surface)

    cx, cy = arc_radius / 2, center_radius
    x1, y1 = pos_on_circle(cx, cy, center_radius, -math.pi / 2)
    x2, y2 = pos_on_circle(cx, cy, center_radius, math.pi / 6)
    x3, y3 = pos_on_circle(cx, cy, center_radius, 5 * math.pi / 6)

    ctx.arc(x1, y1, arc_radius, math.pi / 3, 2 * math.pi / 3)
    ctx.arc(x2, y2, arc_radius, math.pi, 4 * math.pi / 3)
    ctx.arc(x3, y3, arc_radius, 5 * math.pi / 3, 0)
    ctx.fill()