Cartesian to polar coordinates converter for photo spheres

polar.py

from math import atan, hypot, degrees

paths = [
	[
		[100, 0],
		[0, 100],
		[-100, 0],
		[0, -100],
	]
]


def interpolate_points(points):
	def interpolate():
		i = 0.0
		while i < 0.991:
			j = 1.0 - i
			more_points.append([x1 * j + x2 * i, y1 * j + y2 * i])
			i += 0.01

	more_points = []
	[x1, y1] = points[0]
	for i in range(1, len(points)):
		[x2, y2] = points[i]
		interpolate()
		x1 = x2
		y1 = y2

	[x2, y2] = points[0]
	interpolate()
	return more_points


def transform_xy(xy):
	[x, y] = xy
	if x == 0:
		longitude = 270 if y < 0 else 90
	else:
		longitude = degrees(atan(y / x))
		if x < 0:
			longitude += 180
		elif y < 0:
			longitude += 360

	radius = hypot(x, y)
	latitude = 180 - degrees(atan(radius / 100))
	return '%f,%f' % (longitude, latitude)

print '<svg xmlns="http://www.w3.org/2000/svg" width="360" height="180">'
for points in paths:
	points = interpolate_points(points)
	print '<path fill="#ff0" d="M ' + ' '.join(map(transform_xy, points)) + ' Z" />'
print '</svg>'

This script converts the diamond shape specified in paths to what appears as a 2D square at the bottom of a photo sphere (think of it as the bottom face of a cube inside the sphere). You can also flip the results to create the top.

Change paths to one or more shapes of your choice. If one of your paths crosses the positive X axis, you'll need to move some of its points 360px to one side in the resulting SVG file, and make a copy 360px to the other side. I could fix this in the code, but I don't need it.