+"""Computing the grid"""
+
+from math import sqrt, acos, copysign
+from geometry import l2ad, line, intersection
+
+def lines(corners):
+ # TODO Error on triangle
+ corners.sort() # TODO does this help?
+ # TODO refactor this vvv
+ cor_d = [(corners[0], (c[0] - corners[0][0], c[1] - corners[0][1]), c) for c in
+ corners[1:]]
+ cor_d = [(float(a[0] * b[0] + a[1] * b[1]) / (sqrt(a[0] ** 2 + a[1] ** 2) *
+ sqrt(b[0] **2 + b[1] ** 2)), a[0] * b[1] - b[0] * a[1], c) for a, b, c in cor_d]
+ cor_d = sorted([(copysign(acos(min(a, 1)), b), c) for a, b, c in cor_d])
+ corners = [corners[0]] + [c for _, c in cor_d]
+ return (_lines(corners, 0) +
+ [(corners[0], corners[3]), (corners[1], corners[2])],
+ _lines(corners[1:4] + [corners[0]], 0) +
+ [(corners[0], corners[1]), (corners[2], corners[3])])
+
+def _lines(corners, n):
+ # TODO what is this?
+ if n == 0:
+ x = half_line(corners)
+ return (_lines([corners[0], x[0], x[1], corners[3]], 1) + [x] +
+ _lines([x[0], corners[1], corners[2], x[1]], 1))
+ else:
+ x = half_line(corners)
+ c = intersection(line(x[0], corners[2]), line(corners[1], corners[3]))
+ d = intersection(line(corners[0], corners[3]), line(corners[1], corners[2]))
+ if d:
+ l = (intersection(line(corners[0], corners[1]), line(c, d)),
+ intersection(line(corners[2], corners[3]), line(c, d)))
+ else:
+ lx = line(c, (c[0] + corners[0][0] - corners[3][0],
+ c[1] + corners[0][1] - corners[3][1]))
+ l = (intersection(line(corners[0], corners[1]), lx),
+ intersection(line(corners[2], corners[3]), lx))
+ l2 = half_line([corners[0], l[0], l[1], corners[3]])
+ if n == 1:
+ return ([l, l2] + _lines([l[0], l2[0], l2[1], l[1]], 2)
+ + _lines([corners[0], l2[0], l2[1], corners[3]], 2)
+ + _lines([l[0], corners[1], corners[2], l[1]], 2))
+ if n == 2:
+ return [l, l2]
+
+
+def half_line(corners):
+ # TODO what is this?
+ c = center(corners)
+ d = intersection(line(corners[0], corners[3]), line(corners[1], corners[2]))
+ if d:
+ l = line(c, d)
+ else:
+ l = line(c, (c[0] + corners[0][0] - corners[3][0],
+ c[1] + corners[0][1] - corners[3][1]))
+ p1 = intersection(l, line(corners[0], corners[1]))
+ p2 = intersection(l, line(corners[2], corners[3]))
+ return (p1, p2)
+
+def center(corners):
+ """Given a list of four corner points, return the center of the square."""
+ return intersection(line(corners[0], corners[2]),
+ line(corners[1], corners[3]))