def normalize(v):
return v/numpy.linalg.norm(v)


def hat(v):
return numpy.array([-v[1],v[0],0],numpy.float32)


def reverse_angle(c,s):
if abs(c) < abs(s):
a = degrees(acos(c))
if s < 0: a = -a
else:
a = degrees(asin(s))
if c < 0: a = 180 - a
if a < 0:
if a > -0.001:
a = 0
else:
a += 360
return a


vertex = a
normal = normalize(numpy.cross(normalize(b - a),normalize(c - a)))

l = sqrt(normal[0]*normal[0] + normal[2]*normal[2])
if abs(l) < 0.001:
if cy < 0: continue
cy = 1
sy = 0
else:
cy = normal[2]/l
sy = normal[0]/l

cx = l
sx = -normal[1]

Rx = numpy.array([
[1,0,0],
[0,cx,sx],
[0,-sx,cx]],numpy.float32)

Ry = numpy.array([
[cy,0,-sy],
[0,1,0],
[sy,0,cy]],numpy.float32)

v0 = numpy.dot(Rx,numpy.dot(Ry,b - a))
l = sqrt(v0[0]*v0[0] + v0[1]*v0[1])
cz = v0[0]/l
sz = v0[1]/l

Rz = numpy.array([
[cz,sz,0],
[-sz,cz,0],
[0,0,1]],numpy.float32)

v0 = numpy.dot(Rz,v0)
v1 = numpy.dot(Rz,numpy.dot(Rx,numpy.dot(Ry,c - a)))

n0 = normalize(hat(v1 - v0))
n1 = normalize(hat(-v1))

rotation_x = reverse_angle(cx,sx)
rotation_y = reverse_angle(cy,sy)
rotation_z = reverse_angle(cz,sz)