from euclid import Vector3, Matrix4

def makeFrame(p, u, v, w):
    m = Matrix4()
    # axis rotation
    m.a, m.b, m.c = u.x, v.x, w.x
    m.e, m.f, m.g = u.y, v.y, w.y
    m.i, m.j, m.k = u.z, v.z, w.z
    # translation
    m.d, m.h, m.l = p.x, p.y, p.z
    return m


def frenet(points):
    p0 = points.next()
    p1 = points.next()

    u0 = p1 - p0
    u0.normalize()

    # choose axis to project onto
    maxDot = 0.999
    axis = Vector3(1.0, 0.0, 0.0)
    if u0.dot(axis) > maxDot:
        axis = Vector3(0.0, 1.0, 0.0)
        if u0.dot(axis) > maxDot:
            axis = Vector3(0.0, 0.0, 1.0)

    # start frame
    rot = Quaternion.new_rotate_axis(0.5*math.pi, axis)
    v0 = u0.project(axis)
    v0 = rot * v0
    w0 = u0.cross(v0)

    yield makeFrame(p0, v0, w0, u0)
    p0 = p1

    # middle frames
    for p in points:
        u = p -p0
        u.normalize()
        v = u0.project(v0)
        v.normalize()
        if w.dot(w0) < 0.0:
            w = -w
        yield makeFrame(p0, v0, w0, u0)
        p0 = p
        u0 = u
        v0 = v
        w0 = w

    # final frame
    yield makeFrame(p0, v0, w0, u0)