return cos(zeta) * r + sin(zeta) * tw._axis
class MoebiusHalf:
- def __init__(m, nu):
+ def __init__(m, nu, nt):
'''
MoebiusHalf().edge is a Twirler for the edge,
expecting theta = u * tau (see MoebiusHalf().point)
m.edge = Twirler(origin, unit_z, unit_x, -2, tau/2)
m.midline = Twirler(-unit_z, unit_z, unit_y, -0.5, 0)
m.nu = nu
+ m.nt = nt
m._thetas = [ u * tau for u in np.linspace(0, 1, nu+1) ]
m._cp2b = BezierSegment([ (c,) for c in [0.33,0.33, 1.50]])
m._beziers = [ m._bezier(theta) for theta in m._thetas ]
+ m._t_vals = np.linspace(0, 1, m.nt+1)
def _bezier(m, theta, constructor=DoubleCubicBezier):
cp = [None] * 4
cp[0] = m.edge .point(theta)
cp[1] = cp[0] + cp1scale * m.edge .dirn (theta)
cp[2] = cp[3] + cp2scale * m.midline.dirn (theta*2)
return constructor(cp)
- def point(m, iu, t):
+ def point(m, iu, it):
'''
0 <= iu <= nu meaning 0 <= u <= 1
along the extent (well, along the edge)
0 and 1 are both the top half of the flat traverse
0.5 is the bottom half of the flat traverse
- 0 <= t <= 1 across the half-traverse
+ 0 <= it <= nt across the half-traverse
0 is the edge, 1 is the midline
'''
+ t = m._t_vals[it]
return np.array(m._beziers[iu].point_at_t(t))
def details(m, iu, t):
m.nv = nv
m.nw = nw
m.nt = nw/2
- m._t_vals = np.linspace(0, 1, m.nt+1)
- m.h = MoebiusHalf(nu=nv*2)
+ m.h = MoebiusHalf(nu=nv*2, nt=m.nt)
def _vw2tiu_kw(m, v, w):
if w <= m.nt:
iu = m.nv + v
#print('v,w=%d,%d => it,iu=%d,%d' % (v,w,it,iu),
# file=sys.stderr)
- return { 't': m._t_vals[it], 'iu': iu }
+ return { 'it': it, 'iu': iu }
def point(m, v, w):
return m.h.point(**m._vw2tiu_kw(v,w))