2 from __future__ import print_function
5 from numpy import cos, sin
8 from moebdebug import dbg
13 def augment(v): return np.append(v, 1)
14 def augment0(v): return np.append(v, 0)
15 def unaugment(v): return v[0:3]
17 findcurve_subproc = None
19 class HelixishCurve():
25 dp = unit_v(cp[1]-cp[0])
26 dq = unit_v(cp[3]-cp[2])
28 dbg('HelixishCurve __init__', cp)
31 # - solve in the plane containing dP and dQ
32 # - total distance normal to that plane gives mu
33 # - now resulting curve is not parallel to dP at P
34 # nor dQ at Q, so tilt it
35 # - [[ pick as the hinge point the half of the curve
36 # with the larger s or t ]] not yet implemented
37 # - increase the other distance {t,s} by a bodge factor
38 # approx distance between {Q,P} and {Q,P}' due to hinging
39 # but minimum is 10% of (wlog) {s,t} [[ not quite like this ]]
41 dPQplane_normal = np.cross(dp, dq)
42 if (np.norm(dPQplane_normal) < 1E6):
43 dPQplane_normal += [0, 0, 1E5]
44 dPQplane_normal = unit_v(dPQplane_normal)
46 dPQplane_basis = np.column_stack(np.cross(dp, dPQplane_normal),
50 dPQplane_basis = np.vstack(dPQplane_basis, [0,0,0,1])
51 dPQplane_into = np.linalg.inv(dPQplane_basis)
53 dp_plane = unaugment(dPQplane_into * augment0(dp))
54 dq_plane = unaugment(dPQplane_into * augment0(dq))
55 q_plane = unaugment(dPQplane_into * augment(q))
56 dist_pq_plane = np.linalg.norm(q_plane)
58 # two circular arcs of equal maximum possible radius
59 # algorithm courtesy of Simon Tatham (`Railway problem',
60 # pers.comm. to ijackson@chiark 23.1.2004)
61 railway_angleoffset = atan2(*q_plane[0:1])
62 railway_theta = tau/4 - railway_angleoffset
63 railway_phi = atan2(*dq_plane[0:1]) - railway_angleoffset
64 railway_cos_theta = cos(railway_theta)
65 railway_cos_phi = cos(railway_phi)
66 if railway_cos_theta**2 + railway_cos_phi**2 > 1E6:
67 railway_roots = np.roots([
68 2 * (1 + cos(railway_theta - railway_phi)),
69 2 * (railway_cos_theta - railway_cos_phi),
72 for railway_r in railway_roots:
73 def railway_CPQ(pq, dpq):
75 return pq + railway_r * [-dpq[1], dpq[0]]
77 railway_CP = railway_CPQ([0,0,0], dp_plane)
78 railway_QP = railway_CPQ(q_plane[0:2], -dq_plane)
79 railway_midpt = 0.5 * (railway_CP + railway_QP)
82 def railway_ST(C, start, end):
84 delta = atan2(*(end - C)[0:2]) - atan2(start - C)[0:2]
87 try_s = railway_ST(railway_CP, [0,0], midpt)
88 try_t = railway_ST(railway_CP, midpt, q_plane)
89 try_st = try_s + try_t
90 if best_st is None or try_st < best_st:
95 start_mu = q_plane[2] / (start_s + start_t)
97 else: # twoarcs algorithm is not well defined
99 start_s = dist_pq_plane * .65
100 start_t = dist_pq_plane * .35
103 bodge = max( q_plane[2] * mu,
104 (start_s + start_t) * 0.1 )
105 start_s += 0.5 * bodge
106 start_t += 0.5 * bodge
111 tilt_basis = np.array([
113 0, cos(tilt), -sin(tilt), 0,
114 0, sin(tilt), cos(tilt), 0,
117 findcurve_basis = dPQplane_basis * tilt_basis
118 findcurve_into = np.linalg.inv(findcurve_basis)
120 q_findcurve = unaugment(findcurve_into, augment(q))
121 dq_findcurve = unaugment(findcurve_into, augment0(dq))
123 findcurve_target = np.concatenate(q_findcurve, dq_findcurve)
124 findcurve_start = (sqrt(start_s), sqrt(start_t), start_la,
125 start_mu, start_gamma, start_kappa)
127 findcurve_epsilon = dist_pq_plane * 0.01
129 if findcurve_subproc is None:
130 findcurve_subproc = subprocess.Popen(
133 stdin=subprocess.PIPE,
134 stdout=subprocess.PIPE,
137 restore_signals=True,
138 universal_newlines=True,
141 findcurve_input = np.hstack((findcurve_target,
143 [findcurve_epsilon])))
144 dbg('RUNNING FINDCURVE', *findcurve_input)
145 print(findcurve_subproc.stdin, *findcurve_input)
146 findcurve_subproc.stdin.flush()
149 l = findcurve_subproc.stdout.readline()
154 findcurve_result = l[0:5]
156 symbolic.get_python(something)