2 from __future__ import print_function
5 from numpy import cos, sin
10 from moedebug import *
13 from math import atan2, atan, sqrt
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)
32 # - solve in the plane containing dP and dQ
33 # - total distance normal to that plane gives mu
34 # - now resulting curve is not parallel to dP at P
35 # nor dQ at Q, so tilt it
36 # - [[ pick as the hinge point the half of the curve
37 # with the larger s or t ]] not yet implemented
38 # - increase the other distance {t,s} by a bodge factor
39 # approx distance between {Q,P} and {Q,P}' due to hinging
40 # but minimum is 10% of (wlog) {s,t} [[ not quite like this ]]
42 dPQplane_normal = np.cross(dp, dq)
44 if np.linalg.norm(dPQplane_normal) < 1E-6:
45 dbg('dPQplane_normal small')
46 dPQplane_normal = np.cross([1,0,0], dp)
47 if np.linalg.norm(dPQplane_normal) < 1E-6:
48 dbg('dPQplane_normal small again')
49 dPQplane_normal = np.cross([0,1,0], dp)
51 dPQplane_normal = unit_v(dPQplane_normal)
53 dPQplane_basis = np.column_stack((np.cross(dp, dPQplane_normal),
58 dPQplane_basis = np.vstack((dPQplane_basis, [0,0,0,1]))
60 dPQplane_into = np.linalg.inv(dPQplane_basis)
63 p_plane_check = augmatmultiply(dPQplane_into, p)
64 dp_plane = augmatmultiply(dPQplane_into, dp, augwith=0)
65 dq_plane = augmatmultiply(dPQplane_into, dq, augwith=0)
66 q_plane = augmatmultiply(dPQplane_into, q)
67 dist_pq_plane = np.linalg.norm(q_plane)
69 dbg('plane:', p_plane_check, dp_plane, dq_plane, q_plane)
71 # two circular arcs of equal maximum possible radius
72 # algorithm courtesy of Simon Tatham (`Railway problem',
73 # pers.comm. to ijackson@chiark 23.1.2004)
74 railway_angleoffset = atan2(*q_plane[0:2])
75 railway_theta = tau/4 - railway_angleoffset
76 railway_phi = atan2(*dq_plane[0:2]) - railway_angleoffset
77 railway_cos_theta = cos(railway_theta)
78 railway_cos_phi = cos(railway_phi)
79 if railway_cos_theta**2 + railway_cos_phi**2 > 1E6:
80 railway_roots = np.roots([
81 2 * (1 + cos(railway_theta - railway_phi)),
82 2 * (railway_cos_theta - railway_cos_phi),
85 for railway_r in railway_roots:
86 def railway_CPQ(pq, dpq, railway_r):
87 return pq + railway_r * [-dpq[1], dpq[0]]
89 railway_CP = railway_CPQ([0,0,0], dp_plane, railway_r)
90 railway_QP = railway_CPQ(q_plane[0:2], -dq_plane, railway_r)
91 railway_midpt = 0.5 * (railway_CP + railway_QP)
94 def railway_ST(C, start, end, railway_r):
95 delta = atan2(*(end - C)[0:2]) - atan2(start - C)[0:2]
98 try_s = railway_ST(railway_CP, [0,0], midpt, railway_r)
99 try_t = railway_ST(railway_CP, midpt, q_plane, railway_r)
100 try_st = try_s + try_t
101 if best_st is None or try_st < best_st:
106 start_mu = q_plane[2] / (start_s + start_t)
109 else: # twoarcs algorithm is not well defined
112 start_s = dist_pq_plane * .65
113 start_t = dist_pq_plane * .35
116 bodge = max( q_plane[2] * start_mu,
117 (start_s + start_t) * 0.1 )
118 start_s += 0.5 * bodge
119 start_t += 0.5 * bodge
123 tilt = atan(start_mu)
124 tilt_basis = np.array([
126 [ 0, cos(tilt), sin(tilt), 0 ],
127 [ 0, -sin(tilt), cos(tilt), 0 ],
130 findcurve_basis = matmatmultiply(dPQplane_basis, tilt_basis)
131 findcurve_into = np.linalg.inv(findcurve_basis)
133 q_findcurve = augmatmultiply(findcurve_into, q)
134 dq_findcurve = augmatmultiply(findcurve_into, dq, augwith=0)
136 findcurve_target = np.hstack((q_findcurve, dq_findcurve))
137 findcurve_start = (sqrt(start_s), sqrt(start_t), start_la,
138 start_mu, start_gamma, start_kappa)
140 findcurve_epsilon = dist_pq_plane * 0.01
142 global findcurve_subproc
143 if findcurve_subproc is None:
144 dbg('STARTING FINDCURVE')
145 findcurve_subproc = subprocess.Popen(
148 stdin=subprocess.PIPE,
149 stdout=subprocess.PIPE,
152 # restore_signals=True, // want python2 compat, nnng
153 universal_newlines=True,
156 findcurve_input = np.hstack((findcurve_target,
158 [findcurve_epsilon]))
160 def dbg_fmt_params(fcp):
161 return (('s=%10.7f t=%10.7f sh=%10.7f'
162 +' st=%10.7f la=%10.7f mu=%10.7f ga=%10.7f ka=%10.7f')
164 (( fcp[0]**2, fcp[1]**2 ) + tuple(fcp)))
166 #dbg('>> ' + ' '.join(map(str,findcurve_input)))
168 dbg(('RUNNING FINDCURVE' +
170 ' target Q=[%10.7f %10.7f %10.7f] dQ=[%10.7f %10.7f %10.7f]')
172 tuple(findcurve_input[0:6]))
173 dbg(('%s initial') % dbg_fmt_params(findcurve_input[6:12]))
175 print(*findcurve_input, file=findcurve_subproc.stdin)
176 findcurve_subproc.stdin.flush()
178 hc.func = symbolic.get_python()
182 l = findcurve_subproc.stdout.readline()
185 if not l: vdbg().crashing('findcurve EOF')
186 if not l.startswith('['):
194 dbg(('%s Q=[%10.7f %10.7f %10.7f] dQ=[%10.7f %10.7f %10.7f]%s')
196 (( dbg_fmt_params(l[0:6]), ) + tuple(l[6:12]) + (commentary,) ))
199 hc.findcurve_result = l[0:6]
200 hc.threshold = l[0]**2
201 hc.total_dist = hc.threshold + l[1]**2
202 #vdbg().curve( hc.point_at_t )
204 def point_at_t(hc, normalised_parameter):
205 dist = normalised_parameter * hc.total_dist
206 ours = list(hc.findcurve_result)
207 if dist <= hc.threshold:
211 ours[1] = sqrt(dist - hc.threshold)
212 asmat = hc.func(*ours)