from moedebug import *
from moenp import *
+from moebez import *
from math import atan2, atan, sqrt
import symbolic
-findcurve_subproc = None
+findcurve_subprocs = { }
+
+class OptimisedCurve():
+ def __init__(hc, cp, nt):
+ db = DiscreteBezier(cp, nt, constructor=BezierSegment)
+ fc_input = map(db.point_at_it, range(0, nt+1))
+ for end in (False,True):
+ ei = end ? nt : 0
+ fi = end ? nt-1 : 1
+ cp0i = end ? 0 : 3
+ cp1i = end ? 1 : 2
+ e = cp[cp0i]
+ ef_dirn =unit_v(cp[cp1i] - cp[cp0i])
+ ef_len = np.linalg.norm(fc_input[fi] - fc_input[ei])
+ f = e + ef_dirn * ef_len
+ fc_input[ei] = e
+ fc_input[fi] = f
-class HelixishCurve():
- def __init__(hc, cp):
- symbolic.calculate()
-
- p = cp[0]
- q = cp[3]
- dp = unit_v(cp[1]-cp[0])
- dq = unit_v(cp[3]-cp[2])
-
- dbg('HelixishCurve __init__', cp)
- dbg(dp, dq)
-
- vdbg().arrow(p,dp)
- vdbg().arrow(q,dq)
-
- # the initial attempt
- # - solve in the plane containing dP and dQ
- # - total distance normal to that plane gives mu
- # - now resulting curve is not parallel to dP at P
- # nor dQ at Q, so tilt it
- # - [[ pick as the hinge point the half of the curve
- # with the larger s or t ]] not yet implemented
- # - increase the other distance {t,s} by a bodge factor
- # approx distance between {Q,P} and {Q,P}' due to hinging
- # but minimum is 10% of (wlog) {s,t} [[ not quite like this ]]
-
- dPQplane_normal = np.cross(dp, dq)
-
- if np.linalg.norm(dPQplane_normal) < 1E-6:
- dbg('dPQplane_normal small')
- dPQplane_normal = np.cross([1,0,0], dp)
- if np.linalg.norm(dPQplane_normal) < 1E-6:
- dbg('dPQplane_normal small again')
- dPQplane_normal = np.cross([0,1,0], dp)
-
- dPQplane_normal = unit_v(dPQplane_normal)
-
- vdbg().arrow([0,0,0], dPQplane_normal, color=(1,1,0))
-
- dPQplane_basis = np.column_stack((np.cross(dp, dPQplane_normal),
- dp,
- dPQplane_normal,
- p));
- #dbg(dPQplane_basis)
- dPQplane_basis = np.vstack((dPQplane_basis, [0,0,0,1]))
- dbg(dPQplane_basis)
-
- vdbg().basis(dPQplane_basis)
-
- dPQplane_into = np.linalg.inv(dPQplane_basis)
- dbg(dPQplane_into)
-
- p_plane_check = augmatmultiply(dPQplane_into, p)
- dp_plane = augmatmultiply(dPQplane_into, dp, augwith=0)
- dq_plane = augmatmultiply(dPQplane_into, dq, augwith=0)
- q_plane = augmatmultiply(dPQplane_into, q)
- dist_pq_plane = np.linalg.norm(q_plane[0:2])
-
- vdbg_plane = MatrixVisdebug(vdbg(), dPQplane_basis)
-
- dbg('plane p', p_plane_check, 'dp', dp_plane, 'dq', dq_plane,
- 'q', q_plane, 'dist_pq_plane', dist_pq_plane)
- #vdbg_plane.arrow(p_plane_check, dp_plane)
- #vdbg_plane.arrow(q_plane, dq_plane)
-
- railway_inplane_basis_x = np.hstack((q_plane[0:2], [0]))
- railway_inplane_basis = np.column_stack((
- railway_inplane_basis_x,
- -np.cross([0,0,1], railway_inplane_basis_x),
- [0,0,1],
- [0,0,0],
- ))
- #dbg('railway_inplane_basis\n', railway_inplane_basis)
- railway_inplane_basis = np.vstack((railway_inplane_basis,
- [0,0,0,1]))
- dbg('railway_inplane_basis\n', railway_inplane_basis)
- railway_basis = matmatmultiply(dPQplane_basis, railway_inplane_basis)
- dbg('railway_basis\n', railway_basis)
- #vdbg().basis(railway_basis, hue=(1,0,1))
- vdbg_railway = MatrixVisdebug(vdbg(), railway_basis)
-
- # two circular arcs of equal maximum possible radius
- # algorithm courtesy of Simon Tatham (`Railway problem',
- # pers.comm. to ijackson@chiark 23.1.2004)
- railway_angleoffset = atan2(*q_plane[0:2])
- # these two angles are unconventional: clockwise from north
- railway_theta = tau/4 - (atan2(*dp_plane[0:2]) - railway_angleoffset)
- railway_phi = tau/4 - (atan2(*-dq_plane[0:2]) - railway_angleoffset)
- railway_cos_theta = cos(railway_theta)
- railway_cos_phi = cos(railway_phi)
-
- dbg('railway:', railway_theta, railway_phi, railway_angleoffset)
-
- def vdbg_railway_angle(start, angle, **kw):
- #vdbg_railway.arrow(start, [sin(angle), cos(angle), 0], **kw)
- pass
- vdbg_railway_angle([0, 0, 0.1], railway_theta, color=(1, 0.5, 0))
- vdbg_railway_angle([1, 0, 0.1], railway_phi, color=(1, 0.5, 0))
- vdbg_railway_angle([1, 0, 0.1], 0, color=(1, 1.00, 0))
- vdbg_railway_angle([1, 0, 0.1], tau/4, color=(1, 0.75, 0))
-
- if railway_cos_theta**2 + railway_cos_phi**2 > 1E-6:
- railway_polynomial = [
- 2 * (1 + cos(railway_theta - railway_phi)),
- 2 * (railway_cos_theta - railway_cos_phi),
- -1,
- ]
- railway_roots = np.roots(railway_polynomial)
- dbg('railway poly, roots:', railway_polynomial, railway_roots)
-
- #vdbg_railway.circle([0,0,0], [0,0, dist_pq_plane], color=(.5,0,0))
- #vdbg_railway.circle([1,0,0], [0,0, 0.05], color=(.5,0,0))
- #vdbg().circle(p, dPQplane_normal * dist_pq_plane, color=(.5,.5,0))
-
- for railway_r_pq1 in railway_roots:
- # roots for r are calculated based on coordinates where
- # Q is at (1,0) but our PQ distance is different
- railway_r = railway_r_pq1 * dist_pq_plane
- dbg(' twoarcs root r_pq1=', railway_r_pq1, 'r=',railway_r,
- railway_polynomial[0] * railway_r_pq1 * railway_r_pq1 +
- railway_polynomial[1] * railway_r_pq1 +
- railway_polynomial[2]
- )
-
- #vdbg_railway.circle([0,0,0], [0,0, railway_r], color=(1,0,0))
- #vdbg().circle(p, dPQplane_normal * railway_r, color=(1,1,0))
-
- def railway_CPQ(pq, dpq, railway_r):
- CPQ = pq + railway_r * np.array([-dpq[1], dpq[0]])
- dbg('railway_CPQ', railway_r, pq, dpq, CPQ)
- #vdbg_plane.circle( np.hstack((CPQ, [0])),
- # [0, 0, railway_r],
- # color = (1,1,1) )
- #vdbg_plane.circle( np.hstack(( 2*np.asarray(pq) - CPQ, [0])),
- # [0, 0, railway_r],
- # color = (.5,.5,.5) )
- return CPQ
-
- railway_CP = railway_CPQ([0,0], dp_plane, railway_r)
- railway_CQ = railway_CPQ(q_plane[0:2], -dq_plane, railway_r)
- railway_midpt = 0.5 * (railway_CP + railway_CQ)
-
- best_st = None
- def railway_ST(C, start, end, railway_r):
- delta = atan2(*(end - C)[0:2]) - atan2(*(start - C)[0:2])
- dbg('railway_ST C', C, 'start', start, 'end', end, 'delta', delta)
- if delta < 0: delta += tau
- s = delta * railway_r
- dbg('railway_ST delta', delta, 'r', railway_r, 's', s)
- return s
-
- try_s = railway_ST(railway_CP, railway_midpt, [0,0], railway_r)
- try_t = railway_ST(railway_CQ, railway_midpt, q_plane[0:2], railway_r)
- dbg('try_s, _t', try_s, try_t)
-
- try_st = try_s + try_t
- if best_st is None or try_st < best_st:
- start_la = -1/railway_r
- start_s = try_s
- start_t = try_t
- best_st = try_st
- start_mu = q_plane[2] / (start_s + start_t)
- dbg(' ok twoarcs')
-
- else: # twoarcs algorithm is not well defined
- dbg(' no twoarcs')
- start_la = 0.1
- start_s = dist_pq_plane * .65
- start_t = dist_pq_plane * .35
- start_mu = 0.05
-
- bodge = max( q_plane[2] * start_mu,
- (start_s + start_t) * 0.1 )
- start_s += 0.5 * bodge
- start_t += 0.5 * bodge
- start_kappa = 0
- start_gamma = 1
-
- tilt = atan(start_mu)
- tilt_basis = np.array([
- [ 1, 0, 0, 0 ],
- [ 0, cos(tilt), sin(tilt), 0 ],
- [ 0, -sin(tilt), cos(tilt), 0 ],
- [ 0, 0, 0, 1 ],
- ])
- findcurve_basis = matmatmultiply(dPQplane_basis, tilt_basis)
- findcurve_into = np.linalg.inv(findcurve_basis)
-
- for ax in range(0,3):
- vdbg().arrow(findcurve_basis[0:3,3], findcurve_basis[0:3,ax])
-
- q_findcurve = augmatmultiply(findcurve_into, q)
- dq_findcurve = -augmatmultiply(findcurve_into, dq, augwith=0)
-
- findcurve_target = np.hstack((q_findcurve, dq_findcurve))
- findcurve_start = (sqrt(start_s), sqrt(start_t), start_la,
- start_mu, start_gamma, start_kappa)
-
findcurve_epsilon = dist_pq_plane * 0.01
- global findcurve_subproc
- if findcurve_subproc is None:
- dbg('STARTING FINDCURVE')
- findcurve_subproc = subprocess.Popen(
- ['./findcurve'],
+ try:
+ subproc = findcurve_subprocs[nt]
+ except KeyError:
+ dbg('STARTING FINDCURVE %d' % nt)
+ subproc = subprocess.Popen(
+ ['./findcurve', '%d' % nt],
bufsize=1,
stdin=subprocess.PIPE,
stdout=subprocess.PIPE,
# restore_signals=True, // want python2 compat, nnng
universal_newlines=True,
)
+ findcurve_subprocs[nt] = subproc
- findcurve_input = np.hstack((findcurve_target,
- findcurve_start,
- [findcurve_epsilon]))
-
- def dbg_fmt_params(fcp):
- return (('s=%10.7f t=%10.7f sh=%10.7f'
- +' st=%10.7f la=%10.7f mu=%10.7f ga=%10.7f ka=%10.7f')
- %
- (( fcp[0]**2, fcp[1]**2 ) + tuple(fcp)))
-
- #dbg('>> ' + ' '.join(map(str,findcurve_input)))
-
- dbg(('RUNNING FINDCURVE ' +
- ' ' +
- ' target Q=[%10.7f %10.7f %10.7f] dQ=[%10.7f %10.7f %10.7f]')
- %
- tuple(findcurve_input[0:6]))
- dbg(('%s initial') % dbg_fmt_params(findcurve_input[6:12]))
+ dbg(('RUNNING FINDCURVE')
+ findcurve_input = np.hstack(*findcurve_input)
s = ' '.join(map(str, findcurve_input))
+
dbg(('>> %s' % s))
print(s, file=findcurve_subproc.stdin)
findcurve_subproc.stdin.flush()
- hc.func = symbolic.get_python()
- hc.findcurve_basis = findcurve_basis
commentary = ''
while True:
l = eval(l)
if not l: break
- dbg(('%s Q=[%10.7f %10.7f %10.7f] dQ=[%10.7f %10.7f %10.7f]%s')
- %
- (( dbg_fmt_params(l[0:6]), ) + tuple(l[6:12]) + (commentary,) ))
+ dbg('[%s] %s' % (l, commentary))
commentary = ''
hc.findcurve_result = l[0:6]
~ian / moebius3.git / commitdiff