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)
+ 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)
+ 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)
- # 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])
- railway_theta = atan2(*dp_plane[0:2]) - railway_angleoffset
- railway_phi = atan2(*dq_plane[0:2]) - railway_angleoffset
- railway_cos_theta = cos(railway_theta)
- railway_cos_phi = cos(railway_phi)
-
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),
+ -np.cross([0,0,1], railway_inplane_basis_x),
[0,0,1],
[0,0,0],
))
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)
+ 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_roots = np.roots([
+ railway_polynomial = [
2 * (1 + cos(railway_theta - railway_phi)),
2 * (railway_cos_theta - railway_cos_phi),
- -1
- ])
- for railway_r in railway_roots:
- dbg(' twoarcs root r=',railway_r)
+ -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)
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', C, start, end, railway_r, s)
+ dbg('railway_ST delta', delta, 'r', railway_r, 's', s)
return s
try_s = railway_ST(railway_CP, [0,0], railway_midpt, railway_r)
try_t = railway_ST(railway_CP, railway_midpt, q_plane[0:2], railway_r)
dbg('try_s, _t', try_s, try_t)
- if try_s < 0 or try_t < 0:
- continue
try_st = try_s + try_t
if best_st is None or try_st < best_st:
findcurve_subproc.stdin.flush()
hc.func = symbolic.get_python()
+ hc.findcurve_basis = findcurve_basis
commentary = ''
while True:
ours[1] = sqrt(dist - hc.threshold)
asmat = hc.func(*ours)
p = asmat[:,0]
+ p = augmatmultiply(hc.findcurve_basis, p)
return p
~ian / moebius3.git / blobdiff