import symbolic
-def augment(v, augwith=1): return np.append(v, augwith)
-def augment0(v): return augment(v, 0)
-def unaugment(v): return v[0:3]
-
-def matmultiply(mat,vect):
- # both are "array"s
- # we would prefer to write mat @ vect
- # but that doesn't work in Python 2
- return np.array((vect * np.matrix(mat).T))[0,:]
-
-def matmatmultiply(mat1,mat2):
- # both are "array"s
- # we would prefer to write mat1 @ mat2
- # but that doesn't work in Python 2
- return np.array((np.matrix(mat1) * np.matrix(mat2)))
-
-def augmatmultiply(mat,unaugvect, augwith=1):
- return unaugment(matmultiply(mat, augment(unaugvect, augwith)))
-
findcurve_subproc = None
class HelixishCurve():
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
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,
#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)
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)
-
- dbg('plane:', p_plane_check, dp_plane, dq_plane, 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, '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])
- railway_theta = tau/4 - railway_angleoffset
- railway_phi = atan2(*dq_plane[0:2]) - railway_angleoffset
+ # 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)
- if railway_cos_theta**2 + railway_cos_phi**2 > 1E6:
- railway_roots = np.roots([
+
+ 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_polynomial = [
2 * (1 + cos(railway_theta - railway_phi)),
2 * (railway_cos_theta - railway_cos_phi),
- -1
- ])
- for railway_r in railway_roots:
- def railway_CPQ(pq, dpq, railway_r):
- return pq + railway_r * [-dpq[1], dpq[0]]
+ -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))
- railway_CP = railway_CPQ([0,0,0], dp_plane, railway_r)
+ 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_QP = railway_CPQ(q_plane[0:2], -dq_plane, railway_r)
railway_midpt = 0.5 * (railway_CP + railway_QP)
best_st = None
def railway_ST(C, start, end, railway_r):
- delta = atan2(*(end - C)[0:2]) - atan2(start - C)[0:2]
+ 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, [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)
- try_s = railway_ST(railway_CP, [0,0], midpt, railway_r)
- try_t = railway_ST(railway_CP, midpt, q_plane, railway_r)
try_st = try_s + try_t
if best_st is None or try_st < best_st:
- start_la = 1/r
+ start_la = 1/railway_r
start_s = try_s
start_t = try_t
best_st = try_st
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_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