X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=helixish.py;h=d583421dc709602c9cba41aabed33ecc5df53d17;hb=b2743573d3020ce6191e3d3ef0bca824a45131ca;hp=19c592bbeaf1b4cece7195d2fee5aa27fa351e91;hpb=3c403f828eff980a2425952fa5addc681ee5b220;p=moebius3.git diff --git a/helixish.py b/helixish.py index 19c592b..d583421 100644 --- a/helixish.py +++ b/helixish.py @@ -14,25 +14,6 @@ from math import atan2, atan, sqrt import symbolic -def augment(v, augwith=1): return np.append(v, 1) -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(): @@ -47,6 +28,9 @@ 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 @@ -69,6 +53,8 @@ class HelixishCurve(): 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, @@ -76,6 +62,9 @@ class HelixishCurve(): #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) @@ -83,42 +72,108 @@ class HelixishCurve(): 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) + 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 - ]) - 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) - railway_QP = railway_CPQ(q_plane[0:2], -dq_plane, railway_r) - railway_midpt = 0.5 * (railway_CP + railway_QP) + 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] + 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_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 @@ -142,13 +197,16 @@ class HelixishCurve(): 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, 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) @@ -176,37 +234,51 @@ class HelixishCurve(): findcurve_start, [findcurve_epsilon])) - dbg(('RUNNING FINDCURVE ' + - ' target Q=[%5.2f %5.2f %5.2f] dQ=[%5.2f %5.2f %5.2f]') + 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=%5.2f t=%5.2f la=%5.2f mu=%5.2f ga=%5.2f ka=%5.2f initial') - % - (( findcurve_input[6]**2, findcurve_input[7]**2 ) + - tuple(findcurve_input[8:12]))) + dbg(('%s initial') % dbg_fmt_params(findcurve_input[6:12])) print(*findcurve_input, file=findcurve_subproc.stdin) findcurve_subproc.stdin.flush() hc.func = symbolic.get_python() + hc.findcurve_basis = findcurve_basis + commentary = '' while True: l = findcurve_subproc.stdout.readline() l = l.rstrip() - #dbg('GOT ', l) + dbg('<< ', l) if not l: vdbg().crashing('findcurve EOF') + if not l.startswith('['): + commentary += ' ' + commentary += l + continue + l = eval(l) - if l is None: break + if not l: break - dbg(('s=%5.2f t=%5.2f la=%5.2f mu=%5.2f ga=%5.2f ka=%5.2f' + - ' Q=[%5.2f %5.2f %5.2f] dQ=[%5.2f %5.2f %5.2f]') + dbg(('%s Q=[%10.7f %10.7f %10.7f] dQ=[%10.7f %10.7f %10.7f]%s') % - (( l[0]**2, l[1]**2 ) + tuple(l[2:12]))) + (( dbg_fmt_params(l[0:6]), ) + tuple(l[6:12]) + (commentary,) )) + commentary = '' hc.findcurve_result = l[0:6] + #hc.findcurve_result = findcurve_start hc.threshold = l[0]**2 hc.total_dist = hc.threshold + l[1]**2 - vdbg().curve( hc.point_at_t ) + #vdbg().curve( hc.point_at_t ) def point_at_t(hc, normalised_parameter): dist = normalised_parameter * hc.total_dist @@ -218,4 +290,5 @@ class HelixishCurve(): ours[1] = sqrt(dist - hc.threshold) asmat = hc.func(*ours) p = asmat[:,0] + p = augmatmultiply(hc.findcurve_basis, p) return p