X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=helixish.py;h=27485eac5e965293e7311976f39466fef807ca08;hb=f888ccc82f4228b3acfbc66560f185a649ac4730;hp=3479910e1451a3c44dcbf15b6acd154c7873ec1d;hpb=8861686be59d123e7506170ce12fc5fbd2d85cee;p=moebius3.git diff --git a/helixish.py b/helixish.py index 3479910..27485ea 100644 --- a/helixish.py +++ b/helixish.py @@ -5,22 +5,31 @@ import numpy as np from numpy import cos, sin import sys -from moebdebug import dbg +import subprocess -def augment(v): return np.append(v, 1) -def augment0(v): return np.append(v, 0) -def unaugment(v): return v[0:3] +from moedebug import * +from moenp import * + +from math import atan2, atan, sqrt + +import symbolic findcurve_subproc = None 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 @@ -34,94 +43,181 @@ class HelixishCurve(): # but minimum is 10% of (wlog) {s,t} [[ not quite like this ]] dPQplane_normal = np.cross(dp, dq) - if (np.norm(dPQplane_normal) < 1E6): - dPQplane_normal += [0, 0, 1E5] + + 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) - dPQplane_basis = np.column_stack(np.cross(dp, dPQplane_normal), - dp, - dPQplane_normal, - p); - dPQplane_basis = np.vstack(dPQplane_basis, [0,0,0,1]) + 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) - dp_plane = unaugment(dPQplane_into * augment0(dp)) - dq_plane = unaugment(dPQplane_into * augment0(dq)) - q_plane = unaugment(dPQplane_into * augment(q)) - dist_pq_plane = np.linalg.norm(q_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[0:1]) - railway_theta = tau/4 - railway_angleoffset - railway_phi = atan2(*dq_plane[0:1]) - railway_angleoffset + 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) - 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): - nonlocal railway_r - return pq + railway_r * [-dpq[1], dpq[0]] - - railway_CP = railway_CPQ([0,0,0], dp_plane) - railway_QP = railway_CPQ(q_plane[0:2], -dq_plane) + -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_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): - nonlocal railway_r - delta = atan2(*(end - C)[0:2]) - atan2(start - C)[0:2] + 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, [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) - try_t = railway_ST(railway_CP, midpt, q_plane) 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 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] * mu, + 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(mu) + 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, + [ 1, 0, 0, 0 ], + [ 0, cos(tilt), sin(tilt), 0 ], + [ 0, -sin(tilt), cos(tilt), 0 ], + [ 0, 0, 0, 1 ], ]) - findcurve_basis = dPQplane_basis * tilt_basis + findcurve_basis = matmatmultiply(dPQplane_basis, tilt_basis) findcurve_into = np.linalg.inv(findcurve_basis) - q_findcurve = unaugment(findcurve_into, augment(q)) - dq_findcurve = unaugment(findcurve_into, augment0(dq)) + 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.concatenate(q_findcurve, dq_findcurve) + 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'], bufsize=1, @@ -129,23 +225,68 @@ class HelixishCurve(): stdout=subprocess.PIPE, stderr=None, close_fds=False, - restore_signals=True, + # restore_signals=True, // want python2 compat, nnng universal_newlines=True, ) findcurve_input = np.hstack((findcurve_target, findcurve_start, - [findcurve_epsilon]))) - dbg('RUNNING FINDCURVE', *findcurve_input) - print(findcurve_subproc.stdin, *findcurve_input) + [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])) + + 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 - findcurve_result = l[0:5] + 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,) )) + commentary = '' + + hc.findcurve_result = l[0:6] + hc.threshold = l[0]**2 + hc.total_dist = hc.threshold + l[1]**2 + #vdbg().curve( hc.point_at_t ) + + def point_at_t(hc, normalised_parameter): + dist = normalised_parameter * hc.total_dist + ours = list(hc.findcurve_result) + if dist <= hc.threshold: + ours[0] = sqrt(dist) + ours[1] = 0 + else: + ours[1] = sqrt(dist - hc.threshold) + asmat = hc.func(*ours) + p = asmat[:,0] + p = augmatmultiply(hc.findcurve_basis, p) + return p