X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=curveopt.py;h=00019762d8f20a01b1c5b93378fa544c8641c16f;hb=c1001cc933c7a48935777908ba8338673cd091dc;hp=77c311b34097692d8558208b243baa438ba46e0c;hpb=db022f0eefab2b280a45997e6a2076188f81f3d3;p=moebius3.git diff --git a/curveopt.py b/curveopt.py index 77c311b..0001976 100644 --- a/curveopt.py +++ b/curveopt.py @@ -4,266 +4,92 @@ from __future__ import print_function import numpy as np from numpy import cos, sin +import six import sys import subprocess +import math from moedebug import * from moenp import * +from moebez 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 - # - 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'], - bufsize=1, - stdin=subprocess.PIPE, - stdout=subprocess.PIPE, - stderr=None, - close_fds=False, - # restore_signals=True, // want python2 compat, nnng - universal_newlines=True, - ) - - 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])) - - 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 +class OptimisedCurve(): + counter = 0 + + def _dbg(oc, s): + dbg('OC#%04d %s' % (oc._counter, s)) + + def __init__(oc, cp, nt): + oc._counter = OptimisedCurve.counter + OptimisedCurve.counter += 1 + oc._dbg('cp= ' + ' '.join(map(vec2dbg, cp))) + + db = DiscreteBezier(cp, nt, bezier_constructor=BezierSegment) + + fc_input = map(db.point_at_it, range(0, nt+1)) + oc._dbg(repr(fc_input)) + + for end in (False,True): + ei = nt if end else 0 + fi = nt-1 if end else 1 + cp0i = 3 if end else 0 + cp1i = 2 if end else 1 + e = np.array(cp[cp0i]) + ef_dirn = unit_v(cp[cp1i] - cp[cp0i]) + ef_len = np.linalg.norm(np.array(fc_input[fi]) - np.array(fc_input[ei])) + f = e + ef_dirn * ef_len + oc._dbg(repr((end, e,f, ef_dirn, ef_len))) + fc_input[ei] = e + fc_input[fi] = f + + oc._dbg(repr(fc_input)) + + findcurve_epsilon = 0.01 + + cl = ['./findcurve', '%d' % (nt+1), '%.18g' % findcurve_epsilon] + oc._dbg('STARTING FINDCURVE %s' % cl) + subproc = subprocess.Popen( + cl, + bufsize=1, + stdin=subprocess.PIPE, + stdout=subprocess.PIPE, + stderr=None, + close_fds=False, + # restore_signals=True, // want python2 compat, nnng + universal_newlines=True, + ) + + oc._dbg('RUNNING FINDCURVE') + + fc_input = np.hstack(fc_input) + s = ' '.join(map(str, fc_input)) + + oc._dbg(('>> %s' % s)) + + print(s, file=subproc.stdin) + subproc.stdin.flush() + + oc.subproc = subproc + oc.nt = nt + + def _await_subproc(oc): + subproc = oc.subproc + if subproc is None: return + + oc._dbg('(awaiting)') commentary = '' while True: - l = findcurve_subproc.stdout.readline() + l = subproc.stdout.readline() + if not l: + oc._dbg('findcurve EOF') + vdbg().crashing('findcurve EOF') l = l.rstrip() - dbg('<< ', l) - if not l: vdbg().crashing('findcurve EOF') + oc._dbg('<< ' + l) if not l.startswith('['): commentary += ' ' commentary += l @@ -272,26 +98,31 @@ class HelixishCurve(): 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,) )) + oc._dbg('[%s] %s' % (l, 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 ) - - 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 + findcurve_result = l + + subproc.stdin.close() + subproc.wait() + assert(subproc.returncode == 0) + oc.subproc = None + + oc._result = np.reshape(findcurve_result, (-1,3), 'C') + oc._dbg(repr(oc._result)) + + #vdbg().curve( oc.point_at_t ) + + def point_at_it(oc, it): + oc._await_subproc() + oc._dbg(repr((it,))) + return oc._result[it] + + def point_at_t(oc, t): + itd = t * oc.nt + it0 = int(math.floor(itd)) + it1 = int(math.ceil(itd)) + p0 = oc.point_at_it(it0) + p1 = oc.point_at_it(it1) + return p0 + (p1-p0) * (itd-it0) +