X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=helixish.py;h=27485eac5e965293e7311976f39466fef807ca08;hb=f888ccc82f4228b3acfbc66560f185a649ac4730;hp=39d525a4e9e19cf8652b49af0f66aff6fe625ee8;hpb=995951970a5656d0f53efb7a3508fe22320e7862;p=moebius3.git diff --git a/helixish.py b/helixish.py index 39d525a..27485ea 100644 --- a/helixish.py +++ b/helixish.py @@ -53,6 +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, @@ -60,10 +62,8 @@ class HelixishCurve(): #dbg(dPQplane_basis) dPQplane_basis = np.vstack((dPQplane_basis, [0,0,0,1])) dbg(dPQplane_basis) - - for ax in range(0,3): - vdbg().arrow(dPQplane_basis[0:3,3], dPQplane_basis[0:3,ax], - colour= [ c * (1.0 - ax*0.2) for c in (1,1,1) ]) + + vdbg().basis(dPQplane_basis) dPQplane_into = np.linalg.inv(dPQplane_basis) dbg(dPQplane_into) @@ -72,35 +72,85 @@ 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) + dist_pq_plane = np.linalg.norm(q_plane[0:2]) vdbg_plane = MatrixVisdebug(vdbg(), dPQplane_basis) - dbg('plane:', p_plane_check, dp_plane, dq_plane, 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) + 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) + 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) @@ -110,15 +160,15 @@ class HelixishCurve(): 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: @@ -202,6 +252,7 @@ class HelixishCurve(): findcurve_subproc.stdin.flush() hc.func = symbolic.get_python() + hc.findcurve_basis = findcurve_basis commentary = '' while True: @@ -237,4 +288,5 @@ class HelixishCurve(): ours[1] = sqrt(dist - hc.threshold) asmat = hc.func(*ours) p = asmat[:,0] + p = augmatmultiply(hc.findcurve_basis, p) return p