X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=moebius.py;h=e5a81acad9d0d458bbc823769b5cea55176e0801;hb=906edec3ef60cf3e0567c713b2a68688edb634d4;hp=de569809d798ce360f114fd5d6e5099ae519fc5b;hpb=bae7c377014524d0adea4238f824209fdd6f1e48;p=moebius3.git diff --git a/moebius.py b/moebius.py index de56980..e5a81ac 100644 --- a/moebius.py +++ b/moebius.py @@ -5,15 +5,33 @@ import numpy as np from numpy import cos, sin from bezier import BezierSegment +from helixish import HelixishCurve +from moenp import * import sys -tau = np.pi * 2 - -origin = np.array((0,0,0)) -unit_x = np.array((1,0,0)) -unit_y = np.array((0,1,0)) -unit_z = np.array((0,0,1)) +class DoubleCubicBezier(): + def __init__(db, cp): + single = BezierSegment(cp) + midpoint = np.array(single.point_at_t(0.5)) + mid_dirn = single.point_at_t(0.5 + 0.001) - midpoint + mid_dirn /= np.linalg.norm(mid_dirn) + ocp_factor = 0.5 + mid_scale = ocp_factor * 0.5 * (np.linalg.norm(cp[1] - cp[0]) + + np.linalg.norm(cp[3] - cp[2])) + db.b0 = BezierSegment([ cp[0], + cp[1] * ocp_factor + cp[0] * (1-ocp_factor), + midpoint - mid_dirn * mid_scale, + midpoint ]) + db.b1 = BezierSegment([ midpoint, + midpoint + mid_dirn * mid_scale, + cp[2] * ocp_factor + cp[3] * (1-ocp_factor), + cp[3] ]) + def point_at_t(db, t): + if t < 0.5: + return db.b0.point_at_t(t*2) + else: + return db.b1.point_at_t(t*2 - 1) class ParametricCircle: def __init__(pc, c, r0, r1): @@ -61,22 +79,106 @@ class MoebiusHalf: m.edge = Twirler(origin, unit_z, unit_x, -2, tau/2) m.midline = Twirler(-unit_z, unit_z, unit_y, -0.5, 0) m.nu = nu - m._beziers = [ m._bezier(u) for u in np.linspace(0, 1, nu+1) ] - def _bezier(m,u): - theta = u * tau + m._thetas = [ u * tau for u in np.linspace(0, 1, nu+1) ] + m._cp2b = BezierSegment([ (c,) for c in [0.33,0.33, 1.50]]) + m._beziers = [ m._bezier(theta, HelixishCurve) for theta in m._thetas ] + #check = int(nu/3) + #m._beziers[check] = m._bezier(m._thetas[check], HelixishCurve) + def _bezier(m, theta, constructor=DoubleCubicBezier): cp = [None] * 4 cp[0] = m.edge .point(theta) - cp[1] = cp[0] + 0.75 * m.edge .dirn (theta) cp[3] = m.midline.point(theta*2) - cp[2] = cp[3] + np.linalg.norm(cp[3]) * m.midline.dirn (theta*2) - return BezierSegment(cp) + ncp3 = np.linalg.norm(cp[3]) + cpt = ncp3 * ncp3 / 4 + cp2scale = m._cp2b.point_at_t(ncp3/2) + cp1scale = 1.0 * cpt + 0.33 * (1-cpt) + #print('u=%d ncp3=%f cp2scale=%f' % (u, ncp3, cp2scale), + # file=sys.stderr) + cp[1] = cp[0] + cp1scale * m.edge .dirn (theta) + cp[2] = cp[3] + cp2scale * m.midline.dirn (theta*2) + return constructor(cp) def point(m, iu, t): ''' 0 <= iu <= nu meaning 0 <= u <= 1 - along the extent + along the extent (well, along the edge) 0 and 1 are both the top half of the flat traverse 0.5 is the bottom half of the flat traverse 0 <= t <= 1 across the half-traverse 0 is the edge, 1 is the midline ''' - return m._beziers[iu].point_at_t(t) + return np.array(m._beziers[iu].point_at_t(t)) + + def details(m, iu, t): + ''' + returns tuple of 4 vectors: + - point location + - normal (+ve is in the +ve y direction at iu=t=0) unit vector + - along extent (towrds +ve iu) unit vector + - along traverse (towards +ve t) unit vector + ''' + if iu == m.nu: + return m.details(0, t) + p = m.point(iu, t) + vec_t = unit_v( m.point(iu, t + 0.01) - p ) + if t == 0: + normal = m.edge.dirn(m._thetas[iu], extra_zeta=-tau/4) + vec_u = np.cross(vec_t, normal) + else: + vec_u = unit_v( m.point(iu+1, t) - p ) + normal = np.cross(vec_u, vec_t) + return p, normal, vec_u, vec_t + + def point_offset(m, iu, t, offset): + ''' + offset by offset perpendicular to the surface + at the top (iu=t=0), +ve offset is in the +ve y direction + ''' + p, normal, dummy, dummy = m.details(iu, t) + return p + offset * normal + +class Moebius(): + def __init__(m, nv, nw): + ''' + 0 <= v <= nw along the extent, v=0 is the flat traverse + 0 <= w <= nv across the traverse nw must be even + the top is both v=0, w=0 v=nv, w=nw + ''' + assert(nw % 1 == 0) + m.nv = nv + m.nw = nw + m.nt = nw/2 + m._t_vals = np.linspace(0, 1, m.nt+1) + m.h = MoebiusHalf(nu=nv*2) + + def _vw2tiu_kw(m, v, w): + if w <= m.nt: + it = w + iu = v + else: + it = m.nw - w + iu = m.nv + v + #print('v,w=%d,%d => it,iu=%d,%d' % (v,w,it,iu), + # file=sys.stderr) + return { 't': m._t_vals[it], 'iu': iu } + + def point(m, v, w): + return m.h.point(**m._vw2tiu_kw(v,w)) + + def point_offset(m, v, w, offset): + return m.h.point_offset(offset= + offset if w <= m.nt else -offset, + **m._vw2tiu_kw(v,w)) + + def details(m, v, w): + ''' + returns tuple of 4 vectors: + - point location + - normal (+ve is in the +ve y direction at iu=t=0) unit vector + - along extent (towrds +ve v) unit vector + - along traverse (towards +ve w) unit vector + ''' + p, normal, vec_v, vec_w = m.h.details(**m._vw2tiu_kw(v,w)) + if w > m.nt: + normal = -normal + vec_w = -vec_w + return p, normal, vec_v, vec_w