with offsets

Signed-off-by: Ian Jackson <ijackson@chiark.greenend.org.uk>

diff --git a/check.py b/check.py
index 1f9875d35d8f6f2d36324eda4abfb86af2556dc3..2737f448a18f566b52f96292da8d247f6f95514d 100644 (file)
--- a/check.py
+++ b/check.py
@@ -27,3 +27,12 @@ for v in vs:
 
 for w in ws:
   c3 = curve( color=color.yellow, pos = [ m.point(v,w) for v in vs ] )
+
+
+for v in vs:
+  c4 = curve( color=color.blue,
+              pos = [ m.point_offset(v,w, 0.1) for w in ws ] )
+
+for w in ws:
+  c3 = curve( color=(1,0,1), pos = [ m.point_offset(v,w, -0.1) for v in vs ] )
+

diff --git a/moebius.py b/moebius.py
index 9fe6e3c709fdbefd4bb3a94a9ecd9580c119bf89..a5ed8d1891c2bd7ebdf321ce9009207b5dea3140 100644 (file)
--- a/moebius.py
+++ b/moebius.py
@@ -61,20 +61,18 @@ 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._cp2b = BezierSegment([(x,) for x in [0.2, 0.2, 1]])
-    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._beziers = [ m._bezier(theta) for theta in m._thetas ]
+  def _bezier(m, theta):
     cp = [None] * 4
     cp[0] =               m.edge   .point(theta)
     cp[3] =               m.midline.point(theta*2)
     ncp3 = np.linalg.norm(cp[3])
     cpt = ncp3 * ncp3 / 4
-    #cp2scale = m._cp2b.point_at_t(ncp3)[0]
     cp2scale = 1.50 * cpt + 0.33 * (1-cpt)
     cp1scale = 0.75 * cpt + 0.33 * (1-cpt)
-    print('u=%d ncp3=%f cp2scale=%f' % (u, ncp3, cp2scale),
-          file=sys.stderr)
+    #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 BezierSegment(cp)
@@ -87,7 +85,23 @@ class MoebiusHalf:
     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 point_offset(m, iu, t, offset):
+    '''
+    offset by offset perpendicular to the surface
+     at the top (iu=t=0), in the y direction
+    '''
+    p = MoebiusHalf.point(m, iu, t)
+    if t == 0:
+      dirn = m.edge.dirn(m._thetas[iu], extra_zeta=-tau/4)
+    elif iu == m.nu:
+      return MoebiusHalf.point_offset(m, 0, 1-t, -offset)
+    else:
+      vec_t = MoebiusHalf.point(m, iu,   t + 0.01) - p
+      vec_u = MoebiusHalf.point(m, iu+1, t)        - p
+      dirn =  np.cross(vec_u, vec_t)
+    return p + offset * dirn / np.linalg.norm(dirn)
 
 class Moebius(MoebiusHalf):
   def __init__(m, nv, nw):
@@ -116,3 +130,9 @@ class Moebius(MoebiusHalf):
 
   def point(m, v, w):
     return MoebiusHalf.point(m, **m._vw2tiu_kw(v,w))
+
+  def point_offset(m, v, w, offset):
+    return MoebiusHalf.point_offset(m,
+                                    offset=
+                                    offset if w <= m.nt else -offset,
+                                    **m._vw2tiu_kw(v,w))