fixed #6

A proper warning with helpful hints added, to allow the user
to avoid undercut issues. Rack gears are especially prone
to undercuts, but this is not an issue specific to racks. Closed fixed here.

gears-dev.py

@@ -112,6 +112,13 @@ def undercut_max_k(teeth, pitch_angle=20.0):
     x = sin(radians(pitch_angle))
     return 0.5 * teeth * x * x
 
+def undercut_min_angle(teeth, k=1.0):
+    """ computes the minimum pitch angle, to that the given teeth count (and
+        profile shift) cause no undercut.
+    """
+    return degrees(asin(min(0.9135, sqrt(2.0*k/teeth))))	# max 59.9 deg
+
+
 def have_undercut(teeth, pitch_angle=20.0, k=1.0):
     """ returns true if the specified gear dimensions would
         cause an undercut.
@@ -461,6 +468,12 @@ def effect(self):
         undercut = int(ceil(undercut_min_teeth( angle )))
         needs_undercut = teeth < undercut
 
+	if have_undercut(teeth, angle, 1.0):
+	    min_teeth = int(ceil(undercut_min_teeth(angle, 1.0)))
+	    min_angle = undercut_min_angle(teeth, 1.0) + .1
+	    max_k = undercut_max_k(teeth, angle)
+	    inkex.debug("Undercut Warning: This gear will not work well. Try tooth count of %d or more, or a pressure angle of %.1f ° or more, or try a profile shift of %d %% (not yet implemented). Or other decent combinations." % (min_teeth, min_angle, int(100.*max_k)-100.))
+
         # Dedendum: Radial distance from pitch circle to root diameter.
         dedendum = addendum + clearance