#! /usr/bin/env python
# -*- coding: utf-8 -*-
'''
Copyright (C) 2007 Aaron Spike  (aaron @ ekips.org)
Copyright (C) 2007 Tavmjong Bah (tavmjong @ free.fr)
Copyright (C) http://cnc-club.ru/forum/viewtopic.php?f=33&t=434&p=2594#p2500
Copyright (C) 2014 Jürgen Weigert (juewei@fabmail.org)
Copyright (C) 2017 David Grimberg (sentinel @ bardicgrove.org)

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

2014-03-20 jw@suse.de 0.2  Option --accuracy=0 for automatic added.
2014-03-21                 sent upstream: https://bugs.launchpad.net/inkscape/+bug/1295641
2014-03-21 jw@suse.de 0.3  Fixed center of rotation for gears with odd number of teeth.
2014-04-04 juewei     0.7  Revamped calc_unit_factor(). 
2014-04-05 juewei    0.7a  Correctly positioned rack gear.
                       The geometry above the meshing line is wrong.
2014-04-06 juewei    0.7b  Undercut detection added. Reference:
               http://nptel.ac.in/courses/IIT-MADRAS/Machine_Design_II/pdf/2_2.pdf
               Manually merged https://github.com/jnweiger/inkscape-gears-dev/pull/15
2014-04-07 juewei    0.7c  Manually merged https://github.com/jnweiger/inkscape-gears-dev/pull/17
2014-04-09 juewei    0.8   Fixed https://github.com/jnweiger/inkscape-gears-dev/issues/19
			   Ring gears are ready for production now. Thanks neon22 for driving this.
			   Profile shift implemented (Advanced Tab), fixing 
			   https://github.com/jnweiger/inkscape-gears-dev/issues/9
2015-05-29 juewei 0.9 	ported to inkscape 0.91
			AttributeError: 'module' object inkex has no attribute 'uutounit'
			Fixed https://github.com/jnweiger/inkscape-gears-dev
2017-04-27 sentinel 0.10  Fixed calc_circular_pitch to use unit_factor freeing the
      Tooth system from any specific unitary system.  Previously Module was tied
      to millimeters while Circular and Diametral Pitch were tied to inches.  Now
      they take their units from the Unit input just like all the other measures.
'''

import inkex, simplestyle
from os import devnull # for debugging
from math import pi, cos, sin, tan, radians, degrees, ceil, asin, acos, sqrt
two_pi = 2 * pi


__version__ = '0.9'

def uutounit(self,nn,uu):
  try:
    return self.uutounit(nn,uu)		# inkscape 0.91
  except:
    return inkex.uutounit(nn,uu)	# inkscape 0.48

def linspace(a,b,n):
    """ return list of linear interp of a to b in n steps
        - if a and b are ints - you'll get an int result.
        - n must be an integer
    """
    return [a+x*(b-a)/(n-1) for x in range(0,n)]

def involute_intersect_angle(Rb, R):
    " "
    Rb, R = float(Rb), float(R)
    return (sqrt(R**2 - Rb**2) / (Rb)) - (acos(Rb / R))

def point_on_circle(radius, angle):
    " return xy coord of the point at distance radius from origin at angle "
    x = radius * cos(angle)
    y = radius * sin(angle)
    return (x, y)
    
def points_to_bbox(p):
    """ from a list of points (x,y pairs)
        - return the lower-left xy and upper-right xy
    """
    llx = urx = p[0][0]
    lly = ury = p[0][1]
    for x in p[1:]:
        if   x[0] < llx: llx = x[0]
        elif x[0] > urx: urx = x[0]
        if   x[1] < lly: lly = x[1]
        elif x[1] > ury: ury = x[1]
    return (llx, lly, urx, ury)

def points_to_bbox_center(p):
    """ from a list of points (x,y pairs)
        - find midpoint of bounding box around all points
        - return (x,y)
    """
    bbox = points_to_bbox(p)
    return ((bbox[0]+bbox[2])/2.0, (bbox[1]+bbox[3])/2.0)
                
def points_to_svgd(p):
    " convert list of points into a closed SVG path list"
    f = p[0]
    p = p[1:]
    svgd = 'M%.4f,%.4f' % f
    for x in p:
        svgd += 'L%.4f,%.4f' % x
    svgd += 'z'
    return svgd

def draw_SVG_circle(parent, r, cx, cy, name, style):
    " add an SVG circle entity to parent "
    circ_attribs = {'style': simplestyle.formatStyle(style),
                    'cx': str(cx), 'cy': str(cy), 
                    'r': str(r),
                    inkex.addNS('label','inkscape'):name}
    circle = inkex.etree.SubElement(parent, inkex.addNS('circle','svg'), circ_attribs )


### Undercut support functions
def undercut_min_teeth(pitch_angle, k=1.0):
    """ computes the minimum tooth count for a 
        spur gear so that no undercut with the given pitch_angle (in deg) 
        and an addendum = k * metric_module, where 0 < k < 1
    Note:
    The return value should be rounded upwards for perfect safety. E.g.
    min_teeth = int(math.ceil(undercut_min_teeth(20.0)))    # 18, not 17
    """
    x = sin(radians(pitch_angle))
    return 2*k /(x*x)

def undercut_max_k(teeth, pitch_angle=20.0):
    """ computes the maximum k value for a given teeth count and pitch_angle
        so that no undercut occurs.
    """
    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(0.856, 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 number of teeth would
        cause an undercut.
    """
    return (teeth < undercut_min_teeth(pitch_angle, k))


## gather all basic gear calculations in one place
def gear_calculations(num_teeth, circular_pitch, pressure_angle, clearance=0, ring_gear=False, profile_shift=0.):
    """ Put base calcs for spur/ring gears in one place.
        - negative profile shifting helps against undercut. 
    """
    diametral_pitch = pi / circular_pitch
    pitch_diameter = num_teeth / diametral_pitch
    pitch_radius = pitch_diameter / 2.0
    addendum = 1 / diametral_pitch
    #dedendum = 1.157 / diametral_pitch # auto calc clearance
    dedendum = addendum
    dedendum *= 1+profile_shift
    addendum *= 1-profile_shift
    if ring_gear:
        addendum = addendum + clearance # our method
    else:
        dedendum = dedendum + clearance # our method
    #
    #
    base_radius = pitch_diameter * cos(radians(pressure_angle)) / 2.0
    outer_radius = pitch_radius + addendum
    root_radius =  pitch_radius - dedendum
    # Tooth thickness: Tooth width along pitch circle.
    tooth_thickness  = ( pi * pitch_diameter ) / ( 2.0 * num_teeth )
    # we don't use these
    working_depth = 2 / diametral_pitch
    whole_depth = 2.157 / diametral_pitch
    #outside_diameter = (num_teeth + 2) / diametral_pitch
    #
    return (pitch_radius, base_radius,
            addendum, dedendum, outer_radius, root_radius,
            tooth_thickness
            )

 
def generate_rack_points(tooth_count, pitch, addendum, pressure_angle,
                       base_height, tab_length, clearance=0, draw_guides=False):
        """ Return path (suitable for svg) of the Rack gear.
            - rack gear uses straight sides
                - involute on a circle of infinite radius is a simple linear ramp
            - the meshing circle touches at y = 0, 
            - the highest elevation of the teeth is at y = +addendum
            - the lowest elevation of the teeth is at y = -addendum-clearance
            - the base_height extends downwards from the lowest elevation.
            - we generate this middle tooth exactly centered on the y=0 line.
              (one extra tooth on the right hand side, if number of teeth is even)
        """
        spacing = 0.5 * pitch # rolling one pitch distance on the spur gear pitch_diameter.
        # roughly center rack in drawing, exact position is so that it meshes
        # nicely with the spur gear.
        # -0.5*spacing has a gap in the center.
        # +0.5*spacing has a tooth in the center.
        fudge = +0.5 * spacing

        tas  = tan(radians(pressure_angle)) * addendum
        tasc = tan(radians(pressure_angle)) * (addendum+clearance)
        base_top = addendum+clearance
        base_bot = addendum+clearance+base_height

        x_lhs = -pitch * int(0.5*tooth_count-.5) - spacing - tab_length - tasc + fudge
        #inkex.debug("angle=%s spacing=%s"%(pressure_angle, spacing))
        # Start with base tab on LHS
        points = [] # make list of points
        points.append((x_lhs, base_bot))
        points.append((x_lhs, base_top))
        x = x_lhs + tab_length+tasc

        # An involute on a circle of infinite radius is a simple linear ramp.
        # We need to add curve at bottom and use clearance.
        for i in range(tooth_count):
            # move along path, generating the next 'tooth'
            # pitch line is at y=0. the left edge hits the pitch line at x
            points.append((x-tasc, base_top))
            points.append((x+tas, -addendum))
            points.append((x+spacing-tas, -addendum))
            points.append((x+spacing+tasc, base_top)) 
            x += pitch
        x -= spacing # remove last adjustment
        # add base on RHS
        x_rhs = x+tasc+tab_length
        points.append((x_rhs, base_top))
        points.append((x_rhs, base_bot))
        # We don't close the path here. Caller does it.
        # points.append((x_lhs, base_bot))

        # Draw line representing the pitch circle of infinite diameter
        guide_path = None
        if draw_guides:
            p = []
            p.append( (x_lhs + 0.5 * tab_length, 0) )
            p.append( (x_rhs - 0.5 * tab_length, 0) )
            guide_path = points_to_svgd(p)
        # return points ready for use in an SVG 'path'
        return (points, guide_path)
    

def generate_spur_points(teeth, base_radius, pitch_radius, outer_radius, root_radius, accuracy_involute, accuracy_circular):
    """ given a set of core gear params
        - generate the svg path for the gear
    """
    half_thick_angle = two_pi / (4.0 * teeth ) #?? = pi / (2.0 * teeth)
    pitch_to_base_angle  = involute_intersect_angle( base_radius, pitch_radius )
    pitch_to_outer_angle = involute_intersect_angle( base_radius, outer_radius ) - pitch_to_base_angle

    start_involute_radius = max(base_radius, root_radius)
    radii = linspace(start_involute_radius, outer_radius, accuracy_involute)
    angles = [involute_intersect_angle(base_radius, r) for r in radii]

    centers = [(x * two_pi / float( teeth) ) for x in range( teeth ) ]
    points = []

    for c in centers:
        # Angles
        pitch1 = c - half_thick_angle
        base1  = pitch1 - pitch_to_base_angle
        offsetangles1 = [ base1 + x for x in angles]
        points1 = [ point_on_circle( radii[i], offsetangles1[i]) for i in range(0,len(radii)) ]

        pitch2 = c + half_thick_angle
        base2  = pitch2 + pitch_to_base_angle
        offsetangles2 = [ base2 - x for x in angles] 
        points2 = [ point_on_circle( radii[i], offsetangles2[i]) for i in range(0,len(radii)) ]

        points_on_outer_radius = [ point_on_circle(outer_radius, x) for x in linspace(offsetangles1[-1], offsetangles2[-1], accuracy_circular) ]

        if root_radius > base_radius:
            pitch_to_root_angle = pitch_to_base_angle - involute_intersect_angle(base_radius, root_radius )
            root1 = pitch1 - pitch_to_root_angle
            root2 = pitch2 + pitch_to_root_angle
            points_on_root = [point_on_circle (root_radius, x) for x in linspace(root2, root1+(two_pi/float(teeth)), accuracy_circular) ]
            p_tmp = points1 + points_on_outer_radius[1:-1] + points2[::-1] + points_on_root[1:-1] # [::-1] reverses list; [1:-1] removes first and last element
        else:
            points_on_root = [point_on_circle (root_radius, x) for x in linspace(base2, base1+(two_pi/float(teeth)), accuracy_circular) ]
            p_tmp = points1 + points_on_outer_radius[1:-1] + points2[::-1] + points_on_root # [::-1] reverses list

        points.extend( p_tmp )
    return (points)


def generate_spokes_path(root_radius, spoke_width, spoke_count, mount_radius, mount_hole,
                         unit_factor, unit_label):
    """ given a set of constraints
        - generate the svg path for the gear spokes
        - lies between mount_radius (inner hole) and root_radius (bottom of the teeth)
        - spoke width also defines the spacing at the root_radius
        - mount_radius is adjusted so that spokes fit if there is room
        - if no room (collision) then spokes not drawn
    """
    # Spokes
    collision = False # assume we draw spokes
    messages = []     # messages to send back about changes.
    path = ''
    r_outer = root_radius - spoke_width
    # checks for collision with spokes
    # check for mount hole collision with inner spokes
    if mount_radius <= mount_hole/2:
        adj_factor = (r_outer - mount_hole/2) / 5
        if adj_factor < 0.1:
            # not enough reasonable room
            collision = True
        else:
            mount_radius = mount_hole/2 + adj_factor # small fix
            messages.append("Mount support too small. Auto increased to %2.2f%s." % (mount_radius/unit_factor*2, unit_label))
            
    # then check to see if cross-over on spoke width
    if spoke_width * spoke_count +0.5 >= two_pi * mount_radius:
        adj_factor = 1.2 # wrong value. its probably one of the points distances calculated below
        mount_radius += adj_factor
        messages.append("Too many spokes. Increased Mount support by %2.3f%s" % (adj_factor/unit_factor, unit_label))
    
    # check for collision with outer rim
    if r_outer <= mount_radius:
        # not enough room to draw spokes so cancel
        collision = True
    if collision: # don't draw spokes if no room.
        messages.append("Not enough room for Spokes. Decrease Spoke width.")
    else: # draw spokes
        for i in range(spoke_count):
            points = []
            start_a, end_a = i * two_pi / spoke_count, (i+1) * two_pi / spoke_count
            # inner circle around mount
            asin_factor = spoke_width/mount_radius/2
            # check if need to clamp radius
            asin_factor = max(-1.0, min(1.0, asin_factor)) # no longer needed - resized above
            a = asin(asin_factor)
            points += [ point_on_circle(mount_radius, start_a + a), point_on_circle(mount_radius, end_a - a)]
            # is inner circle too small
            asin_factor = spoke_width/r_outer/2
            # check if need to clamp radius
            asin_factor = max(-1.0, min(1.0, asin_factor)) # no longer needed - resized above
            a = asin(asin_factor)
            points += [point_on_circle(r_outer, end_a - a), point_on_circle(r_outer, start_a + a) ]

            path += (
                    "M %f,%f" % points[0] +
                    "A  %f,%f %s %s %s %f,%f" % tuple((mount_radius, mount_radius, 0, 0 if spoke_count!=1 else 1, 1 ) + points[1]) +
                    "L %f,%f" % points[2] +
                    "A  %f,%f %s %s %s %f,%f" % tuple((r_outer, r_outer, 0, 0 if spoke_count!=1 else 1, 0 ) + points[3]) +
                    "Z"
                    )
    return (path, messages)


class Gears(inkex.Effect):
    def __init__(self):
        inkex.Effect.__init__(self)
        # an alternate way to get debug info:
        # could use inkex.debug(string) instead...
        try:
            self.tty = open("/dev/tty", 'w')
        except:
            self.tty = open(devnull, 'w')  # '/dev/null' for POSIX, 'nul' for Windows.
            # print >>self.tty, "gears-dev " + __version__
        self.OptionParser.add_option("-t", "--teeth",
                                     action="store", type="int",
                                     dest="teeth", default=24,
                                     help="Number of teeth")
        
        self.OptionParser.add_option("-s", "--system",
                                     action="store", type="string", 
                                     dest="system", default='CP',
                                     help="Select system: 'CP' (Cyclic Pitch (default)), 'DP' (Diametral Pitch), 'MM' (Metric Module)")
        
        self.OptionParser.add_option("-d", "--dimension",
                                     action="store", type="float",
                                     dest="dimension", default=1.0,
                                     help="Tooth size, depending on system (which defaults to CP)")


        self.OptionParser.add_option("-a", "--angle",
                                     action="store", type="float",
                                     dest="angle", default=20.0,
                                     help="Pressure Angle (common values: 14.5, 20, 25 degrees)")

        self.OptionParser.add_option("-p", "--profile-shift",
                                     action="store", type="float",
                                     dest="profile_shift", default=20.0,
                                     help="Profile shift [in percent of the module]. Negative values help against undercut")

        self.OptionParser.add_option("-u", "--units",
                                     action="store", type="string",
                                     dest="units", default='mm',
                                     help="Units this dialog is using")

        self.OptionParser.add_option("-A", "--accuracy",
                                     action="store", type="int",
                                     dest="accuracy", default=0,
                                     help="Accuracy of involute: automatic: 5..20 (default), best: 20(default), medium 10, low: 5; good acuracy is important with a low tooth count")
        # Clearance: Radial distance between top of tooth on one gear to bottom of gap on another.
        self.OptionParser.add_option("", "--clearance",
                                     action="store", type="float",
                                     dest="clearance", default=0.0,
                                     help="Clearance between bottom of gap of this gear and top of tooth of another")

        self.OptionParser.add_option("", "--annotation",
                                     action="store", type="inkbool", 
                                     dest="annotation", default=False,
                                     help="Draw annotation text")

        self.OptionParser.add_option("-i", "--internal-ring",
                                     action="store", type="inkbool",
                                     dest="internal_ring", default=False,
                                     help="Ring (or Internal) gear style (default: normal spur gear)")

        self.OptionParser.add_option("", "--mount-hole",
                                     action="store", type="float",
                                     dest="mount_hole", default=5,
                                     help="Mount hole diameter")

        self.OptionParser.add_option("", "--mount-diameter",
                                     action="store", type="float",
                                     dest="mount_diameter", default=15,
                                     help="Mount support diameter")

        self.OptionParser.add_option("", "--spoke-count",
                                     action="store", type="int",
                                     dest="spoke_count", default=3,
                                     help="Spokes count")

        self.OptionParser.add_option("", "--spoke-width",
                                     action="store", type="float",
                                     dest="spoke_width", default=5,
                                     help="Spoke width")

        self.OptionParser.add_option("", "--holes-rounding",
                                     action="store", type="float",
                                     dest="holes_rounding", default=5,
                                     help="Holes rounding")

        self.OptionParser.add_option("", "--active-tab",
                                     action="store", type="string",
                                     dest="active_tab", default='',
                                     help="Active tab. Not used now.")
                        
        self.OptionParser.add_option("-x", "--centercross",
                                     action="store", type="inkbool", 
                                     dest="centercross", default=False,
                                     help="Draw cross in center")
        
        self.OptionParser.add_option("-c", "--pitchcircle",
                                     action="store", type="inkbool",
                                     dest="pitchcircle", default=False,
                                     help="Draw pitch circle (for mating)")

        self.OptionParser.add_option("-r", "--draw-rack",
                                     action="store", type="inkbool", 
                                     dest="drawrack", default=False,
                                     help="Draw rack gear instead of spur gear")
        
        self.OptionParser.add_option("", "--rack-teeth-length",
                                     action="store", type="int",
                                     dest="teeth_length", default=12,
                                     help="Length (in teeth) of rack")
        
        self.OptionParser.add_option("", "--rack-base-height",
                                     action="store", type="float",
                                     dest="base_height", default=8,
                                     help="Height of base of rack")
        
        self.OptionParser.add_option("", "--rack-base-tab",
                                     action="store", type="float",
                                     dest="base_tab", default=14,
                                     help="Length of tabs on ends of rack")

        self.OptionParser.add_option("", "--undercut-alert",
                                     action="store", type="inkbool", 
                                     dest="undercut_alert", default=False,
                                     help="Let the user confirm a warning dialog if undercut occurs. This dialog also shows helpful hints against undercut")

    
    def add_text(self, node, text, position, text_height=12):
        """ Create and insert a single line of text into the svg under node.
            - use 'text' type and label as anootation
            - where color is Ponoko Orange - so ignored when lasercutting
        """
        line_style = {'font-size': '%dpx' % text_height, 'font-style':'normal', 'font-weight': 'normal',
                     'fill': '#F6921E', 'font-family': 'Bitstream Vera Sans,sans-serif',
                     'text-anchor': 'middle', 'text-align': 'center'}
        line_attribs = {inkex.addNS('label','inkscape'): 'Annotation',
                       'style': simplestyle.formatStyle(line_style),
                       'x': str(position[0]),
                       'y': str((position[1] + text_height) * 1.2)
                       }
        line = inkex.etree.SubElement(node, inkex.addNS('text','svg'), line_attribs)
        line.text = text

           
    def calc_unit_factor(self):
        """ return the scale factor for all dimension conversions.
            - The document units are always irrelevant as
              everything in inkscape is expected to be in 90dpi pixel units
        """
        # namedView = self.document.getroot().find(inkex.addNS('namedview', 'sodipodi'))
        # doc_units = uutounit(self, 1.0, namedView.get(inkex.addNS('document-units', 'inkscape')))
        dialog_units = uutounit(self, 1.0, self.options.units)
        unit_factor = 1.0 / dialog_units
        return unit_factor

    def calc_circular_pitch(self, unit_factor):
        """ We use math based on circular pitch.
            Expressed in inkscape units which is 90dpi 'pixel' units.
        """
        dimension = self.options.dimension
        # print >> self.tty, "unit_factor=%s, doc_units=%s, dialog_units=%s (%s), system=%s" % (unit_factor, doc_units, dialog_units, self.options.units, self.options.system)
        if   self.options.system == 'CP': # circular pitch
            circular_pitch = dimension
        elif self.options.system == 'DP': # diametral pitch 
            circular_pitch = pi / dimension
        elif self.options.system == 'MM': # module (metric)
            circular_pitch = dimension * pi
        else:
            inkex.debug("unknown system '%s', try CP, DP, MM" % self.options.system)
        # circular_pitch defines the size in inches.
        # We divide the internal inch factor (px = 90dpi), to remove the inch 
        # unit.
        # The internal inkscape unit is always px, 
        # it is independent of the doc_units!
        return circular_pitch * unit_factor



    def effect(self):
        """ Calculate Gear factors from inputs.
            - Make list of radii, angles, and centers for each tooth and 
              iterate through them
            - Turn on other visual features e.g. cross, rack, annotations, etc
        """
        path_stroke = '#000000'  # might expose one day
        path_fill   = 'none'     # no fill - just a line
        path_stroke_width  = 0.6            # might expose one day
        path_stroke_light  = path_stroke_width * 0.25   # guides are thinner
        #
        warnings = [] # list of extra messages to be shown in annotations
        # calculate unit factor for units defined in dialog. 
        unit_factor = self.calc_unit_factor()
        # User defined options
        teeth = self.options.teeth
        # Angle of tangent to tooth at circular pitch wrt radial line.
        angle = self.options.angle 
        # Clearance: Radial distance between top of tooth on one gear to 
        # bottom of gap on another.
        clearance = self.options.clearance * unit_factor
        mount_hole = self.options.mount_hole * unit_factor
        # for spokes
        mount_radius = self.options.mount_diameter * 0.5 * unit_factor
        spoke_count = self.options.spoke_count
        spoke_width = self.options.spoke_width * unit_factor
        holes_rounding = self.options.holes_rounding * unit_factor # unused
        # visible guide lines
        centercross = self.options.centercross # draw center or not (boolean)
        pitchcircle = self.options.pitchcircle # draw pitch circle or not (boolean)
        # Accuracy of teeth curves
        accuracy_involute = 20 # Number of points of the involute curve
        accuracy_circular = 9  # Number of points on circular parts
        if self.options.accuracy is not None:
            if self.options.accuracy == 0:  
                # automatic
                if   teeth < 10: accuracy_involute = 20
                elif teeth < 30: accuracy_involute = 12
                else:            accuracy_involute = 6
            else:
                accuracy_involute = self.options.accuracy
            accuracy_circular = max(3, int(accuracy_involute/2) - 1) # never less than three
        # print >>self.tty, "accuracy_circular=%s accuracy_involute=%s" % (accuracy_circular, accuracy_involute)
        # Pitch (circular pitch): Length of the arc from one tooth to the next)
        # Pitch diameter: Diameter of pitch circle.
        pitch = self.calc_circular_pitch(unit_factor)
        # Replace section below with this call to get the combined gear_calculations() above
        (pitch_radius, base_radius, addendum, dedendum,
         outer_radius, root_radius, tooth) = gear_calculations(teeth, pitch, angle, clearance, self.options.internal_ring, self.options.profile_shift*0.01)

        # Detect Undercut of teeth
##        undercut = int(ceil(undercut_min_teeth( angle )))
##        needs_undercut = teeth < undercut #? no longer needed ?
        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)
            msg = "Undercut Warning: This gear (%d teeth) will not work well.\nTry tooth count of %d or more,\nor a pressure angle of %.1f [deg] or more,\nor try a profile shift of %d %%.\nOr other decent combinations." % (teeth, min_teeth, min_angle, int(100.*max_k)-100.)
            # alas annotation cannot handle the degree symbol. Also it ignore newlines.
            # so split and make a list
            warnings.extend(msg.split("\n"))
	    if self.options.undercut_alert:
                inkex.debug(msg)
	    else:
                print >>self.tty, msg

        # All base calcs done. Start building gear
        points = generate_spur_points(teeth, base_radius, pitch_radius, outer_radius, root_radius, accuracy_involute, accuracy_circular)
        
##        half_thick_angle = two_pi / (4.0 * teeth ) #?? = pi / (2.0 * teeth)
##        pitch_to_base_angle  = involute_intersect_angle( base_radius, pitch_radius )
##        pitch_to_outer_angle = involute_intersect_angle( base_radius, outer_radius ) - pitch_to_base_angle
##
##        start_involute_radius = max(base_radius, root_radius)
##        radii = linspace(start_involute_radius, outer_radius, accuracy_involute)
##        angles = [involute_intersect_angle(base_radius, r) for r in radii]
##
##        centers = [(x * two_pi / float( teeth) ) for x in range( teeth ) ]
##        points = []
##
##        for c in centers:
##            # Angles
##            pitch1 = c - half_thick_angle
##            base1  = pitch1 - pitch_to_base_angle
##            offsetangles1 = [ base1 + x for x in angles]
##            points1 = [ point_on_circle( radii[i], offsetangles1[i]) for i in range(0,len(radii)) ]
##
##            pitch2 = c + half_thick_angle
##            base2  = pitch2 + pitch_to_base_angle
##            offsetangles2 = [ base2 - x for x in angles] 
##            points2 = [ point_on_circle( radii[i], offsetangles2[i]) for i in range(0,len(radii)) ]
##
##            points_on_outer_radius = [ point_on_circle(outer_radius, x) for x in linspace(offsetangles1[-1], offsetangles2[-1], accuracy_circular) ]
##
##            if root_radius > base_radius:
##                pitch_to_root_angle = pitch_to_base_angle - involute_intersect_angle(base_radius, root_radius )
##                root1 = pitch1 - pitch_to_root_angle
##                root2 = pitch2 + pitch_to_root_angle
##                points_on_root = [point_on_circle (root_radius, x) for x in linspace(root2, root1+(two_pi/float(teeth)), accuracy_circular) ]
##                p_tmp = points1 + points_on_outer_radius[1:-1] + points2[::-1] + points_on_root[1:-1] # [::-1] reverses list; [1:-1] removes first and last element
##            else:
##                points_on_root = [point_on_circle (root_radius, x) for x in linspace(base2, base1+(two_pi/float(teeth)), accuracy_circular) ]
##                p_tmp = points1 + points_on_outer_radius[1:-1] + points2[::-1] + points_on_root # [::-1] reverses list
##
##            points.extend( p_tmp )

        path = points_to_svgd( points )
        bbox_center = points_to_bbox_center( points )

        # Spokes (add to current path)
        if not self.options.internal_ring:  # only draw internals if spur gear
            spokes_path, msg = generate_spokes_path(root_radius, spoke_width, spoke_count, mount_radius, mount_hole,
                                                    unit_factor, self.options.units)
            warnings.extend(msg)
            path += spokes_path

            # Draw mount hole
            # A : rx,ry  x-axis-rotation, large-arch-flag, sweepflag  x,y
            r = mount_hole / 2
            path += (
                    "M %f,%f" % (0,r) +
                    "A  %f,%f %s %s %s %f,%f" % (r,r, 0,0,0, 0,-r) +
                    "A  %f,%f %s %s %s %f,%f" % (r,r, 0,0,0, 0,r) 
                    )
        else:
            # its a ring gear
            # which only has an outer ring where width = spoke width
            r = outer_radius + spoke_width
            path += (
                    "M %f,%f" % (0,r) +
                    "A  %f,%f %s %s %s %f,%f" % (r,r, 0,0,0, 0,-r) +
                    "A  %f,%f %s %s %s %f,%f" % (r,r, 0,0,0, 0,r) 
                    )
        
        # Embed gear in group to make animation easier:
        #  Translate group, Rotate path.
        t = 'translate(' + str( self.view_center[0] ) + ',' + str( self.view_center[1] ) + ')'
        g_attribs = { inkex.addNS('label','inkscape'):'Gear' + str( teeth ),
                      inkex.addNS('transform-center-x','inkscape'): str(-bbox_center[0]),
                      inkex.addNS('transform-center-y','inkscape'): str(-bbox_center[1]),
                      'transform':t,
                      'info':'N:'+str(teeth)+'; Pitch:'+ str(pitch) + '; Pressure Angle: '+str(angle) }
        # add the group to the current layer
        g = inkex.etree.SubElement(self.current_layer, 'g', g_attribs )

        # Create gear path under top level group
        style = { 'stroke': path_stroke, 'fill': path_fill, 'stroke-width': path_stroke_width }
        gear_attribs = { 'style': simplestyle.formatStyle(style), 'd': path }
        gear = inkex.etree.SubElement(g, inkex.addNS('path','svg'), gear_attribs )

        # Add center
        if centercross:
            style = { 'stroke': path_stroke, 'fill': path_fill, 'stroke-width': path_stroke_light }
            cs = str(pitch / 3) # centercross length
            d = 'M-'+cs+',0L'+cs+',0M0,-'+cs+'L0,'+cs  # 'M-10,0L10,0M0,-10L0,10'
            center_attribs = { inkex.addNS('label','inkscape'): 'Center cross',
                               'style': simplestyle.formatStyle(style), 'd': d }
            center = inkex.etree.SubElement(g, inkex.addNS('path','svg'), center_attribs )

        # Add pitch circle (for mating)
        if pitchcircle:
            style = { 'stroke': path_stroke, 'fill': path_fill, 'stroke-width': path_stroke_light }
            draw_SVG_circle(g, pitch_radius, 0, 0, 'Pitch circle', style)

        # Add Rack (below)
        if self.options.drawrack:
            base_height = self.options.base_height * unit_factor
            tab_width = self.options.base_tab * unit_factor
            tooth_count = self.options.teeth_length
            (points, guide_path) = generate_rack_points(tooth_count, pitch, addendum, angle,
                                                        base_height, tab_width, clearance, pitchcircle)
            path = points_to_svgd(points)
            # position below Gear, so that it meshes nicely
            # xoff = 0          ## if teeth % 4 == 2.
            # xoff = -0.5*pitch     ## if teeth % 4 == 0.
            # xoff = -0.75*pitch    ## if teeth % 4 == 3.
            # xoff = -0.25*pitch    ## if teeth % 4 == 1.
            xoff = (-0.5, -0.25, 0, -0.75)[teeth % 4] * pitch
            t = 'translate(' + str( xoff ) + ',' + str( pitch_radius ) + ')'
            g_attribs = { inkex.addNS('label', 'inkscape'): 'RackGear' + str(tooth_count),
                          'transform': t }
            rack = inkex.etree.SubElement(g, 'g', g_attribs)

            # Create SVG Path for gear
            style = {'stroke': path_stroke, 'fill': 'none', 'stroke-width': path_stroke_width }
            gear_attribs = { 'style': simplestyle.formatStyle(style), 'd': path }
            gear = inkex.etree.SubElement(
                rack, inkex.addNS('path', 'svg'), gear_attribs)
            if guide_path is not None:
                style2 = { 'stroke': path_stroke, 'fill': 'none', 'stroke-width': path_stroke_light }
                gear_attribs2 = { 'style': simplestyle.formatStyle(style2), 'd': guide_path }
                gear = inkex.etree.SubElement(
                    rack, inkex.addNS('path', 'svg'), gear_attribs2)


        # Add Annotations (above)
        if self.options.annotation:
            outer_dia = outer_radius * 2
            if self.options.internal_ring:
                outer_dia += 2 * spoke_width
            notes = []
            notes.extend(warnings)
            #notes.append('Document (%s) scale conversion = %2.4f' % (self.document.getroot().find(inkex.addNS('namedview', 'sodipodi')).get(inkex.addNS('document-units', 'inkscape')), unit_factor))
            notes.extend(['Teeth: %d   CP: %2.4f(%s) ' % (teeth, pitch / unit_factor, self.options.units),
                          'DP: %2.3f Module: %2.4f' % (pi / pitch * unit_factor, pitch / pi * 25.4),
                          'Pressure Angle: %2.2f degrees' % (angle),
                          'Pitch diameter: %2.3f %s' % (pitch_radius * 2 / unit_factor, self.options.units),
                          'Outer diameter: %2.3f %s' % (outer_dia / unit_factor, self.options.units),
                          'Root diameter:  %2.3f %s' % (root_radius * 2 / unit_factor, self.options.units),
                          'Base diameter:  %2.3f %s' % (base_radius * 2 / unit_factor, self.options.units)#,
                          #'Addendum:      %2.4f %s'  % (addendum / unit_factor, self.options.units),
                          #'Dedendum:      %2.4f %s'  % (dedendum / unit_factor, self.options.units)
                          ])
            # text height relative to gear size.
            # ranges from 10 to 22 over outer radius size 60 to 360
            text_height = max(10, min(10+(outer_dia-60)/24, 22))
            # position above
            y = - outer_radius - (len(notes)+1) * text_height * 1.2
            for note in notes:
                self.add_text(g, note, [0,y], text_height)
                y += text_height * 1.2

if __name__ == '__main__':
    e = Gears()
    e.affect()

# Notes

