222 lines
8.6 KiB
Python
222 lines
8.6 KiB
Python
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#! /usr/bin/env python
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'''
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Copyright (C) 2013 Matthew Dockrey (gfish @ cyphertext.net)
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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Based on gears.py by Aaron Spike and Tavmjong Bah
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'''
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import inkex
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import simplestyle
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import sys
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from math import *
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from fablabchemnitz_svg import *
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class Sprockets(inkex.Effect):
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def __init__(self):
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inkex.Effect.__init__(self)
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self.OptionParser.add_option("-t", "--teeth",
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action="store", type="int",
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dest="teeth", default=24,
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help="Number of teeth")
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self.OptionParser.add_option("-s", "--size",
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action="store", type="string",
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dest="size", default="ANSI #40",
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help="Chain size (common values ANSI #35, ANSI #40, ANSI #60)")
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def get_pitch(self, size):
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return self.unittouu({
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'ANSI #25': '6.35mm',
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'ANSI #35': '9.53mm',
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'ANSI #40': '12.70mm',
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'ANSI #41': '12.70mm',
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'ANSI #50': '15.88mm',
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'ANSI #60': '19.05mm',
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'ANSI #80': '25.40mm',
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'ANSI #100': '31.75mm',
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'ANSI #120': '38.10mm',
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'ANSI #140': '44.45mm',
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'ANSI #160': '50.80mm',
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'ANSI #180': '57.15mm',
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'ANSI #200': '63.50mm',
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'ANSI #240': '76.20mm'
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}[size])
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def get_roller_diameter(self, size):
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return self.unittouu({
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'ANSI #25': '3.30mm',
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'ANSI #35': '5.08mm',
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'ANSI #40': '7.77mm',
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'ANSI #41': '7.92mm',
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'ANSI #50': '10.16mm',
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'ANSI #60': '11.91mm',
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'ANSI #80': '15.88mm',
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'ANSI #100': '19.05mm',
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'ANSI #120': '22.23mm',
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'ANSI #140': '25.40mm',
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'ANSI #160': '28.58mm',
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'ANSI #180': '37.08mm',
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'ANSI #200': '39.67mm',
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'ANSI #240': '47.63mm'
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}[size])
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def invertX(self, p):
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return (-p[0], p[1])
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def effect(self):
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size = self.options.size
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P = self.get_pitch(size)
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N = self.options.teeth
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PD = P / sin(pi / N)
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PR = PD / 2
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# Equations taken from
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# http://www.gearseds.com/files/design_draw_sprocket_5.pdf
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# Also referenced:
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# http://en.wikipedia.org/wiki/Roller_chain (of course)
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# and
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# Chains for Power Transmission and Material Handling:
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# Design and Applications Handbook
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# American Chain Association, 1982
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Dr = self.get_roller_diameter(size)
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Ds = 1.0005 * Dr + self.unittouu('0.003in')
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R = Ds / 2 # seating curve radius
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A = radians(35 + 60 / N)
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B = radians(18 - 56 / N)
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ac = 0.8 * Dr
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M = ac * cos(A)
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T = ac * sin(A)
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E = 1.3025 * Dr + self.unittouu('0.0015in') # transition radius
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ab = 1.4 * Dr
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W = ab * cos(pi / N)
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V = ab * sin(pi / N)
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F = Dr * (0.8 * cos(radians(18 - 56 / N)) + 1.4 * cos(radians(17 - 64 / N)) - 1.3025) - self.unittouu('0.0015in') # topping curve radius
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svg = ""
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t_inc = 2.0 * pi / float(N)
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thetas = [(x * t_inc) for x in range(N)]
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for theta in thetas:
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# Seating curve center
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seatC = (0, -PR)
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# Transitional curve center
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c = (M, -PR - T)
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# Calculate line cx, angle A from x axis
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# Y = mX + b
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cx_m = -tan(A) # Negative because we're in -Y space
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cx_b = c[1] - cx_m * c[0]
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# Calculate intersection of cx with circle S to get point x
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# http://math.stackexchange.com/questions/228841/how-do-i-calculate-the-intersections-of-a-straight-line-and-a-circle
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qA = cx_m * cx_m + 1
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qB = 2 * (cx_m * cx_b - cx_m * seatC[1] - seatC[0])
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qC = seatC[1] * seatC[1] - R * R + seatC[0] * seatC[0] - 2 * cx_b * seatC[1] + cx_b * cx_b
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cx_X = (-qB - sqrt(qB * qB - 4 * qA * qC)) / (2 * qA)
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# Seating curve/Transitional curve junction
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x = (cx_X, cx_m * cx_X + cx_b)
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# Calculate line cy, angle B past cx
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cy_m = -tan(A - B)
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cy_b = c[1] - cy_m * c[0]
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# Calculate point y (E along cy from c)
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# http://www.physicsforums.com/showthread.php?t=419561
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yX = c[0] - E / sqrt(1 + cy_m * cy_m)
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# Transitional curve/Tangent line junction
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y = (yX, cy_m * yX + cy_b)
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# Solve for circle T with radius E which passes through x and y
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# http://mathforum.org/library/drmath/view/53027.html
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# http://stackoverflow.com/questions/12264841/determine-circle-center-based-on-two-points-radius-known-with-solve-optim
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z = ((x[0] + y[0]) / 2, (x[1] + y[1]) / 2)
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x_diff = y[0] - x[0]
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y_diff = y[1] - x[1]
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q = sqrt(x_diff * x_diff + y_diff * y_diff)
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tX = z[0] + sqrt(E * E - (q / 2) * (q / 2)) * (x[1] - y[1]) / q
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tY = z[1] + sqrt(E * E - (q / 2) * (q / 2)) * (y[0] - x[0]) / q
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# Transitional curve center
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tranC = (tX, tY)
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# Tangent line -- tangent to transitional curve at point y
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tanl_m = -(tranC[0] - y[0]) / (tranC[1] - y[1])
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tanl_b = -y[0] * tanl_m + y[1]
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t_off = (y[0] - 10, tanl_m * (y[0] - 10) + tanl_b)
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# Topping curve center
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topC = (-W, -PR + V)
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# Adjust F to force topping curve tangent to tangent line
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F = abs(topC[1] - tanl_m * topC[0] - tanl_b) / sqrt(tanl_m * tanl_m + 1) * 1.0001 # Final fudge needed to overcome numerical instability
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# Find intersection point between topping curve and tangent line
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ttA = tanl_m * tanl_m + 1
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ttB = 2 * (tanl_m * tanl_b - tanl_m * topC[1] - topC[0])
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ttC = topC[1] * topC[1] - F * F + topC[0] * topC[0] - 2 * tanl_b * topC[1] + tanl_b * tanl_b
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tanl_X = (-ttB - sqrt(ttB * ttB - 4 * ttA * ttC)) / (2 * ttA)
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# Tagent line/Topping curve junction
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tanl = (tanl_X, tanl_m * tanl_X + tanl_b)
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# Calculate tip line, angle t_inc/2 from Y axis
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tip_m = -tan(pi / 2 + t_inc / 2) # Negative because we're in -Y space
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tip_b = 0
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# Calculate intersection of tip line with topping curve
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tA = tip_m * tip_m + 1
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tB = 2 * (tip_m * tip_b - tip_m * topC[1] - topC[0])
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tC = topC[1] * topC[1] - F * F + topC[0] * topC[0] - 2 * tip_b * topC[1] + tip_b * tip_b
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tip_X = (-tB - sqrt(tB * tB - 4 * tA * tC)) / (2 * tA)
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# Topping curve top
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tip = (tip_X, tip_m * tip_X + tip_b)
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# Set initial location if needed
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if (theta == 0):
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svg += SVG_move(tip, theta)
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svg += SVG_circle(tanl, F, 1, theta) # Topping curve left
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svg += SVG_line(y, theta) # Tangent line left
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svg += SVG_circle(x, E, 0, theta) # Transitional curve left
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svg += SVG_circle(self.invertX(x), R, 0, theta) # Seating curve
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svg += SVG_circle(self.invertX(y), E, 0, theta) # Transitionl curve right
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svg += SVG_line(self.invertX(tanl), theta) # Tangent line right
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svg += SVG_circle(self.invertX(tip), F, 1, theta) # Topping curve right
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svg += SVG_close()
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# Insert as a new element
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sprocket_style = { 'stroke': '#000000',
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'stroke-width': '0.1',
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'fill': 'none'
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}
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g_attribs = {inkex.addNS('label','inkscape'): 'Sprocket ' + size + "-" + str(N),
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'transform': 'translate(' + str(self.view_center[0]) + ',' + str(self.view_center[1]) + ')',
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'style' : simplestyle.formatStyle(sprocket_style),
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'd' : svg }
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g = inkex.etree.SubElement(self.current_layer, inkex.addNS('path','svg'), g_attribs)
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if __name__ == '__main__':
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e = Sprockets()
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e.affect()
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