Added and fixed speira (archimedian spiral)

extensions/fablabchemnitz_archimedesspiral.inx

@@ -0,0 +1,36 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<inkscape-extension xmlns="http://www.inkscape.org/namespace/inkscape/extension">
+   <_name>The Spiral of Archimedes</_name>
+   <id>fablabchemnitz.de.archimedesspiral</id>
+   <param name="name" appearance="header" type="description">R = r + aθ</param>
+   <param name="r" type="int" min="0" max="1000000" _gui-text="r (mm)">50</param>
+   <param name="a" type="float" min="0" max="1000000" _gui-text="a">3</param>
+   <param name="step" type="int" min="1" max="300" _gui-text="Step">50</param>
+   <param name="trl" type="optiongroup" _gui-text="Turn direction">
+      <option value="0">Left</option>
+      <option value="1">Right</option>
+   </param>
+   <param name="length" type="float" min="0" max="1000000" _gui-text="Length (mm)">0</param>
+   <param name="turns" type="int" min="1" max="1000000" _gui-text="Turns">5</param>
+   <param name="desc" appearance="header" type="description">Notes</param>
+   <param name="desc_text" type="description">
+The option "turns" only works if you set "length (mm)" to 0.0. 
+Otherwise the length value will be used to calculate the 
+spiral for given length. The higher the "step" value is 
+set the better the accuracy is. If you set the step value 
+really low the resulting length will not be precise and 
+the curve is maybe not drawn at all. You can validate the 
+length by using the extension "Visualize Path > Measure Path"
+   </param>
+   <effect>
+      <object-type>all</object-type>
+      <effects-menu>
+         <submenu _name="FabLab Chemnitz">
+            <submenu _name="Shape/Pattern from Generator" />
+         </submenu>
+      </effects-menu>
+   </effect>
+   <script>
+      <command reldir="extensions" interpreter="python">fablabchemnitz_archimedesspiral.py</command>
+   </script>
+</inkscape-extension>

extensions/fablabchemnitz_archimedesspiral.py

@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+""" 
+Copyright (C) 2017 Panagiotis Loukas
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WAphiANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WAphiANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+Version 0.2
+This script was written by Panagiotis Loukas to make spiral easy. 
+It simply,
+
+Have fun :)
+PS. 
+  Written on Arch. 
+"""
+
+import inkex
+from lxml import etree
+from math import cos, sin, pi, log, sqrt
+
+class Archimedes(inkex.Effect):
+    def __init__(self):
+        inkex.Effect.__init__(self)
+        self.arg_parser.add_argument('--r', type = int, default = '50')
+        self.arg_parser.add_argument('--a', type = float, default = '3')
+        self.arg_parser.add_argument('--step', type = int, default = '50')
+        self.arg_parser.add_argument('--trl', default = '1')
+        self.arg_parser.add_argument('--turns', type = float, default = '5')
+        self.arg_parser.add_argument('--length', type = float, default = '500')
+		
+    def effect(self):
+        th = pi / 3
+        a = self.options.a
+        r = self.options.r
+		
+        length = self.options.length
+        if length > 0:
+            turns = self.angle(a, r, length, th) / (2 * pi)
+        else: 
+            turns = self.options.turns
+		
+        if self.options.trl == '1':
+            step = -self.options.step
+        else:
+            step = self.options.step
+        
+        layer = etree.SubElement(self.document.getroot(),'g')
+        path = etree.Element(inkex.addNS('path','svg'))
+        path.set('d', self.built(r, step, a, turns))
+        path.set('style',"opacity:0.8;fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.8;stroke-miterlimit:4;stroke-dashaphiay:none;stroke-opacity:1")
+        layer.append(path)
+
+    def built(self, r0, st = 4, a = 4, k = 1, th = 0):
+        step = 2 * pi / st
+        r = r0
+        s = "M " + str(r * cos(th)) + ", " + str(-r * sin(th))
+        for i in range(0, int(k * (abs(st)))):
+            prin = th + i * step
+            meta = th + (i + 1) * step
+            rp = r0 + abs(a * prin)# instead we put the absolute value the spiral will drift inwards
+            rm = r0 + abs(a * meta)# at the absolute price closes outwards
+  
+            s += "a " + str(rm) + "," + str(rm) + " 0 0," + self.options.trl + " " + str(-rp * cos(prin) + rm * cos(meta)) + "," + str(rp * sin(prin) -rm * sin(meta))       
+        return s
+
+    # see https://mathepedia.de/Archimedische_Spirale.html for formula of total arc length
+    def spirallength(self, a, r0, th):
+        phi = (r0 / a) + th
+        phi_sqrt = sqrt(phi ** 2 + 1)
+        return (a / 2) * (phi * phi_sqrt + log(phi + phi_sqrt))
+
+    def ds(self, a, r0, th):
+        return self.spirallength(a, r0, th) - self.spirallength(a, r0, 0)
+		
+    def angle(self, a, r0, length, th):        
+        i = 0.0
+        while (True):
+            ls=self.ds(a, r0, i)
+            if length - ls > 100:
+                i += 0.01
+            elif length - ls > 10: i += 0.001
+            elif length - ls > 1: i += 0.0001
+            elif length - ls > 0.1: i += 0.00001
+            elif length - ls > 0.01: i += 0.000001
+            else: break
+        return i
+
+Archimedes().run()