Add burn correction to the gears

boxes/gears.py

@@ -43,6 +43,7 @@ from os import devnull # for debugging
 from math import pi, cos, sin, tan, radians, degrees, ceil, asin, acos, sqrt
 two_pi = 2 * pi
 import argparse
+from boxes.vectors import kerf
 
 __version__ = '0.9'
 
@@ -493,7 +494,9 @@ class Gears():
                                      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 drawPoints(self, lines):
+    def drawPoints(self, lines, kerfdir=1):
+        if kerfdir != 0:
+            lines = kerf(lines, self.boxes.burn*kerfdir)
         self.boxes.ctx.save()
         self.boxes.ctx.move_to(*lines[0])
         for x, y in lines[1:]:

boxes/vectors.py

@@ -0,0 +1,57 @@
+# Copyright (C) 2013-2014 Florian Festi
+#
+#   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 3 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, see <http://www.gnu.org/licenses/>.
+
+def normalize(v):
+    "set lenght of vector to one"
+    l = (v[0]**2+v[1]**2)**0.5
+    return (v[0]/l, v[1]/l)
+
+def vdiff(p1, p2):
+    "vector from point1 to point2"
+    return (p2[0]-p1[0], p2[1]-p1[1])
+
+def vadd(v1, v2):
+    "Sum of two vectors"
+    return (v1[0]+ v2[0], v1[1]+v2[1])
+
+def vorthogonal(v):
+    "orthogonal vector"
+    "Orthogonal vector"
+    return (-v[1], v[0])
+
+def vscalmul(v, a):
+    "scale vector by a"
+    return (a*v[0], a*v[1])
+
+def dotproduct(v1, v2):
+    "Dot product"
+    return v1[0]*v2[0]+v1[1]*v2[1]
+
+def kerf(points, k):
+    """Outset points by k
+    Assumes a closed loop of points
+    """
+    result = []
+    lp = len(points)
+    for i in range(len(points)):
+        # get normalized orthogonals of both segments
+        v1 = vorthogonal(normalize(vdiff(points[i-1], points[i])))
+        v2 = vorthogonal(normalize(vdiff(points[i], points[(i+1) % lp])))
+        # direction the point has to move
+        d = normalize(vadd(v1, v2))
+        # cos of the half the angle between the segments
+        cos_alpha = dotproduct(v1, d)
+        result.append(vadd(points[i], vscalmul(d, -k/cos_alpha)))
+    return result