added cookie_cutter extension

extensions/fablabchemnitz/cookie_cutter/README.md

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+Convert SVG (text is not supported; convert text to paths) and HPGL to gcode for a 3-axis GCode machine, 
+where the Z-axis controls the pen height.
+
+You can also convert the same SVG subset to HPGL.
+
+Run with no arguments for some help.
+
+Note on multiple pen usage:
+
+The pen definition file is one-pen per line, in the format:
+
+    n (x,y) svgcolor comment
+
+Here, n is the pen number (pen 1 is assumed to be loaded at the start), (x,y) is the offset from the 
+default pen position (note: gcodeplot.py will correct the offset and will NOT check for clipping at 
+drawing edges--it is your responsibility to make sure your tool doesn't crash into anything due to 
+offset), svgcolor is a color specification in svg format, e.g., rgb(255,255,00), #FFFF00 or yellow, 
+and the comment is a human-readable comment.

extensions/fablabchemnitz/cookie_cutter/cookiecutter.inx

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+<?xml version="1.0" encoding="UTF-8"?>
+<inkscape-extension xmlns="http://www.inkscape.org/namespace/inkscape/extension">
+    <name>OpenSCAD Cookie Cutter Export</name>
+    <id>fablabchemnitz.de.cookie_cutter</id>
+    <output>
+        <extension>.scad</extension>
+        <mimetype>text/plain</mimetype>
+        <filetypename>OpenSCAD cookie cutter file (*.scad)</filetypename>
+        <filetypetooltip>Export an OpenSCAD cookie cutter file</filetypetooltip>
+        <dataloss>true</dataloss>
+    </output>
+    <script>
+        <command location="inx" interpreter="python">svg2cookiecutter.py</command>
+    </script>
+</inkscape-extension>

extensions/fablabchemnitz/cookie_cutter/meta.json

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+[
+  {
+    "name": "OpenSCAD Cookie Cutter Export",
+    "id": "fablabchemnitz.de.cookie_cutter",
+    "path": "cookie_cutte",
+    "dependent_extensions": null,
+    "original_name": "OpenSCAD Cookie Cutter Export",
+    "original_id": "mobi.omegacentauri.cookiecutter",
+    "license": "MIT License",
+    "license_url": "https://inkscape.org/~arpruss/%E2%98%85openscad-cookie-cutter-file-output",
+    "comment": "",
+    "source_url": "https://gitea.fablabchemnitz.de/FabLab_Chemnitz/mightyscape-1.2/src/branch/master/extensions/fablabchemnitz/cookie_cutter",
+    "fork_url": "https://github.com/arpruss/gcodeplot",
+    "documentation_url": "https://stadtfabrikanten.org/display/IFM/OpenSCAD+cookie+cutter+file+output",
+    "inkscape_gallery_url": null,
+    "main_authors": [
+      "github.com/arpruss",
+      "github.com/eridur-de"
+    ]
+  }
+]

extensions/fablabchemnitz/cookie_cutter/svg2cookiecutter.py

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+import sys
+import svgpath.parser as parser
+
+# colors: RED = outer wall
+#         GREEN = inner wall
+#         BLACK = inside feature (not cutting all the way)
+
+PRELIM = """// OpenSCAD file automatically generated by svg2cookiercutter.py
+// parameters tunable by user
+wallHeight = 12;
+minWallThickness = 2;
+maxWallThickness = 3;
+minInsideWallThickness = 1;
+maxInsideWallThickness = 3;
+
+wallFlareWidth = 5;
+wallFlareThickness = 3;
+insideWallFlareWidth = 5;
+insideWallFlareThickness = 3;
+
+featureHeight = 8;
+minFeatureThickness = 1;
+maxFeatureThickness = 3;
+
+connectorThickness = 1.75;
+cuttingTaperHeight = 2.5;
+cuttingEdgeThickness = 1.25;
+// set to non-zero value to generate a demoulding plate
+demouldingPlateHeight = 0;
+demouldingPlateSlack = 1.5;
+
+// sizing
+function clamp(t,minimum,maximum) = min(maximum,max(t,minimum));
+function featureThickness(t)      = clamp(t,minFeatureThickness,maxFeatureThickness);
+function wallThickness(t)         = clamp(t,minWallThickness,maxWallThickness);
+function insideWallThickness(t)   = clamp(t,minInsideWallThickness,maxInsideWallThickness);
+
+size = $OVERALL_SIZE$;
+scale = size/$OVERALL_SIZE$;
+
+// helper modules: subshapes
+module ribbon(points, thickness=1) {
+    union() {
+        for (i=[1:len(points)-1]) {
+            hull() {
+                translate(points[i-1]) circle(d=thickness, $fn=8);
+                translate(points[i]) circle(d=thickness, $fn=8);
+            }
+        }
+    }
+}
+
+
+module wall(points,height,thickness) {
+    module profile() {
+        if (height>=cuttingTaperHeight && cuttingTaperHeight>0 && cuttingEdgeThickness<thickness) {
+            cylinder(h=height-cuttingTaperHeight+0.001,d=thickness,$fn=8);
+            translate([0,0,height-cuttingTaperHeight]) cylinder(h=cuttingTaperHeight,d1=thickness,d2=cuttingEdgeThickness);
+        }
+        else {
+            cylinder(h=height,d=thickness,$fn=8);
+        }
+    }
+    for (i=[1:len(points)-1]) {
+        hull() {
+            translate(points[i-1]) profile();
+            translate(points[i])   profile();
+        }
+    }
+}
+
+
+module outerFlare(path) {
+  difference() {
+    render(convexity=10) linear_extrude(height=wallFlareThickness) ribbon(path,thickness=wallFlareWidth);
+    translate([0,0,-0.01]) linear_extrude(height=wallFlareThickness+0.02) polygon(points=path);
+  }
+}
+
+module innerFlare(path) {
+  intersection() {
+    render(convexity=10) linear_extrude(height=insideWallFlareThickness) ribbon(path,thickness=insideWallFlareWidth);
+    translate([0,0,-0.01]) linear_extrude(height=insideWallFlareThickness+0.02) polygon(points=path);
+  }
+}
+
+module fill(path,height) {
+  render(convexity=10) linear_extrude(height=height) polygon(points=path);
+}
+
+"""
+
+def isRed(rgb):
+    return rgb is not None and rgb[0] >= 0.4 and rgb[1]+rgb[2] < rgb[0] * 0.25
+
+def isGreen(rgb):
+    return rgb is not None and rgb[1] >= 0.4 and rgb[0]+rgb[2] < rgb[1] * 0.25
+
+def isBlack(rgb):
+    return rgb is not None and rgb[0]+rgb[1]+rgb[2]<0.2
+
+class Line(object):
+    def __init__(self, pathName, points, fill, stroke, strokeWidth):
+        self.pathName = pathName
+        self.points = points
+        self.fill = fill
+        self.stroke = stroke
+        self.strokeWidth = strokeWidth
+
+    def pathCode(self):
+        return self.pathName + ' = scale * [' + ','.join(('[%.3f,%.3f]'%tuple(p) for p in self.points)) + '];'
+
+    def shapesCode(self):
+        code = []
+        if self.stroke:
+            code.append('wall('+self.pathName+','+self.height+','+self.width+');')
+            if self.hasOuterFlare:
+                code.append('  outerFlare('+self.pathName+');')
+            elif self.hasInnerFlare:
+                code.append('  innerFlare('+self.pathName+');')
+        if self.fill:
+            code.append('  fill('+self.pathName+','+self.fillHeight+');')
+        return '\n'.join(code) # + '\n'
+
+class OuterWall(Line):
+    def __init__(self, pathName, points, fill, stroke, strokeWidth):
+        super(OuterWall, self).__init__(pathName, points, fill, stroke, strokeWidth)
+        self.height = "wallHeight"
+        self.width = "wallThickness(%.3f)" % self.strokeWidth
+        self.fillHeight = "wallHeight"
+        self.hasOuterFlare = True
+        self.hasInnerFlare = False
+
+class InnerWall(Line):
+    def __init__(self, pathName, points, fill, stroke, strokeWidth):
+        super(InnerWall, self).__init__(pathName, points, fill, stroke, strokeWidth)
+        self.height = "wallHeight"
+        self.width = "insideWallThickness(%.3f)" % self.strokeWidth
+        self.fillHeight = "wallHeight"
+        self.hasOuterFlare = False
+        self.hasInnerFlare = True
+
+class Feature(Line):
+    def __init__(self, pathName, points, fill, stroke, strokeWidth):
+        super(Feature, self).__init__(pathName, points, fill, stroke, strokeWidth)
+        self.height = "featureHeight"
+        self.width = "featureThickness(%.3f)" % self.strokeWidth
+        self.fillHeight = "featureHeight"
+        self.hasOuterFlare = False
+        self.hasInnerFlare = False
+
+class Connector(Line):
+    def __init__(self, pathName, points, fill):
+        super(Connector, self).__init__(pathName, points, fill, False, None) # no stroke for connectors, thus no use of self.height and self.width
+        self.width = None
+        self.fillHeight = "connectorThickness"
+        self.hasOuterFlare = False
+        self.hasInnerFlare = False
+
+def svgToCookieCutter(filename, tolerance=0.1, strokeAll = False):
+    lines = []
+    pathCount = 0;
+    minXY = [float("inf"), float("inf")]
+    maxXY = [float("-inf"), float("-inf")]
+
+    for superpath in parser.getPathsFromSVGFile(filename)[0]:
+        for path in superpath.breakup():
+            pathName = '_'+str(pathCount)
+            pathCount += 1
+            fill = path.svgState.fill is not None
+            stroke = strokeAll or path.svgState.stroke is not None
+            if not stroke and not fill: continue
+
+            linearPath = path.linearApproximation(error=tolerance)
+            points = [(-l.start.real,l.start.imag) for l in linearPath]
+            points.append((-linearPath[-1].end.real, linearPath[-1].end.imag))
+
+            if isRed    (path.svgState.fill) or isRed  (path.svgState.stroke):
+                line = OuterWall('outerWall'+pathName, points, fill, stroke, path.svgState.strokeWidth)
+            elif isGreen(path.svgState.fill) or isGreen(path.svgState.stroke):
+                line = InnerWall('innerWall'+pathName, points, fill, stroke, path.svgState.strokeWidth)
+            elif isBlack(path.svgState.fill) or isBlack(path.svgState.stroke):
+                line = Feature  ('feature'  +pathName, points, fill, stroke, path.svgState.strokeWidth)
+            else:
+                line = Connector('connector'+pathName, points, fill)
+
+            for i in range(2):
+                minXY[i] = min(minXY[i], min(p[i] for p in line.points))
+                maxXY[i] = max(maxXY[i], max(p[i] for p in line.points))
+            lines.append(line)
+
+    size = max(maxXY[0]-minXY[0], maxXY[1]-minXY[1])
+
+    code = [PRELIM]
+    code.append('// data from svg file')
+    code += [line.pathCode()+'\n' for line in lines]
+    code.append(
+        '// main modules\n'
+        'module cookieCutter() {')
+    code += ['  ' + line.shapesCode() for line in lines]
+    code.append('}\n')
+
+    # demoulding plate module
+    positives =        [line for line in lines if     isinstance(line, OuterWall) and line.stroke and not line.fill]
+    negatives_stroke = [line for line in lines]
+    negatives_fill   = [line for line in lines if not isinstance(line, OuterWall) and line.fill]
+    code.append(
+        "module demouldingPlate(){\n"
+        "  // a plate to help push on the cookie to turn it out\n"
+	"  render(convexity=10) difference() {\n"
+	"    linear_extrude(height=demouldingPlateHeight) union() {")
+    for line in positives:
+        code.append('      polygon(points='+line.pathName+');')
+
+    code.append("    }\n"
+      "    translate([0,0,-0.01]) linear_extrude(height=demouldingPlateHeight+0.02) union() {")
+    for line in negatives_stroke:
+        code.append('      ribbon('+line.pathName+',thickness=demouldingPlateSlack'+('+'+line.width if line.stroke else '')+');')
+    for line in negatives_fill:
+        code.append('      polygon(points='+line.pathName+');')
+        # TODO: we should remove the interior of polygonal inner walls
+    code.append('    }\n  }\n}\n')
+
+    code.append('////////////////////////////////////////////////////////////////////////////////')
+    code.append('// final call, use main modules')
+    code.append('translate([%.3f*scale + wallFlareWidth/2,  %.3f*scale + wallFlareWidth/2,0])'    % (-minXY[0],-minXY[1]))
+    code.append('  cookieCutter();\n')
+
+    code.append('// translate([-40,15,0]) cylinder(h=wallHeight+10,d=5,$fn=20); // handle')
+    code.append('if (demouldingPlateHeight>0)')
+    code.append('  mirror([1,0,0])')
+    code.append('    translate([%.3f*scale + wallFlareWidth/2,  %.3f*scale + wallFlareWidth/2,0])' % (-minXY[0],-minXY[1]))
+    code.append('      demouldingPlate();')
+
+    return '\n'.join(code).replace('$OVERALL_SIZE$', '%.3f' % size)
+
+if __name__ == '__main__':
+    print(svgToCookieCutter(sys.argv[1]))

extensions/fablabchemnitz/cookie_cutter/svgpath/__init__.py

@@ -0,0 +1,2 @@
+from .path import Path, Line, Arc, CubicBezier, QuadraticBezier
+from .parser import parse_path

extensions/fablabchemnitz/cookie_cutter/svgpath/parser.py

@@ -0,0 +1,700 @@
+# SVG Path specification parser
+
+import re
+from . import path
+import xml.etree.ElementTree as ET
+import re
+import math
+
+COMMANDS = set('MmZzLlHhVvCcSsQqTtAa')
+UPPERCASE = set('MZLHVCSQTA')
+
+COMMAND_RE = re.compile("([MmZzLlHhVvCcSsQqTtAa])")
+FLOAT_RE = re.compile("[-+]?[0-9]*\.?[0-9]+(?:[eE][-+]?[0-9]+)?")
+
+SVG_COLORS = {
+"aliceblue": (0.941176,0.972549,1),
+"antiquewhite": (0.980392,0.921569,0.843137),
+"aqua": (0,1,1),
+"aquamarine": (0.498039,1,0.831373),
+"azure": (0.941176,1,1),
+"beige": (0.960784,0.960784,0.862745),
+"bisque": (1,0.894118,0.768627),
+"black": (0,0,0),
+"blanchedalmond": (1,0.921569,0.803922),
+"blue": (0,0,1),
+"blueviolet": (0.541176,0.168627,0.886275),
+"brown": (0.647059,0.164706,0.164706),
+"burlywood": (0.870588,0.721569,0.529412),
+"cadetblue": (0.372549,0.619608,0.627451),
+"chartreuse": (0.498039,1,0),
+"chocolate": (0.823529,0.411765,0.117647),
+"coral": (1,0.498039,0.313725),
+"cornflowerblue": (0.392157,0.584314,0.929412),
+"cornsilk": (1,0.972549,0.862745),
+"crimson": (0.862745,0.0784314,0.235294),
+"cyan": (0,1,1),
+"darkblue": (0,0,0.545098),
+"darkcyan": (0,0.545098,0.545098),
+"darkgoldenrod": (0.721569,0.52549,0.0431373),
+"darkgray": (0.662745,0.662745,0.662745),
+"darkgreen": (0,0.392157,0),
+"darkgrey": (0.662745,0.662745,0.662745),
+"darkkhaki": (0.741176,0.717647,0.419608),
+"darkmagenta": (0.545098,0,0.545098),
+"darkolivegreen": (0.333333,0.419608,0.184314),
+"darkorange": (1,0.54902,0),
+"darkorchid": (0.6,0.196078,0.8),
+"darkred": (0.545098,0,0),
+"darksalmon": (0.913725,0.588235,0.478431),
+"darkseagreen": (0.560784,0.737255,0.560784),
+"darkslateblue": (0.282353,0.239216,0.545098),
+"darkslategray": (0.184314,0.309804,0.309804),
+"darkslategrey": (0.184314,0.309804,0.309804),
+"darkturquoise": (0,0.807843,0.819608),
+"darkviolet": (0.580392,0,0.827451),
+"deeppink": (1,0.0784314,0.576471),
+"deepskyblue": (0,0.74902,1),
+"dimgray": (0.411765,0.411765,0.411765),
+"dimgrey": (0.411765,0.411765,0.411765),
+"dodgerblue": (0.117647,0.564706,1),
+"firebrick": (0.698039,0.133333,0.133333),
+"floralwhite": (1,0.980392,0.941176),
+"forestgreen": (0.133333,0.545098,0.133333),
+"fuchsia": (1,0,1),
+"gainsboro": (0.862745,0.862745,0.862745),
+"ghostwhite": (0.972549,0.972549,1),
+"gold": (1,0.843137,0),
+"goldenrod": (0.854902,0.647059,0.12549),
+"gray": (0.501961,0.501961,0.501961),
+"grey": (0.501961,0.501961,0.501961),
+"green": (0,0.501961,0),
+"greenyellow": (0.678431,1,0.184314),
+"honeydew": (0.941176,1,0.941176),
+"hotpink": (1,0.411765,0.705882),
+"indianred": (0.803922,0.360784,0.360784),
+"indigo": (0.294118,0,0.509804),
+"ivory": (1,1,0.941176),
+"khaki": (0.941176,0.901961,0.54902),
+"lavender": (0.901961,0.901961,0.980392),
+"lavenderblush": (1,0.941176,0.960784),
+"lawngreen": (0.486275,0.988235,0),
+"lemonchiffon": (1,0.980392,0.803922),
+"lightblue": (0.678431,0.847059,0.901961),
+"lightcoral": (0.941176,0.501961,0.501961),
+"lightcyan": (0.878431,1,1),
+"lightgoldenrodyellow": (0.980392,0.980392,0.823529),
+"lightgray": (0.827451,0.827451,0.827451),
+"lightgreen": (0.564706,0.933333,0.564706),
+"lightgrey": (0.827451,0.827451,0.827451),
+"lightpink": (1,0.713725,0.756863),
+"lightsalmon": (1,0.627451,0.478431),
+"lightseagreen": (0.12549,0.698039,0.666667),
+"lightskyblue": (0.529412,0.807843,0.980392),
+"lightslategray": (0.466667,0.533333,0.6),
+"lightslategrey": (0.466667,0.533333,0.6),
+"lightsteelblue": (0.690196,0.768627,0.870588),
+"lightyellow": (1,1,0.878431),
+"lime": (0,1,0),
+"limegreen": (0.196078,0.803922,0.196078),
+"linen": (0.980392,0.941176,0.901961),
+"magenta": (1,0,1),
+"maroon": (0.501961,0,0),
+"mediumaquamarine": (0.4,0.803922,0.666667),
+"mediumblue": (0,0,0.803922),
+"mediumorchid": (0.729412,0.333333,0.827451),
+"mediumpurple": (0.576471,0.439216,0.858824),
+"mediumseagreen": (0.235294,0.701961,0.443137),
+"mediumslateblue": (0.482353,0.407843,0.933333),
+"mediumspringgreen": (0,0.980392,0.603922),
+"mediumturquoise": (0.282353,0.819608,0.8),
+"mediumvioletred": (0.780392,0.0823529,0.521569),
+"midnightblue": (0.0980392,0.0980392,0.439216),
+"mintcream": (0.960784,1,0.980392),
+"mistyrose": (1,0.894118,0.882353),
+"moccasin": (1,0.894118,0.709804),
+"navajowhite": (1,0.870588,0.678431),
+"navy": (0,0,0.501961),
+"oldlace": (0.992157,0.960784,0.901961),
+"olive": (0.501961,0.501961,0),
+"olivedrab": (0.419608,0.556863,0.137255),
+"orange": (1,0.647059,0),
+"orangered": (1,0.270588,0),
+"orchid": (0.854902,0.439216,0.839216),
+"palegoldenrod": (0.933333,0.909804,0.666667),
+"palegreen": (0.596078,0.984314,0.596078),
+"paleturquoise": (0.686275,0.933333,0.933333),
+"palevioletred": (0.858824,0.439216,0.576471),
+"papayawhip": (1,0.937255,0.835294),
+"peachpuff": (1,0.854902,0.72549),
+"peru": (0.803922,0.521569,0.247059),
+"pink": (1,0.752941,0.796078),
+"plum": (0.866667,0.627451,0.866667),
+"powderblue": (0.690196,0.878431,0.901961),
+"purple": (0.501961,0,0.501961),
+"red": (1,0,0),
+"rosybrown": (0.737255,0.560784,0.560784),
+"royalblue": (0.254902,0.411765,0.882353),
+"saddlebrown": (0.545098,0.270588,0.0745098),
+"salmon": (0.980392,0.501961,0.447059),
+"sandybrown": (0.956863,0.643137,0.376471),
+"seagreen": (0.180392,0.545098,0.341176),
+"seashell": (1,0.960784,0.933333),
+"sienna": (0.627451,0.321569,0.176471),
+"silver": (0.752941,0.752941,0.752941),
+"skyblue": (0.529412,0.807843,0.921569),
+"slateblue": (0.415686,0.352941,0.803922),
+"slategray": (0.439216,0.501961,0.564706),
+"slategrey": (0.439216,0.501961,0.564706),
+"snow": (1,0.980392,0.980392),
+"springgreen": (0,1,0.498039),
+"steelblue": (0.27451,0.509804,0.705882),
+"tan": (0.823529,0.705882,0.54902),
+"teal": (0,0.501961,0.501961),
+"thistle": (0.847059,0.74902,0.847059),
+"tomato": (1,0.388235,0.278431),
+"turquoise": (0.25098,0.878431,0.815686),
+"violet": (0.933333,0.509804,0.933333),
+"wheat": (0.960784,0.870588,0.701961),
+"white": (1,1,1),
+"whitesmoke": (0.960784,0.960784,0.960784),
+"yellow": (1,1,0),
+"yellowgreen": (0.603922,0.803922,0.196078),
+}
+
+def _tokenize_path(pathdef):
+    for x in COMMAND_RE.split(pathdef):
+        if x in COMMANDS:
+            yield x
+        for token in FLOAT_RE.findall(x):
+            yield token
+
+def applyMatrix(matrix, z):
+    return complex(z.real * matrix[0] + z.imag * matrix[1] + matrix[2], 
+             z.real * matrix[3] + z.imag * matrix[4] + matrix[5] )
+             
+def matrixMultiply(matrix1, matrix2):
+    if matrix1 is None:
+        return matrix2
+    elif matrix2 is None:
+        return matrix1
+        
+    m1 = [matrix1[0:3], matrix1[3:6] ] # don't need last row
+    m2 = [matrix2[0:3], matrix2[3:6], [0,0,1]]
+
+    out = []
+    
+    for i in range(2):
+        for j in range(3):
+            out.append( sum(m1[i][k]*m2[k][j] for k in range(3)) )
+            
+    return out
+
+def parse_path(pathdef, current_pos=0j, matrix = None, svgState=None):
+    if matrix is None:
+        scaler=lambda z : z
+    else:
+        scaler=lambda z : applyMatrix(matrix, z)
+    if svgState is None:
+        svgState = path.SVGState()
+
+    # In the SVG specs, initial movetos are absolute, even if
+    # specified as 'm'. This is the default behavior here as well.
+    # But if you pass in a current_pos variable, the initial moveto
+    # will be relative to that current_pos. This is useful.
+    elements = list(_tokenize_path(pathdef))
+    # Reverse for easy use of .pop()
+    elements.reverse()
+
+    segments = path.Path(svgState = svgState)
+    start_pos = None
+    command = None
+
+    while elements:
+
+        if elements[-1] in COMMANDS:
+            # New command.
+            last_command = command  # Used by S and T
+            command = elements.pop()
+            absolute = command in UPPERCASE
+            command = command.upper()
+        else:
+            # If this element starts with numbers, it is an implicit command
+            # and we don't change the command. Check that it's allowed:
+            if command is None:
+                raise ValueError("Unallowed implicit command in %s, position %s" % (
+                    pathdef, len(pathdef.split()) - len(elements)))
+            last_command = command  # Used by S and T
+
+        if command == 'M':
+            # Moveto command.
+            x = elements.pop()
+            y = elements.pop()
+            pos = float(x) + float(y) * 1j
+            if absolute:
+                current_pos = pos
+            else:
+                current_pos += pos
+
+            # when M is called, reset start_pos
+            # This behavior of Z is defined in svg spec:
+            # http://www.w3.org/TR/SVG/paths.html#PathDataClosePathCommand
+            start_pos = current_pos
+
+            # Implicit moveto commands are treated as lineto commands.
+            # So we set command to lineto here, in case there are
+            # further implicit commands after this moveto.
+            command = 'L'
+
+        elif command == 'Z':
+            # Close path
+            if current_pos != start_pos:
+                segments.append(path.Line(scaler(current_pos), scaler(start_pos)))
+            if len(segments):
+                segments.closed = True
+            current_pos = start_pos
+            start_pos = None
+            command = None  # You can't have implicit commands after closing.
+
+        elif command == 'L':
+            x = elements.pop()
+            y = elements.pop()
+            pos = float(x) + float(y) * 1j
+            if not absolute:
+                pos += current_pos
+            segments.append(path.Line(scaler(current_pos), scaler(pos)))
+            current_pos = pos
+
+        elif command == 'H':
+            x = elements.pop()
+            pos = float(x) + current_pos.imag * 1j
+            if not absolute:
+                pos += current_pos.real
+            segments.append(path.Line(scaler(current_pos), scaler(pos)))
+            current_pos = pos
+
+        elif command == 'V':
+            y = elements.pop()
+            pos = current_pos.real + float(y) * 1j
+            if not absolute:
+                pos += current_pos.imag * 1j
+            segments.append(path.Line(scaler(current_pos), scaler(pos)))
+            current_pos = pos
+
+        elif command == 'C':
+            control1 = float(elements.pop()) + float(elements.pop()) * 1j
+            control2 = float(elements.pop()) + float(elements.pop()) * 1j
+            end = float(elements.pop()) + float(elements.pop()) * 1j
+
+            if not absolute:
+                control1 += current_pos
+                control2 += current_pos
+                end += current_pos
+
+            segments.append(path.CubicBezier(scaler(current_pos), scaler(control1), scaler(control2), scaler(end)))
+            current_pos = end
+
+        elif command == 'S':
+            # Smooth curve. First control point is the "reflection" of
+            # the second control point in the previous path.
+
+            if last_command not in 'CS':
+                # If there is no previous command or if the previous command
+                # was not an C, c, S or s, assume the first control point is
+                # coincident with the current point.
+                control1 = scaler(current_pos)
+            else:
+                # The first control point is assumed to be the reflection of
+                # the second control point on the previous command relative
+                # to the current point.
+                control1 = 2 * scaler(current_pos) - segments[-1].control2
+
+            control2 = float(elements.pop()) + float(elements.pop()) * 1j
+            end = float(elements.pop()) + float(elements.pop()) * 1j
+
+            if not absolute:
+                control2 += current_pos
+                end += current_pos
+
+            segments.append(path.CubicBezier(scaler(current_pos), control1, scaler(control2), scaler(end)))
+            current_pos = end
+
+        elif command == 'Q':
+            control = float(elements.pop()) + float(elements.pop()) * 1j
+            end = float(elements.pop()) + float(elements.pop()) * 1j
+
+            if not absolute:
+                control += current_pos
+                end += current_pos
+
+            segments.append(path.QuadraticBezier(scaler(current_pos), scaler(control), scaler(end)))
+            current_pos = end
+
+        elif command == 'T':
+            # Smooth curve. Control point is the "reflection" of
+            # the second control point in the previous path.
+
+            if last_command not in 'QT':
+                # If there is no previous command or if the previous command
+                # was not an Q, q, T or t, assume the first control point is
+                # coincident with the current point.
+                control = scaler(current_pos)
+            else:
+                # The control point is assumed to be the reflection of
+                # the control point on the previous command relative
+                # to the current point.
+                control = 2 * scaler(current_pos) - segments[-1].control
+
+            end = float(elements.pop()) + float(elements.pop()) * 1j
+
+            if not absolute:
+                end += current_pos
+
+            segments.append(path.QuadraticBezier(scaler(current_pos), control, scaler(end)))
+            current_pos = end
+
+        elif command == 'A':
+            radius = float(elements.pop()) + float(elements.pop()) * 1j
+            rotation = float(elements.pop())
+            arc = float(elements.pop())
+            sweep = float(elements.pop())
+            end = float(elements.pop()) + float(elements.pop()) * 1j
+           
+            if not absolute:
+                end += current_pos
+
+            segments.append(path.Arc(current_pos, radius, rotation, arc, sweep, end, scaler))
+            current_pos = end
+
+    return segments
+
+def path_from_ellipse(x, y, rx, ry, matrix, state):
+    arc = "M %.9f %.9f " % (x-rx,y)
+    arc += "A %.9f %.9f 0 0 1 %.9f %.9f " % (rx, ry, x+rx,y) 
+    arc += "A %.9f %.9f 0 0 1 %.9f %.9f" % (rx, ry, x-rx,y) 
+    return parse_path(arc, matrix=matrix, svgState=state)
+
+def path_from_rect(x,y,w,h,rx,ry, matrix,state):
+    if not rx and not ry:
+        rect = "M %.9f %.9f h %.9f v %.9f h %.9f Z" % (x,y,w,h,-w)
+    else:
+        if rx is None:
+            rx = ry
+        elif ry is None:
+            ry = rx
+        rect = "M %.9f %.9f h %.9f " % (x+rx,y,w-2*rx)
+        rect += "a %.9f %.9f 0 0 1 %.9f %.9f " % (rx, ry, rx, ry)
+        rect += "v %.9f " % (h-2*ry)
+        rect += "a %.9f %.9f 0 0 1 %.9f %.9f " % (rx, ry, -rx, ry)
+        rect += "h %.9f " % -(w-2*rx)
+        rect += "a %.9f %.9f 0 0 1 %.9f %.9f " % (rx, ry, -rx, -ry)
+        rect += "v %.9f " % -(h-2*ry)
+        rect += "a %.9f %.9f 0 0 1 %.9f %.9f Z" % (rx, ry, rx, -ry)
+    return parse_path(rect, matrix=matrix, svgState=state)
+    
+def sizeFromString(text):
+    """
+    Returns size in mm, if possible.
+    """
+    text = re.sub(r'\s',r'', text)
+    try:
+        return float(text)*25.4/96 # px
+    except:
+        if text[-1] == '%':
+            return float(text[:-1]) # NOT mm
+        units = text[-2:].lower()
+        x = float(text[:-2])
+        convert = { 'mm':1, 'cm':10, 'in':25.4, 'px':25.4/96, 'pt':25.4/72, 'pc':12*25.4/72 }
+        try:
+            return x * convert[units]
+        except:
+            return x # NOT mm
+
+def rgbFromColor(colorName):
+    colorName = colorName.strip().lower()
+    if colorName == 'none':
+        return None
+    cmd = re.split(r'[\s(),]+', colorName)
+    if cmd[0] == 'rgb':
+        colors = cmd[1:4]
+        outColor = []
+        for c in colors:
+            if c.endswith('%'):
+                outColor.append(float(c[:-1]) / 100.)
+            else:
+                outColor.append(float(c) / 255.)
+        return tuple(outColor)
+    elif colorName.startswith('#'):
+        if len(colorName) == 4:
+            return (int(colorName[1],16)/15., int(colorName[2],16)/15., int(colorName[3],16)/15.)
+        else:
+            return (int(colorName[1:3],16)/255., int(colorName[3:5],16)/255., int(colorName[5:7],16)/255.)
+    else:
+        return SVG_COLORS[colorName]        
+        
+        
+def getPathsFromSVG(svg):
+    def updateStateCommand(state,cmd,arg):
+        if cmd == 'fill':
+            state.fill = rgbFromColor(arg)
+        elif cmd == 'fill-opacity':
+            state.fillOpacity = float(arg)
+        elif cmd == 'fill-rule':
+            state.fillRule = arg
+#            if state.fill is None:
+#                state.fill = (0.,0.,0.)
+        elif cmd == 'stroke':
+            state.stroke = rgbFromColor(arg)
+        elif cmd == 'stroke-opacity':
+            state.strokeOpacity = rgbFromColor(arg)
+        elif cmd == 'stroke-width':
+            state.strokeWidth = float(arg)
+        elif cmd == 'vector-effect':
+            state.strokeWidthScaling = 'non-scaling-stroke' not in cmd
+            # todo better scaling for non-uniform cases?
+    
+    def updateState(tree,state,matrix):
+        state = state.clone()
+        try:
+            style = re.sub(r'\s',r'', tree.attrib['style']).lower()
+            for item in style.split(';'):
+                cmd,arg = item.split(':')[:2]
+                updateStateCommand(state,cmd,arg)
+        except:
+            pass
+            
+        for item in tree.attrib:
+            try:
+                updateStateCommand(state,item,tree.attrib[item])
+            except:
+                pass
+                
+        if state.strokeWidth and state.strokeWidthScaling:
+            # this won't work great for non-uniform scaling
+            h = abs(applyMatrix(matrix, complex(0,state.strokeWidth)) - applyMatrix(matrix, 0j))
+            w = abs(applyMatrix(matrix, complex(state.strokeWidth,0)) - applyMatrix(matrix, 0j))
+            state.strokeWidth = (h+w)/2
+        return state
+        
+    def reorder(a,b,c,d,e,f):
+        return [a,c,e, b,d,f]            
+        
+    def updateMatrix(tree, matrix):
+        try:
+            transformList = re.split(r'\)[\s,]+', tree.attrib['transform'].strip().lower())
+        except KeyError:
+            return matrix
+            
+        for transform in transformList:
+            cmd = re.split(r'[,()\s]+', transform)
+            
+            updateMatrix = None
+            
+            if cmd[0] == 'matrix':
+                updateMatrix = reorder(*list(map(float, cmd[1:7])))
+            elif cmd[0] == 'translate':
+                x = float(cmd[1])
+                if len(cmd) >= 3 and cmd[2] != '':
+                    y = float(cmd[2])
+                else:
+                    y = 0
+                updateMatrix = reorder(1,0,0,1,x,y)
+            elif cmd[0] == 'scale':
+                x = float(cmd[1])
+                if len(cmd) >= 3 and cmd[2] != '':
+                    y = float(cmd[2])
+                else:
+                    y = x
+                updateMatrix = reorder(x,0,0, y,0,0)
+            elif cmd[0] == 'rotate':
+                theta = float(cmd[1]) * math.pi / 180.
+                c = math.cos(theta)
+                s = math.sin(theta)
+                updateMatrix = [c, -s, 0,  s, c, 0]
+                if len(cmd) >= 4 and cmd[2] != '':
+                    x = float(cmd[2])
+                    y = float(cmd[3])
+                    updateMatrix = matrixMultiply(updateMatrix, [1,0,-x, 0,1,-y])
+                    updateMatrix = matrixMultiply([1,0,x, 0,1,y], updateMatrix)
+            elif cmd[0] == 'skewX':
+                theta = float(cmd[1]) * math.pi / 180.
+                updateMatrix = [1, math.tan(theta), 0,  0,1,0]
+            elif cmd[0] == 'skewY':
+                theta = float(cmd[1]) * math.pi / 180.
+                updateMatrix = [1,0,0, math.tan(theta),1,0]
+                
+            matrix = matrixMultiply(matrix, updateMatrix)
+            
+        return matrix
+        
+    def updateStateAndMatrix(tree,state,matrix):
+        matrix = updateMatrix(tree,matrix)
+        return updateState(tree,state,matrix),matrix
+        
+    def getPaths(paths, matrix, tree, state, savedElements):
+        def getFloat(attribute,default=0.):
+            try:
+                return float(tree.attrib[attribute].strip())
+            except KeyError:
+                return default
+
+        tag = re.sub(r'.*}', '', tree.tag).lower()
+        try:
+            savedElements[tree.attrib['id']] = tree
+        except KeyError:
+            pass
+            
+        state, matrix = updateStateAndMatrix(tree, state, matrix)
+        if tag == 'path':
+            path = parse_path(tree.attrib['d'], matrix=matrix, svgState=state)
+            if len(path):
+                paths.append(path)
+        elif tag == 'circle':
+            path = path_from_ellipse(getFloat('cx'), getFloat('cy'), getFloat('r'), getFloat('r'), matrix, state)
+            paths.append(path)
+        elif tag == 'ellipse':
+            path = path_from_ellipse(getFloat('cx'), getFloat('cy'), getFloat('rx'), getFloat('ry'), matrix, state)
+            paths.append(path)
+        elif tag == 'line':
+            x1 = getFloat('x1')
+            y1 = getFloat('y1')
+            x2 = getFloat('x2')
+            y2 = getFloat('y2')
+            p = 'M %.9f %.9f L %.9f %.9f' % (x1,y1,x2,y2)
+            path = parse_path(p, matrix=matrix, svgState=state)
+            paths.append(path)
+        elif tag == 'polygon':
+            points = re.split(r'[\s,]+', tree.attrib['points'].strip())
+            p = ' '.join(['M', points[0], points[1], 'L'] + points[2:] + ['Z'])
+            path = parse_path(p, matrix=matrix, svgState=state)
+            paths.append(path)
+        elif tag == 'polyline':
+            points = re.split(r'[\s,]+', tree.attrib['points'].strip())
+            p = ' '.join(['M', points[0], points[1], 'L'] + points[2:])
+            path = parse_path(p, matrix=matrix, svgState=state)
+            paths.append(path)
+        elif tag == 'rect':
+            x = getFloat('x')
+            y = getFloat('y')
+            w = getFloat('width')
+            h = getFloat('height')
+            rx = getFloat('rx',default=None)
+            ry = getFloat('ry',default=None)
+            path = path_from_rect(x,y,w,h,rx,ry, matrix,state)
+            paths.append(path)
+        elif tag == 'g' or tag == 'svg':
+            for child in tree:
+                getPaths(paths, matrix, child, state, savedElements)
+        elif tag == 'use':
+            try:
+                link = None
+                for tag in tree.attrib:
+                    if tag.strip().lower().endswith("}href"):
+                        link = tree.attrib[tag]
+                        break
+                if link is None or link[0] != '#':
+                    raise KeyError
+                source = savedElements[link[1:]]
+                x = 0
+                y = 0
+                try:
+                    x = float(tree.attrib['x'])
+                except:
+                    pass
+                try:
+                    y = float(tree.attrib['y'])
+                except:
+                    pass
+                # TODO: handle width and height? (Inkscape does not)
+                matrix = matrixMultiply(matrix, reorder(1,0,0,1,x,y))
+                getPaths(paths, matrix, source, state, dict(savedElements))
+            except KeyError:
+                pass
+
+    def scale(width, height, viewBox, z):
+        x = (z.real - viewBox[0]) / (viewBox[2] - viewBox[0]) * width
+        y = (viewBox[3]-z.imag) / (viewBox[3] - viewBox[1]) * height
+        return complex(x,y)
+        
+    paths = []
+
+    try:
+        width = sizeFromString(svg.attrib['width'].strip())
+    except KeyError:
+        width = None
+    try:
+        height = sizeFromString(svg.attrib['height'].strip())
+    except KeyError:
+        height = None
+    
+    try:
+        viewBox = list(map(float, re.split(r'[\s,]+', svg.attrib['viewBox'].strip())))
+    except KeyError:
+        if width is None or height is None:
+            raise KeyError
+        viewBox = [0, 0, width*96/25.4, height*96/25.4]
+        
+    if width is None:
+        width = viewBox[2] * 25.4/96
+    
+    if height is None:
+        height = viewBox[3] * 25.4/96
+        
+    viewBoxWidth = viewBox[2]
+    viewBoxHeight = viewBox[3]
+    
+    viewBox[2] += viewBox[0]
+    viewBox[3] += viewBox[1]
+    
+    try:
+        preserve = svg.attrib['preserveAspectRatio'].strip().lower().split()
+        if len(preserve[0]) != 8:
+            raise KeyError
+        if len(preserve)>=2 and preserve[1] == 'slice':
+            if viewBoxWidth/viewBoxHeight > width/height:
+                # viewbox is wider than viewport, so scale by height to ensure
+                # viewbox covers the viewport
+                rescale = height / viewBoxHeight
+            else:
+                rescale = width / viewBoxWidth
+        else:
+            if viewBoxWidth/viewBoxHeight > width/height:
+                # viewbox is wider than viewport, so scale by width to ensure
+                # viewport covers the viewbox
+                rescale = width / viewBoxWidth
+            else:
+                rescale = height / viewBoxHeight
+        matrix = [rescale, 0, 0,    
+                  0, rescale, 0];
+
+        if preserve[0][0:4] == 'xmin':
+            # viewBox[0] to 0
+            matrix[2] = -viewBox[0] * rescale
+        elif preserve[0][0:4] == 'xmid':
+            # viewBox[0] to width/2
+            matrix[2] = -viewBox[0] * rescale + width/2
+        else: # preserve[0][0:4] == 'xmax':
+            # viewBox[0] to width
+            matrix[2] = -viewBox[0] * rescale + width
+        
+        if preserve[0][4:8] == 'ymin':
+            # viewBox[1] to 0
+            matrix[5] = -viewBox[1] * rescale
+        elif preserve[0][4:8] == 'ymid':
+            # viewBox[0] to width/2
+            matrix[5] = -viewBox[1] * rescale + height/2
+        else: # preserve[0][4:8] == 'xmax':
+            # viewBox[0] to width
+            matrix[5] = -viewBox[1] * rescale + height
+    except:
+        matrix = [ width/viewBoxWidth, 0, -viewBox[0]* width/viewBoxWidth,  
+                   0, -height/viewBoxHeight, viewBox[3]*height/viewBoxHeight ]
+        
+    getPaths(paths, matrix, svg, path.SVGState(), {})
+
+    return ( paths, applyMatrix(matrix, complex(viewBox[0], viewBox[1])), 
+                applyMatrix(matrix, complex(viewBox[2], viewBox[3])) )
+
+def getPathsFromSVGFile(filename):
+    return getPathsFromSVG(ET.parse(filename).getroot())
+    

extensions/fablabchemnitz/cookie_cutter/svgpath/path.py

@@ -0,0 +1,646 @@
+from __future__ import division
+from math import sqrt, cos, sin, acos, degrees, radians, log
+from collections.abc import MutableSequence
+
+# This file contains classes for the different types of SVG path segments as
+# well as a Path object that contains a sequence of path segments.
+
+MIN_DEPTH = 5
+ERROR = 1e-12
+
+def segment_length(curve, start, end, start_point, end_point, error, min_depth, depth):
+    """Recursively approximates the length by straight lines"""
+    mid = (start + end) / 2
+    mid_point = curve.point(mid)
+    length = abs(end_point - start_point)
+    first_half = abs(mid_point - start_point)
+    second_half = abs(end_point - mid_point)
+
+    length2 = first_half + second_half
+    if (length2 - length > error) or (depth < min_depth):
+        # Calculate the length of each segment:
+        depth += 1
+        return (segment_length(curve, start, mid, start_point, mid_point,
+                               error, min_depth, depth) +
+                segment_length(curve, mid, end, mid_point, end_point,
+                               error, min_depth, depth))
+    # This is accurate enough.
+    return length2
+
+def approximate(path, start, end, start_point, end_point, max_error, depth, max_depth):
+    if depth >= max_depth:
+        return [start_point, end_point]
+    actual_length = path.measure(start, end, error=max_error/4)
+    linear_length = abs(end_point - start_point)
+    # Worst case deviation given a fixed linear_length and actual_length would probably be 
+    # a symmetric tent shape (I haven't proved it -- TODO).
+    deviationSquared = (actual_length/2)**2 - (linear_length/2)**2
+    if deviationSquared <= max_error ** 2:
+        return [start_point, end_point]
+    else:
+        mid = (start+end)/2.
+        mid_point = path.point(mid)
+        return ( approximate(path, start, mid, start_point, mid_point, max_error, depth+1, max_depth)[:-1] + 
+                    approximate(path, mid, end, mid_point, end_point, max_error, depth+1, max_depth) )
+                    
+def removeCollinear(points, error, pointsToKeep=set()):
+    out = []
+    
+    lengths = [0]
+
+    for i in range(1,len(points)):
+        lengths.append(lengths[-1] + abs(points[i]-points[i-1]))
+        
+    def length(a,b):
+        return lengths[b] - lengths[a]
+    
+    i = 0
+    
+    while i < len(points):
+        j = len(points) - 1
+        while i < j:
+            deviationSquared = (length(i, j)/2)**2 - (abs(points[j]-points[i])/2)**2
+            if deviationSquared <= error ** 2 and set(range(i+1,j)).isdisjoint(pointsToKeep):
+                out.append(points[i])
+                i = j
+                break
+            j -= 1
+        out.append(points[j])
+        i += 1
+
+    return out
+
+class Segment(object):
+    def __init__(self, start, end):
+        self.start = start
+        self.end = end
+        
+    def measure(self, start, end, error=ERROR, min_depth=MIN_DEPTH):
+        return Path(self).measure(start, end, error=error, min_depth=min_depth)
+
+    def getApproximatePoints(self, error=0.001, max_depth=32):
+        points = approximate(self, 0., 1., self.point(0.), self.point(1.), error, 0, max_depth)
+        return points
+
+class Line(Segment):
+    def __init__(self, start, end):
+        super(Line, self).__init__(start,end)
+
+    def __repr__(self):
+        return 'Line(start=%s, end=%s)' % (self.start, self.end)
+
+    def __eq__(self, other):
+        if not isinstance(other, Line):
+            return NotImplemented
+        return self.start == other.start and self.end == other.end
+
+    def __ne__(self, other):
+        if not isinstance(other, Line):
+            return NotImplemented
+        return not self == other
+        
+    def getApproximatePoints(self, error=0.001, max_depth=32):
+        return [self.start, self.end]
+
+    def point(self, pos):
+        if pos == 0.:
+            return self.start
+        elif pos == 1.:
+            return self.end
+        distance = self.end - self.start
+        return self.start + distance * pos
+
+    def length(self, error=None, min_depth=None):
+        distance = (self.end - self.start)
+        return sqrt(distance.real ** 2 + distance.imag ** 2)
+
+
+class CubicBezier(Segment):
+    def __init__(self, start, control1, control2, end):
+        super(CubicBezier, self).__init__(start,end)
+        self.control1 = control1
+        self.control2 = control2
+
+    def __repr__(self):
+        return 'CubicBezier(start=%s, control1=%s, control2=%s, end=%s)' % (
+               self.start, self.control1, self.control2, self.end)
+
+    def __eq__(self, other):
+        if not isinstance(other, CubicBezier):
+            return NotImplemented
+        return self.start == other.start and self.end == other.end and \
+               self.control1 == other.control1 and self.control2 == other.control2
+
+    def __ne__(self, other):
+        if not isinstance(other, CubicBezier):
+            return NotImplemented
+        return not self == other
+
+    def is_smooth_from(self, previous):
+        """Checks if this segment would be a smooth segment following the previous"""
+        if isinstance(previous, CubicBezier):
+            return (self.start == previous.end and
+                    (self.control1 - self.start) == (previous.end - previous.control2))
+        else:
+            return self.control1 == self.start
+
+    def point(self, pos):
+        """Calculate the x,y position at a certain position of the path"""
+        if pos == 0.:
+            return self.start
+        elif pos == 1.:
+            return self.end
+        return ((1 - pos) ** 3 * self.start) + \
+               (3 * (1 - pos) ** 2 * pos * self.control1) + \
+               (3 * (1 - pos) * pos ** 2 * self.control2) + \
+               (pos ** 3 * self.end)
+
+    def length(self, error=ERROR, min_depth=MIN_DEPTH):
+        """Calculate the length of the path up to a certain position"""
+        start_point = self.point(0)
+        end_point = self.point(1)
+        return segment_length(self, 0, 1, start_point, end_point, error, min_depth, 0)
+
+
+class QuadraticBezier(Segment):
+    def __init__(self, start, control, end):
+        super(QuadraticBezier, self).__init__(start,end)
+        self.control = control
+
+    def __repr__(self):
+        return 'QuadraticBezier(start=%s, control=%s, end=%s)' % (
+               self.start, self.control, self.end)
+
+    def __eq__(self, other):
+        if not isinstance(other, QuadraticBezier):
+            return NotImplemented
+        return self.start == other.start and self.end == other.end and \
+               self.control == other.control
+
+    def __ne__(self, other):
+        if not isinstance(other, QuadraticBezier):
+            return NotImplemented
+        return not self == other
+
+    def is_smooth_from(self, previous):
+        """Checks if this segment would be a smooth segment following the previous"""
+        if isinstance(previous, QuadraticBezier):
+            return (self.start == previous.end and
+                    (self.control - self.start) == (previous.end - previous.control))
+        else:
+            return self.control == self.start
+
+    def point(self, pos):
+        if pos == 0.:
+            return self.start
+        elif pos == 1.:
+            return self.end
+        return (1 - pos) ** 2 * self.start + 2 * (1 - pos) * pos * self.control + \
+               pos ** 2 * self.end
+
+    def length(self, error=None, min_depth=None):
+        a = self.start - 2*self.control + self.end
+        b = 2*(self.control - self.start)
+        a_dot_b = a.real*b.real + a.imag*b.imag
+
+        if abs(a) < 1e-12:
+            s = abs(b)
+        elif abs(a_dot_b + abs(a)*abs(b)) < 1e-12:
+            k = abs(b)/abs(a)
+            if k >= 2:
+                s = abs(b) - abs(a)
+            else:
+                s = abs(a)*(k**2/2 - k + 1)
+        else:
+            # For an explanation of this case, see
+            # http://www.malczak.info/blog/quadratic-bezier-curve-length/
+            A = 4 * (a.real ** 2 + a.imag ** 2)
+            B = 4 * (a.real * b.real + a.imag * b.imag)
+            C = b.real ** 2 + b.imag ** 2
+
+            Sabc = 2 * sqrt(A + B + C)
+            A2 = sqrt(A)
+            A32 = 2 * A * A2
+            C2 = 2 * sqrt(C)
+            BA = B / A2
+
+            s = (A32 * Sabc + A2 * B * (Sabc - C2) + (4 * C * A - B ** 2) *
+                    log((2 * A2 + BA + Sabc) / (BA + C2))) / (4 * A32)
+        return s
+
+class Arc(Segment):
+    def __init__(self, start, radius, rotation, arc, sweep, end, scaler=lambda z:z):
+        """radius is complex, rotation is in degrees,
+           large and sweep are 1 or 0 (True/False also work)"""
+
+        super(Arc, self).__init__(scaler(start),scaler(end))
+        self.start0 = start
+        self.end0 = end
+        self.radius = radius
+        self.rotation = rotation
+        self.arc = bool(arc)
+        self.sweep = bool(sweep)
+        self.scaler = scaler
+
+        self._parameterize()
+        
+    def __repr__(self):
+        return 'Arc(start0=%s, radius=%s, rotation=%s, arc=%s, sweep=%s, end0=%s, scaler=%s)' % (
+               self.start0, self.radius, self.rotation, self.arc, self.sweep, self.end0, self.scaler)
+
+    def __eq__(self, other):
+        if not isinstance(other, Arc):
+            return NotImplemented
+        return self.start == other.start and self.end == other.end and \
+               self.radius == other.radius and self.rotation == other.rotation and \
+               self.arc == other.arc and self.sweep == other.sweep
+
+    def __ne__(self, other):
+        if not isinstance(other, Arc):
+            return NotImplemented
+        return not self == other
+
+    def _parameterize(self):
+        # Conversion from endpoint to center parameterization
+        # http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
+
+        cosr = cos(radians(self.rotation))
+        sinr = sin(radians(self.rotation))
+        dx = (self.start0.real - self.end0.real) / 2
+        dy = (self.start0.imag - self.end0.imag) / 2
+        x1prim = cosr * dx + sinr * dy
+        x1prim_sq = x1prim * x1prim
+        y1prim = -sinr * dx + cosr * dy
+        y1prim_sq = y1prim * y1prim
+
+        rx = self.radius.real
+        rx_sq = rx * rx
+        ry = self.radius.imag
+        ry_sq = ry * ry
+
+        # Correct out of range radii
+        radius_check = (x1prim_sq / rx_sq) + (y1prim_sq / ry_sq)
+        if radius_check > 1:
+            rx *= sqrt(radius_check)
+            ry *= sqrt(radius_check)
+            rx_sq = rx * rx
+            ry_sq = ry * ry
+
+        t1 = rx_sq * y1prim_sq
+        t2 = ry_sq * x1prim_sq
+        c = sqrt(abs((rx_sq * ry_sq - t1 - t2) / (t1 + t2)))
+
+        if self.arc == self.sweep:
+            c = -c
+        cxprim = c * rx * y1prim / ry
+        cyprim = -c * ry * x1prim / rx
+
+        self.center = complex((cosr * cxprim - sinr * cyprim) +
+                              ((self.start0.real + self.end0.real) / 2),
+                              (sinr * cxprim + cosr * cyprim) +
+                              ((self.start0.imag + self.end0.imag) / 2))
+
+        ux = (x1prim - cxprim) / rx
+        uy = (y1prim - cyprim) / ry
+        vx = (-x1prim - cxprim) / rx
+        vy = (-y1prim - cyprim) / ry
+        n = sqrt(ux * ux + uy * uy)
+        p = ux
+        theta = degrees(acos(p / n))
+        if uy < 0:
+            theta = -theta
+        self.theta = theta % 360
+
+        n = sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy))
+        p = ux * vx + uy * vy
+        d = p/n
+        # In certain cases the above calculation can through inaccuracies
+        # become just slightly out of range, f ex -1.0000000000000002.
+        if d > 1.0:
+            d = 1.0
+        elif d < -1.0:
+            d = -1.0
+        delta = degrees(acos(d))
+        if (ux * vy - uy * vx) < 0:
+            delta = -delta
+        self.delta = delta % 360
+        if not self.sweep:
+            self.delta -= 360
+            
+    def point(self, pos):
+        if pos == 0.:
+            return self.start
+        elif pos == 1.:
+            return self.end
+        angle = radians(self.theta + (self.delta * pos))
+        cosr = cos(radians(self.rotation))
+        sinr = sin(radians(self.rotation))
+
+        x = (cosr * cos(angle) * self.radius.real - sinr * sin(angle) *
+             self.radius.imag + self.center.real)
+        y = (sinr * cos(angle) * self.radius.real + cosr * sin(angle) *
+             self.radius.imag + self.center.imag)
+        return self.scaler(complex(x, y))
+
+    def length(self, error=ERROR, min_depth=MIN_DEPTH):
+        """The length of an elliptical arc segment requires numerical
+        integration, and in that case it's simpler to just do a geometric
+        approximation, as for cubic bezier curves.
+        """
+        start_point = self.point(0)
+        end_point = self.point(1)
+        return segment_length(self, 0, 1, start_point, end_point, error, min_depth, 0)
+
+class SVGState(object):
+    def __init__(self, fill=(0.,0.,0.), fillOpacity=None, fillRule='nonzero', stroke=None, strokeOpacity=None, strokeWidth=0.1, strokeWidthScaling=True):
+        self.fill = fill
+        self.fillOpacity = fillOpacity
+        self.fillRule = fillRule
+        self.stroke = stroke
+        self.strokeOpacity = strokeOpacity
+        self.strokeWidth = strokeWidth
+        self.strokeWidthScaling = strokeWidthScaling
+                
+    def clone(self):
+        return SVGState(fill=self.fill, fillOpacity=self.fillOpacity, fillRule=self.fillRule, stroke=self.stroke, strokeOpacity=self.strokeOpacity,
+                strokeWidth=self.strokeWidth, strokeWidthScaling=self.strokeWidthScaling)
+        
+class Path(MutableSequence):
+    """A Path is a sequence of path segments"""
+
+    # Put it here, so there is a default if unpickled.
+    _closed = False
+
+    def __init__(self, *segments, **kw):
+        self._segments = list(segments)
+        self._length = None
+        self._lengths = None
+        if 'closed' in kw:
+            self.closed = kw['closed']
+        if 'svgState' in kw:
+            self.svgState = kw['svgState']
+        else:
+            self.svgState = SVGState()
+
+    def __getitem__(self, index):
+        return self._segments[index]
+
+    def __setitem__(self, index, value):
+        self._segments[index] = value
+        self._length = None
+
+    def __delitem__(self, index):
+        del self._segments[index]
+        self._length = None
+
+    def insert(self, index, value):
+        self._segments.insert(index, value)
+        self._length = None
+
+    def reverse(self):
+        # Reversing the order of a path would require reversing each element
+        # as well. That's not implemented.
+        raise NotImplementedError
+
+    def __len__(self):
+        return len(self._segments)
+
+    def __repr__(self):
+        return 'Path(%s, closed=%s)' % (
+            ', '.join(repr(x) for x in self._segments), self.closed)
+
+    def __eq__(self, other):
+        if not isinstance(other, Path):
+            return NotImplemented
+        if len(self) != len(other):
+            return False
+        for s, o in zip(self._segments, other._segments):
+            if not s == o:
+                return False
+        return True
+
+    def __ne__(self, other):
+        if not isinstance(other, Path):
+            return NotImplemented
+        return not self == other
+
+    def _calc_lengths(self, error=ERROR, min_depth=MIN_DEPTH):
+    ## TODO: check if error has decreased since last calculation
+        if self._length is not None:
+            return
+
+        lengths = [each.length(error=error, min_depth=min_depth) for each in self._segments]
+        self._length = sum(lengths)
+        self._lengths = [each / (1 if self._length==0. else self._length) for each in lengths]
+
+    def point(self, pos, error=ERROR):
+        # Shortcuts
+        if pos == 0.0:
+            return self._segments[0].point(pos)
+        if pos == 1.0:
+            return self._segments[-1].point(pos)
+
+        self._calc_lengths(error=error)
+        # Find which segment the point we search for is located on:
+        segment_start = 0
+        for index, segment in enumerate(self._segments):
+            segment_end = segment_start + self._lengths[index]
+            if segment_end >= pos:
+                # This is the segment! How far in on the segment is the point?
+                segment_pos = (pos - segment_start) / (segment_end - segment_start)
+                break
+            segment_start = segment_end
+
+        return segment.point(segment_pos)
+
+    def length(self, error=ERROR, min_depth=MIN_DEPTH):
+        self._calc_lengths(error, min_depth)
+        return self._length
+        
+    def measure(self, start, end, error=ERROR, min_depth=MIN_DEPTH):
+        self._calc_lengths(error=error)
+        if start == 0.0 and end == 1.0:
+            return self.length()
+        length = 0
+        segment_start = 0
+        for index, segment in enumerate(self._segments):
+            if end <= segment_start:
+                break
+            segment_end = segment_start + self._lengths[index]
+            if start < segment_end:
+                # this segment intersects the part of the path we want
+                if start <= segment_start and segment_end <= end:
+                    # whole segment is contained in the part of the path
+                    length += self._lengths[index] * self._length
+                else:
+                    if start <= segment_start:
+                        start_in_segment = 0. 
+                    else:
+                        start_in_segment = (start-segment_start)/(segment_end-segment_start)
+                    if segment_end <= end:
+                        end_in_segment = 1.
+                    else:
+                        end_in_segment = (end-segment_start)/(segment_end-segment_start)
+                    segment = self._segments[index]
+                    length += segment_length(segment, start_in_segment, end_in_segment, segment.point(start_in_segment), 
+                                segment.point(end_in_segment), error, MIN_DEPTH, 0)
+            segment_start = segment_end
+        return length
+        
+    def _is_closable(self):
+        """Returns true if the end is on the start of a segment"""
+        try:
+            end = self[-1].end
+        except:
+            return False
+        for segment in self:
+            if segment.start == end:
+                return True
+        return False
+        
+    def breakup(self):
+        paths = []
+        prevEnd = None
+        segments = []
+        for segment in self._segments:
+            if prevEnd is None or segment.point(0.) == prevEnd:
+                segments.append(segment)
+            else:
+                paths.append(Path(*segments, svgState=self.svgState))
+                segments = [segment]
+            prevEnd = segment.point(1.)
+                
+        if len(segments) > 0:
+            paths.append(Path(*segments, svgState=self.svgState))
+            
+        return paths
+        
+    def linearApproximation(self, error=0.001, max_depth=32):
+        closed = False
+        keepSegmentIndex = 0
+        if self.closed:
+            end = self[-1].end
+            for i,segment in enumerate(self):
+                if segment.start == end:
+                    keepSegmentIndex = i
+                    closed = True
+                    break
+        
+        keepSubpathIndex = 0
+        keepPointIndex = 0
+
+        subpaths = []
+        subpath = []
+        prevEnd = None
+        for i,segment in enumerate(self._segments):
+            if prevEnd is None or segment.start == prevEnd:
+                if i == keepSegmentIndex:
+                    keepSubpathIndex = len(subpaths)
+                    keepPointIndex = len(subpath)
+            else:
+                subpaths.append(subpath)
+                subpath = []
+            subpath += segment.getApproximatePoints(error=error/2., max_depth=max_depth)
+            prevEnd = segment.end
+                
+        if len(subpath) > 0:
+            subpaths.append(subpath)
+            
+        linearPath = Path(svgState=self.svgState)
+        
+        for i,subpath in enumerate(subpaths):
+            keep = set((keepPointIndex,)) if i == keepSubpathIndex else set() 
+            special = None
+            if i == keepSubpathIndex:
+                special = subpath[keepPointIndex]
+            points = removeCollinear(subpath, error=error/2., pointsToKeep=keep)
+#            points = subpath
+            
+            for j in range(len(points)-1):
+                linearPath.append(Line(points[j], points[j+1]))
+        
+        linearPath.closed = self.closed and linearPath._is_closable()
+        linearPath.svgState = self.svgState
+
+        return linearPath
+
+    def getApproximateLines(self, error=0.001, max_depth=32):
+        lines = []
+        for subpath in self.breakup():
+            points = subpath.getApproximatePoints(error=error, max_depth=max_depth)
+            for i in range(len(points)-1):
+                lines.append(points[i],points[i+1])
+        return lines
+
+    @property
+    def closed(self):
+        """Checks that the path is closed"""
+        return self._closed and self._is_closable()
+
+    @closed.setter
+    def closed(self, value):
+        value = bool(value)
+        if value and not self._is_closable():
+            raise ValueError("End does not coincide with a segment start.")
+        self._closed = value
+
+    def d(self):
+        if self.closed:
+            segments = self[:-1]
+        else:
+            segments = self[:]
+
+        current_pos = None
+        parts = []
+        previous_segment = None
+        end = self[-1].end
+
+        for segment in segments:
+            start = segment.start
+            # If the start of this segment does not coincide with the end of
+            # the last segment or if this segment is actually the close point
+            # of a closed path, then we should start a new subpath here.
+            if current_pos != start or (self.closed and start == end):
+                parts.append('M {0:G},{1:G}'.format(start.real, start.imag))
+
+            if isinstance(segment, Line):
+                parts.append('L {0:G},{1:G}'.format(
+                    segment.end.real, segment.end.imag)
+                )
+            elif isinstance(segment, CubicBezier):
+                if segment.is_smooth_from(previous_segment):
+                    parts.append('S {0:G},{1:G} {2:G},{3:G}'.format(
+                        segment.control2.real, segment.control2.imag,
+                        segment.end.real, segment.end.imag)
+                    )
+                else:
+                    parts.append('C {0:G},{1:G} {2:G},{3:G} {4:G},{5:G}'.format(
+                        segment.control1.real, segment.control1.imag,
+                        segment.control2.real, segment.control2.imag,
+                        segment.end.real, segment.end.imag)
+                    )
+            elif isinstance(segment, QuadraticBezier):
+                if segment.is_smooth_from(previous_segment):
+                    parts.append('T {0:G},{1:G}'.format(
+                        segment.end.real, segment.end.imag)
+                    )
+                else:
+                    parts.append('Q {0:G},{1:G} {2:G},{3:G}'.format(
+                        segment.control.real, segment.control.imag,
+                        segment.end.real, segment.end.imag)
+                    )
+
+            elif isinstance(segment, Arc):
+                parts.append('A {0:G},{1:G} {2:G} {3:d},{4:d} {5:G},{6:G}'.format(
+                    segment.radius.real, segment.radius.imag, segment.rotation,
+                    int(segment.arc), int(segment.sweep),
+                    segment.end.real, segment.end.imag)
+                )
+            current_pos = segment.end
+            previous_segment = segment
+
+        if self.closed:
+            parts.append('Z')
+
+        return ' '.join(parts)
+        

extensions/fablabchemnitz/cookie_cutter/svgpath/shader.py

@@ -0,0 +1,136 @@
+import math
+from operator import itemgetter
+
+class Shader(object):
+    MODE_EVEN_ODD = 0
+    MODE_NONZERO = 1
+
+    def __init__(self, unshadedThreshold=1., lightestSpacing=3., darkestSpacing=0.5, angle=45, crossHatch=False):
+        self.unshadedThreshold = unshadedThreshold
+        self.lightestSpacing = lightestSpacing
+        self.darkestSpacing = darkestSpacing
+        self.angle = angle
+        self.secondaryAngle = angle + 90
+        self.crossHatch = False
+        
+    def isActive(self):
+        return self.unshadedThreshold > 0.000001
+        
+    def setDrawingDirectionAngle(self, drawingDirectionAngle):
+        self.drawingDirectionAngle = drawingDirectionAngle
+        
+        if drawingDirectionAngle is None:
+            return
+            
+        if 90 < (self.angle - drawingDirectionAngle) % 360 < 270:
+            self.angle = (self.angle + 180) % 360
+        if 90 < (self.secondaryAngle - drawingDirectionAngle) % 360 < 270:
+            self.secondaryAngle = (self.secondaryAngle + 180) % 360
+        
+    def shade(self, polygon, grayscale, avoidOutline=True, mode=None):
+        if mode is None:
+            mode = Shader.MODE_EVEN_ODD
+        if grayscale >= self.unshadedThreshold:
+            return []
+        intensity = (self.unshadedThreshold-grayscale) / float(self.unshadedThreshold)
+        spacing = self.lightestSpacing * (1-intensity) + self.darkestSpacing * intensity
+        lines = Shader.shadePolygon(polygon, self.angle, spacing, avoidOutline=avoidOutline, mode=mode, alternate=(self.drawingDirectionAngle is None))
+        if self.crossHatch:
+            lines += Shader.shadePolygon(polygon, self.angle+90, spacing, avoidOutline=avoidOutline, mode=mode, alternate=(self.drawingDirectionAngle is None))
+        return lines
+        
+    @staticmethod
+    def shadePolygon(polygon, angleDegrees, spacing, avoidOutline=True, mode=None, alternate=True):
+        if mode is None:
+            mode = Shader.MODE_EVEN_ODD
+    
+        rotate = complex(math.cos(angleDegrees * math.pi / 180.), math.sin(angleDegrees * math.pi / 180.))
+        
+        polygon = [(line[0] / rotate,line[1] / rotate) for line in polygon]
+        
+        spacing = float(spacing)
+
+        toAvoid = list(set(line[0].imag for line in polygon)|set(line[1].imag for line in polygon))
+
+        if len(toAvoid) <= 1:
+            deltaY = (toAvoid[0]-spacing/2.) % spacing
+        else:
+            # find largest interval
+            toAvoid.sort()
+            largestIndex = 0
+            largestLen = 0
+            for i in range(len(toAvoid)):
+                l = ( toAvoid[i] - toAvoid[i-1] ) % spacing
+                if l > largestLen:
+                    largestIndex = i
+                    largestLen = l
+            deltaY = (toAvoid[largestIndex-1] + largestLen / 2.) % spacing
+            
+        minY = min(min(line[0].imag,line[1].imag) for line in polygon)
+        maxY = max(max(line[0].imag,line[1].imag) for line in polygon)
+
+        y = minY + ( - minY ) % spacing + deltaY    
+        
+        if y > minY + spacing:
+            y -= spacing
+            
+        y += 0.01
+        
+        odd = False
+
+        all = []
+        
+        while y < maxY:
+            intersections = []
+            for line in polygon:
+                z = line[0]
+                z1 = line[1]
+                if z1.imag == y or z.imag == y: # roundoff generated corner case -- ignore -- TODO
+                    break
+                if z1.imag < y < z.imag or z.imag < y < z1.imag:
+                    if z1.real == z.real:
+                        intersections.append(( complex(z.real, y), z.imag<y, line))
+                    else:
+                        m = (z1.imag-z.imag)/(z1.real-z.real)
+                        # m * (x - z.real) = y - z.imag
+                        # so: x = (y - z.imag) / m + z.real
+                        intersections.append( (complex((y-z.imag)/m + z.real, y), z.imag<y, line) )
+        
+            intersections.sort(key=lambda datum: datum[0].real)
+            
+            thisLine = []
+            if mode == Shader.MODE_EVEN_ODD:
+                for i in range(0,len(intersections)-1,2):
+                    thisLine.append((intersections[i], intersections[i+1]))
+            elif mode == Shader.MODE_NONZERO:
+                count = 0
+                for i in range(0,len(intersections)-1):
+                    if intersections[i][1]:
+                        count += 1
+                    else:
+                        count -= 1
+                    if count != 0:
+                        thisLine.append((intersections[i], intersections[i+1]))
+            else:
+                raise ValueError()
+                   
+            if odd and alternate:
+                thisLine = list(reversed([(l[1],l[0]) for l in thisLine]))
+                
+            if not avoidOutline and len(thisLine) and len(all) and all[-1][1][2] == thisLine[0][0][2]:
+                # follow along outline to avoid an extra pen bob
+                all.append( (all[-1][1], thisLine[0][0]) )
+                
+            all += thisLine
+                
+            odd = not odd
+                
+            y += spacing
+
+        return [(line[0][0]*rotate, line[1][0]*rotate) for line in all]
+    
+                    
+if __name__ == '__main__':
+    polygon=(0+0j, 10+10j, 10+0j, 0+0j)
+    print(shadePolygon(polygon,90,1))
+