major refactor

Split into classes for Fill, Stroke, and SatinColumn.  Renamed params to be
the same across XML attributes and OptionParser.  Added distinct stitch length
params for satin underlay.  Renamed "satin underlay" to "contour underlay" and
split out "center walk underlay" and "zigzag underlay".

The code is ten times more readable, parameters make more sense, and everything
is specified by the user in millimeters.  Basically, everything is way better.

1 files changed, 853 insertions, 733 deletions

diff --git a/embroider.py b/embroider.py
index aed5007b..eb1261c1 100644
--- a/embroider.py
+++ b/embroider.py
@@ -32,125 +32,865 @@ import simpletransform
 from bezmisc import bezierlength, beziertatlength, bezierpointatt
 from cspsubdiv import cspsubdiv
 import cubicsuperpath
-import PyEmb
 import math
 import lxml.etree as etree
 import shapely.geometry as shgeo
 import shapely.affinity as affinity
 from pprint import pformat
 
+import PyEmb
+
 dbg = open("/tmp/embroider-debug.txt", "w")
 PyEmb.dbg = dbg
 
-# a 0.5pt stroke becomes a straight line.
-STROKE_MIN = 0.5
+SVG_PATH_TAG = inkex.addNS('path', 'svg')
+SVG_DEFS_TAG = inkex.addNS('defs', 'svg')
+SVG_GROUP_TAG = inkex.addNS('g', 'svg')
 
+class EmbroideryElement(object):
+    def __init__(self, node, options):
+        self.node = node
+        self.options = options
 
-def parse_boolean(s):
-    if isinstance(s, bool):
-        return s
-    else:
-        return s and (s.lower() in ('yes', 'y', 'true', 't', '1'))
+    def get_param(self, param, default):
+        value = self.node.get("embroider_" + param, "").strip()
 
+        if not value:
+            value = getattr(self.options, param, None)
 
-def get_param(node, param, default):
-    value = node.get("embroider_" + param)
+        return value
+        
+    def get_boolean_param(self, param, default=None):
+        value = self.get_param(param, default)
+    
+        if isinstance(value, bool):
+            return value
+        else:
+            return value and (value.lower() in ('yes', 'y', 'true', 't', '1'))
+        
+    def get_float_param(self, param, default=None):    
+        try:
+            value = float(self.get_param(param, default))
+        except (TypeError, ValueError):
+            return default
+    
+        if param.endswith('_mm'):
+            print >> dbg, "get_float_param", param, value, "*", self.options.pixels_per_mm
+            value = value * self.options.pixels_per_mm
 
-    if value is None or not value.strip():
-        return default
+        return value
 
-    return value.strip()
+        
+    def get_int_param(self, param, default=None):
+        try:
+            value = int(self.get_param(param, default))
+        except (TypeError, ValueError):
+            return default
 
+        if param.endswith('_mm'):
+            value = int(value * self.options.pixels_per_mm)
 
-def get_boolean_param(node, param, default=False):
-    value = get_param(node, param, default)
+        return value
+    
+    def get_style(self, style_name):
+        style = simplestyle.parseStyle(self.node.get("style"))
+        if (style_name not in style):
+            return None
+        value = style[style_name]
+        if value == 'none':
+            return None
+        return value
+    
+    def has_style(self, style_name):
+        style = simplestyle.parseStyle(self.node.get("style"))
+        return style_name in style
+    
+    def parse_path(self):
+        # A CSP is a  "cubic superpath".
+        # 
+        # A "path" is a sequence of strung-together bezier curves. 
+        #
+        # A "superpath" is a collection of paths that are all in one object.
+        #
+        # The "cubic" bit in "cubic superpath" is because the bezier curves
+        # inkscape uses involve cubic polynomials.
+        #
+        # Each path is a collection of tuples, each of the form:
+        #
+        # (control_before, point, control_after)
+        #
+        # A bezier curve segment is defined by an endpoint, a control point,
+        # a second control point, and a final endpoint.  A path is a bunch of
+        # bezier curves strung together.  One could represent a path as a set
+        # of four-tuples, but there would be redundancy because the ending
+        # point of one bezier is the starting point of the next.  Instead, a
+        # path is a set of 3-tuples as shown above, and one must construct
+        # each bezier curve by taking the appropriate endpoints and control
+        # points.  Bleh. It should be noted that a straight segment is
+        # represented by having the control point on each end equal to that
+        # end's point.
+        #
+        # In a path, each element in the 3-tuple is itself a tuple of (x, y).
+        # Tuples all the way down.  Hasn't anyone heard of using classes?
 
-    return parse_boolean(value)
+        path = cubicsuperpath.parsePath(self.node.get("d"))
+    
+        # print >> sys.stderr, pformat(path)
+    
+        # start with the identity transform
+        transform = [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]]
+    
+        # combine this node's transform with all parent groups' transforms
+        transform = simpletransform.composeParents(self.node, transform)
+    
+        # apply the combined transform to this node's path
+        simpletransform.applyTransformToPath(transform, path)
+    
+        return path    
+
+    def flatten(self, path):
+        """approximate a path containing beziers with a series of points"""
+    
+        path = deepcopy(path)
+    
+        cspsubdiv(path, self.options.flat)
+    
+        flattened = []
+    
+        for comp in path:
+            vertices = []
+            for ctl in comp:
+                vertices.append((ctl[1][0], ctl[1][1]))
+            flattened.append(vertices)
+    
+        return flattened
+
+    def to_patches(self):
+        raise NotImplementedError("%s must implement to_path()" % self.__class__.__name__)
 
+    def fatal(self, message):
+        print >> sys.stderr, "error:", message
+        sys.exit(1)
 
-def get_float_param(node, param, default=None):
-    value = get_param(node, param, default)
 
-    try:
-        return float(value)
-    except ValueError:
-        return default
+class Fill(EmbroideryElement):
+    def __init__(self, *args, **kwargs):
+        super(Fill, self).__init__(*args, **kwargs)
+
+        self.shape = self.get_shape()
+
+    @property
+    def angle(self):
+        return math.radians(self.get_float_param('angle', 0))
+
+    @property
+    def color(self):
+        return self.get_style("fill")
+
+    @property
+    def flip(self):
+        return self.get_boolean_param("flip", False)
+
+    @property
+    def row_spacing(self):
+        return self.get_float_param("row_spacing_mm")
+
+    @property
+    def max_stitch_length(self):
+        return self.get_float_param("max_stitch_length_mm")
+
+    @property
+    def staggers(self):
+        return self.get_int_param("staggers", 4)
+
+    @property
+    def paths(self):
+        return self.flatten(self.parse_path())
+
+    def get_shape(self):
+        poly_ary = []
+        for sub_path in self.paths:
+            point_ary = []
+            last_pt = None
+            for pt in sub_path:
+                if (last_pt is not None):
+                    vp = (pt[0] - last_pt[0], pt[1] - last_pt[1])
+                    dp = math.sqrt(math.pow(vp[0], 2.0) + math.pow(vp[1], 2.0))
+                    # dbg.write("dp %s\n" % dp)
+                    if (dp > 0.01):
+                        # I think too-close points confuse shapely.
+                        point_ary.append(pt)
+                        last_pt = pt
+                else:
+                    last_pt = pt
+            poly_ary.append(point_ary)
+
+        # shapely's idea of "holes" are to subtract everything in the second set
+        # from the first. So let's at least make sure the "first" thing is the
+        # biggest path.
+        # TODO: actually figure out which things are holes and which are shells
+        poly_ary.sort(key=lambda point_list: shgeo.Polygon(point_list).area, reverse=True)
+    
+        polygon = shgeo.MultiPolygon([(poly_ary[0], poly_ary[1:])])
+        # print >> sys.stderr, "polygon valid:", polygon.is_valid
+        return polygon
+
+    def intersect_region_with_grating(self):
+        # the max line length I'll need to intersect the whole shape is the diagonal
+        (minx, miny, maxx, maxy) = self.shape.bounds
+        upper_left = PyEmb.Point(minx, miny)
+        lower_right = PyEmb.Point(maxx, maxy)
+        length = (upper_left - lower_right).length()
+        half_length = length / 2.0
 
+        # Now get a unit vector rotated to the requested angle.  I use -angle
+        # because shapely rotates clockwise, but my geometry textbooks taught
+        # me to consider angles as counter-clockwise from the X axis.
+        direction = PyEmb.Point(1, 0).rotate(-self.angle)
 
-def get_int_param(node, param, default=None):
-    value = get_param(node, param, default)
+        # and get a normal vector
+        normal = direction.rotate(math.pi / 2)
 
-    try:
-        return int(value)
-    except ValueError:
-        return default
+        # I'll start from the center, move in the normal direction some amount,
+        # and then walk left and right half_length in each direction to create
+        # a line segment in the grating.
+        center = PyEmb.Point((minx + maxx) / 2.0, (miny + maxy) / 2.0)
 
+        # I need to figure out how far I need to go along the normal to get to
+        # the edge of the shape.  To do that, I'll rotate the bounding box
+        # angle degrees clockwise and ask for the new bounding box.  The max
+        # and min y tell me how far to go.
 
-def parse_path(node):
-    path = cubicsuperpath.parsePath(node.get("d"))
+        _, start, _, end = affinity.rotate(self.shape, self.angle, origin='center', use_radians=True).bounds
 
-#    print >> sys.stderr, pformat(path)
+        # convert start and end to be relative to center (simplifies things later)
+        start -= center.y
+        end -= center.y
 
-    # start with the identity transform
-    transform = [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]]
+        # offset start slightly so that rows are always an even multiple of
+        # row_spacing_px from the origin.  This makes it so that abutting
+        # fill regions at the same angle and spacing always line up nicely.
+        start -= (start + normal * center) % self.row_spacing
 
-    # combine this node's transform with all parent groups' transforms
-    transform = simpletransform.composeParents(node, transform)
+        rows = []
 
-    # apply the combined transform to this node's path
-    simpletransform.applyTransformToPath(transform, path)
+        while start < end:
+            p0 = center + normal.mul(start) + direction.mul(half_length)
+            p1 = center + normal.mul(start) - direction.mul(half_length)
+            endpoints = [p0.as_tuple(), p1.as_tuple()]
+            grating_line = shgeo.LineString(endpoints)
 
-    return path
+            res = grating_line.intersection(self.shape)
 
+            if (isinstance(res, shgeo.MultiLineString)):
+                runs = map(lambda line_string: line_string.coords, res.geoms)
+            else:
+                if res.is_empty or len(res.coords) == 1:
+                    # ignore if we intersected at a single point or no points
+                    start += self.row_spacing
+                    continue
+                runs = [res.coords]
 
-def flatten(path, flatness):
-    """approximate a path containing beziers with a series of points"""
+            runs.sort(key=lambda seg: (PyEmb.Point(*seg[0]) - upper_left).length())
 
-    path = deepcopy(path)
+            if self.flip:
+                runs.reverse()
+                runs = map(lambda run: tuple(reversed(run)), runs)
 
-    cspsubdiv(path, flatness)
+            rows.append(runs)
 
-    flattened = []
+            start += self.row_spacing
 
-    for comp in path:
-        vertices = []
-        for ctl in comp:
-            vertices.append((ctl[1][0], ctl[1][1]))
-        flattened.append(vertices)
+        return rows
 
-    return flattened
+    def pull_runs(self, rows):
+        # Given a list of rows, each containing a set of line segments,
+        # break the area up into contiguous patches of line segments.
+        #
+        # This is done by repeatedly pulling off the first line segment in
+        # each row and calling that a shape.  We have to be careful to make
+        # sure that the line segments are part of the same shape.  Consider
+        # the letter "H", with an embroidery angle of 45 degrees.  When
+        # we get to the bottom of the lower left leg, the next row will jump
+        # over to midway up the lower right leg.  We want to stop there and
+        # start a new patch.
 
+        # Segments more than this far apart are considered not to be part of
+        # the same run.
+        row_distance_cutoff = self.row_spacing * 1.1
 
-def csp_to_shapely_polygon(path):
-    poly_ary = []
-    for sub_path in path:
-        point_ary = []
-        last_pt = None
-        for pt in sub_path:
-            if (last_pt is not None):
-                vp = (pt[0] - last_pt[0], pt[1] - last_pt[1])
-                dp = math.sqrt(math.pow(vp[0], 2.0) + math.pow(vp[1], 2.0))
-                # dbg.write("dp %s\n" % dp)
-                if (dp > 0.01):
-                    # I think too-close points confuse shapely.
-                    point_ary.append(pt)
-                    last_pt = pt
+        def make_quadrilateral(segment1, segment2):
+            return shgeo.Polygon((segment1[0], segment1[1], segment2[1], segment2[0], segment1[0]))
+
+        def is_same_run(segment1, segment2):
+            if shgeo.LineString(segment1).distance(shgeo.LineString(segment1)) > row_distance_cutoff:
+                return False
+
+            quad = make_quadrilateral(segment1, segment2)
+            quad_area = quad.area
+            intersection_area = self.shape.intersection(quad).area
+
+            return (intersection_area / quad_area) >= 0.9
+
+        # for row in rows:
+        #    print >> sys.stderr, len(row)
+
+        # print >>sys.stderr, "\n".join(str(len(row)) for row in rows)
+
+        runs = []
+        count = 0
+        while (len(rows) > 0):
+            run = []
+            prev = None
+
+            for row_num in xrange(len(rows)):
+                row = rows[row_num]
+                first, rest = row[0], row[1:]
+
+                # TODO: only accept actually adjacent rows here
+                if prev is not None and not is_same_run(prev, first):
+                    break
+
+                run.append(first)
+                prev = first
+
+                rows[row_num] = rest
+
+            # print >> sys.stderr, len(run)
+            runs.append(run)
+            rows = [row for row in rows if len(row) > 0]
+
+            count += 1
+
+        return runs
+
+    def to_patches(self):
+        rows_of_segments = self.intersect_region_with_grating()
+        groups_of_segments = self.pull_runs(rows_of_segments)
+
+        # "east" is the name of the direction that is to the right along a row
+        east = PyEmb.Point(1, 0).rotate(-self.angle)
+
+        # print >> sys.stderr, len(groups_of_segments)
+
+        patches = []
+        for group_of_segments in groups_of_segments:
+            patch = Patch(color=self.color)
+            first_segment = True
+            swap = False
+            last_end = None
+
+            for segment in group_of_segments:
+                # We want our stitches to look like this:
+                #
+                # ---*-----------*-----------
+                # ------*-----------*--------
+                # ---------*-----------*-----
+                # ------------*-----------*--
+                # ---*-----------*-----------
+                #
+                # Each successive row of stitches will be staggered, with
+                # num_staggers rows before the pattern repeats.  A value of
+                # 4 gives a nice fill while hiding the needle holes.  The
+                # first row is offset 0%, the second 25%, the third 50%, and
+                # the fourth 75%.
+                #
+                # Actually, instead of just starting at an offset of 0, we
+                # can calculate a row's offset relative to the origin.  This
+                # way if we have two abutting fill regions, they'll perfectly
+                # tile with each other.  That's important because we often get
+                # abutting fill regions from pull_runs().
+
+                (beg, end) = segment
+
+                if (swap):
+                    (beg, end) = (end, beg)
+
+                beg = PyEmb.Point(*beg)
+                end = PyEmb.Point(*end)
+
+                row_direction = (end - beg).unit()
+                segment_length = (end - beg).length()
+
+                # only stitch the first point if it's a reasonable distance away from the
+                # last stitch
+                if last_end is None or (beg - last_end).length() > 0.5 * self.options.pixels_per_mm:
+                    patch.add_stitch(beg)
+
+                # Now, imagine the coordinate axes rotated by 'angle' degrees, such that
+                # the rows are parallel to the X axis.  We can find the coordinates in these
+                # axes of the beginning point in this way:
+                relative_beg = beg.rotate(self.angle)
+
+                absolute_row_num = round(relative_beg.y / self.row_spacing)
+                row_stagger = absolute_row_num % self.staggers
+                row_stagger_offset = (float(row_stagger) / self.staggers) * self.max_stitch_length
+
+                first_stitch_offset = (relative_beg.x - row_stagger_offset) % self.max_stitch_length
+
+                first_stitch = beg - east * first_stitch_offset
+
+                # we might have chosen our first stitch just outside this row, so move back in
+                if (first_stitch - beg) * row_direction < 0:
+                    first_stitch += row_direction * self.max_stitch_length
+
+                offset = (first_stitch - beg).length()
+
+                while offset < segment_length:
+                    patch.add_stitch(beg + offset * row_direction)
+                    offset += self.max_stitch_length
+
+                if (end - patch.stitches[-1]).length() > 0.1 * self.options.pixels_per_mm:
+                    patch.add_stitch(end)
+
+                last_end = end
+                swap = not swap
+
+            patches.append(patch)
+        return patches
+
+
+class Stroke(EmbroideryElement):
+    @property
+    def color(self):
+        return self.get_style("stroke")
+
+    @property
+    def width(self):
+        stroke_width = self.get_style("stroke-width")
+
+        if stroke_width.endswith("px"):
+            stroke_width = stroke_width[:-2]
+
+        return float(stroke_width)
+
+    @property
+    def dashed(self):
+        return self.get_style("stroke-dasharray") is not None
+
+    @property
+    def running_stitch_length(self):
+        return self.get_float_param("running_stitch_length_mm")
+
+    @property
+    def zigzag_spacing(self):
+        return self.get_float_param("zigzag_spacing_mm")
+
+    @property
+    def repeats(self):
+        return self.get_int_param("repeats", 1)
+
+    @property
+    def paths(self):
+        return self.flatten(self.parse_path())
+
+    def is_running_stitch(self):
+        # stroke width <= 0.5 pixels is deprecated in favor of dashed lines
+        return self.dashed or self.width <= 0.5
+
+    def stroke_points(self, emb_point_list, zigzag_spacing, stroke_width):
+        patch = Patch(color=self.color)
+        p0 = emb_point_list[0]
+        rho = 0.0
+        side = 1
+        last_segment_direction = None
+
+        for repeat in xrange(self.repeats):
+            if repeat % 2 == 0:
+                order = range(1, len(emb_point_list))
             else:
-                last_pt = pt
-        poly_ary.append(point_ary)
-    # shapely's idea of "holes" are to subtract everything in the second set
-    # from the first. So let's at least make sure the "first" thing is the
-    # biggest path.
-    # TODO: actually figure out which things are holes and which are shells
-    poly_ary.sort(key=lambda point_list: shgeo.Polygon(point_list).area, reverse=True)
+                order = range(-2, -len(emb_point_list) - 1, -1)
 
-    polygon = shgeo.MultiPolygon([(poly_ary[0], poly_ary[1:])])
-    # print >> sys.stderr, "polygon valid:", polygon.is_valid
-    return polygon
+            for segi in order:
+                p1 = emb_point_list[segi]
 
+                # how far we have to go along segment
+                seg_len = (p1 - p0).length()
+                if (seg_len == 0):
+                    continue
 
-class Patch:
+                # vector pointing along segment
+                along = (p1 - p0).unit()
+                
+                # vector pointing to edge of stroke width
+                perp = along.rotate_left().mul(stroke_width * 0.5)
+
+                if stroke_width == 0.0 and last_segment_direction is not None:
+                    if abs(1.0 - along * last_segment_direction) > 0.5:
+                        # if greater than 45 degree angle, stitch the corner
+                        rho = self.zigzag_spacing
+                        patch.add_stitch(p0)
+
+                # iteration variable: how far we are along segment
+                while (rho <= seg_len):
+                    left_pt = p0 + along * rho + perp * side
+                    patch.add_stitch(left_pt)
+                    rho += self.zigzag_spacing
+                    side = -side
+
+                p0 = p1
+                last_segment_direction = along
+                rho -= seg_len
 
+            if (p0 - patch.stitches[-1]).length() > 0.1:
+                patch.add_stitch(p0)
+
+        return patch
+
+    def to_patches(self):
+        patches = []
+
+        for path in self.paths:
+            path = [PyEmb.Point(x, y) for x, y in path]
+            if self.is_running_stitch():
+                patch = self.stroke_points(path, self.running_stitch_length, stroke_width=0.0)
+            else:
+                patch = self.stroke_points(path, self.zigzag_spacing/2.0, stroke_width=self.width)
+
+            patches.append(patch)
+
+        return patches
+
+
+class SatinColumn(EmbroideryElement):
+    def __init__(self, *args, **kwargs):
+        super(SatinColumn, self).__init__(*args, **kwargs)
+
+        self.csp = self.parse_path()
+        self.flattened_beziers = self.get_flattened_paths()
+
+        # print >> dbg, "flattened beziers", self.flattened_beziers
+
+    @property
+    def color(self):
+        return self.get_style("stroke")
+
+    @property
+    def zigzag_spacing(self):
+        # peak-to-peak distance between zigzags
+        print >> dbg, "satin zigzag spacing", self.get_float_param("zigzag_spacing_mm")
+        return self.get_float_param("zigzag_spacing_mm")
+
+    @property
+    def pull_compensation(self):
+        # In satin stitch, the stitches have a tendency to pull together and
+        # narrow the entire column.  We can compensate for this by stitching
+        # wider than we desire the column to end up.
+        return self.get_float_param("pull_compensation_mm", 0)
+
+    @property
+    def contour_underlay(self):
+        # "Contour underlay" is stitching just inside the rectangular shape
+        # of the satin column; that is, up one side and down the other.
+        return self.get_boolean_param("contour_underlay")
+
+    @property
+    def contour_underlay_stitch_length(self):
+        # use "contour_underlay_stitch_length", or, if not set, default to "stitch_length"
+        return self.get_float_param("contour_underlay_stitch_length_mm", self.get_float_param("running_stitch_length_mm"))
+
+    @property
+    def contour_underlay_inset(self):
+        # how far inside the edge of the column to stitch the underlay
+        return self.get_float_param("contour_underlay_inset_mm", 0.4)
+
+    @property
+    def center_walk_underlay(self):
+        # "Center walk underlay" is stitching down and back in the centerline
+        # between the two sides of the satin column.
+        return self.get_boolean_param("center_walk_underlay")
+
+    @property
+    def center_walk_underlay_stitch_length(self):
+        # use "center_walk_underlay_stitch_length", or, if not set, default to "stitch_length"
+        return self.get_float_param("center_walk_underlay_stitch_length_mm", self.get_float_param("running_stitch_length_mm"))
+
+    @property
+    def zigzag_underlay(self):
+        return self.get_boolean_param("zigzag_underlay")
+
+    @property
+    def zigzag_underlay_spacing(self):
+        # peak-to-peak distance between zigzags in zigzag underlay
+        return self.get_float_param("zigzag_underlay_spacing_mm", 1)
+
+    @property
+    def zigzag_underlay_inset(self):
+        # how far in from the edge of the satin the points in the zigzags
+        # should be
+
+        # Default to half of the contour underlay inset.  That is, if we're
+        # doing both contour underlay and zigzag underlay, make sure the
+        # points of the zigzag fall outside the contour underlay but inside
+        # the edges of the satin column.
+        return self.get_float_param("zigzag_underlay_inset_mm", self.contour_underlay_inset / 2.0)
+
+    def get_flattened_paths(self):
+        # Given a pair of paths made up of bezier segments, flatten
+        # each individual bezier segment into line segments that approximate
+        # the curves.  Retain the divisions between beziers -- we'll use those
+        # later.
+
+        paths = []
+
+        for path in self.csp:
+            # See the documentation in the parent class for parse_path() for a
+            # description of the format of the CSP.  Each bezier is constructed
+            # using two neighboring 3-tuples in the list.
+
+            flattened_path = []
+
+            # iterate over pairs of 3-tuples
+            for prev, current in zip(path[:-1], path[1:]):
+                flattened_segment = self.flatten([[prev, current]])
+                flattened_segment = [PyEmb.Point(x, y) for x, y in flattened_segment[0]]
+                flattened_path.append(flattened_segment)
+
+            paths.append(flattened_path)
+
+        return zip(*paths)
+
+    def validate_satin_column(self):
+        # The node should have exactly two paths with no fill.  Each
+        # path should have the same number of points, meaning that they
+        # will both be made up of the same number of bezier curves.
+
+        node_id = self.node.get("id")
+
+        if len(self.csp) != 2:
+            self.fatal("satin column: object %s invalid: expected exactly two sub-paths, but there are %s" % (node_id, len(csp)))
+
+        if self.get_style("fill") is not None:
+            self.fatal("satin column: object %s has a fill (but should not)" % node_id)
+
+        if len(self.csp[0]) != len(self.csp[1]):
+            self.fatal("satin column: object %s has two paths with an unequal number of points (%s and %s)" % (node_id, len(self.csp[0]), len(self.csp[1])))
+
+    def offset_points(self, pos1, pos2, offset_px):
+        # Expand or contract two points about their midpoint.  This is
+        # useful for pull compensation and insetting underlay.
+
+        distance = (pos1 - pos2).length()
+
+        if distance < 0.0001:
+            # if they're the same point, we don't know which direction
+            # to offset in, so we have to just return the points
+            return pos1, pos2
+
+        # don't contract beyond the midpoint, or we'll start expanding
+        if offset_px < -distance / 2.0:
+            offset_px = -distance / 2.0
+
+        pos1 = pos1 + (pos1 - pos2).unit() * offset_px
+        pos2 = pos2 + (pos2 - pos1).unit() * offset_px
+
+        return pos1, pos2
+
+    def walk(self, path, start_pos, start_index, distance):
+        # Move <distance> pixels along <path>, which is a sequence of line
+        # segments defined by points.
+
+        # <start_index> is the index of the line segment in <path> that
+        # we're currently on.  <start_pos> is where along that line
+        # segment we are.  Return a new position and index.
+
+        #print >> dbg, "walk", start_pos, start_index, distance
+
+        pos = start_pos
+        index = start_index
+        last_index = len(path) - 1
+        distance_remaining = distance
+
+        while True:
+            if index >= last_index:
+                return pos, index
+
+            segment_end = path[index + 1]
+            segment = segment_end - pos
+            segment_length = segment.length()
+
+            if segment_length > distance_remaining:
+                # our walk ends partway along this segment
+                return pos + segment.unit() * distance_remaining, index
+            else:
+                # our walk goes past the end of this segment, so advance
+                # one point
+                index += 1
+                distance_remaining -= segment_length
+                pos = segment_end
+
+    def walk_paths(self, spacing, offset):
+        # Take a bezier segment from each path in turn, and plot out an
+        # equal number of points on each bezier.  Return the points plotted.
+        # The points will be contracted or expanded by offset using
+        # offset_points().
+
+        points = [[], []]
+
+        def add_pair(pos1, pos2):
+            pos1, pos2 = self.offset_points(pos1, pos2, offset)
+            points[0].append(pos1)
+            points[1].append(pos2)
+
+        # We may not be able to fit an even number of zigzags in each pair of
+        # beziers.  We'll store the remaining bit of the beziers after handling
+        # each section.
+        remainder_path1 = []
+        remainder_path2 = []
+
+        for segment1, segment2 in self.flattened_beziers:
+            subpath1 = remainder_path1 + segment1
+            subpath2 = remainder_path2 + segment2
+
+            len1 = shgeo.LineString(subpath1).length
+            len2 = shgeo.LineString(subpath2).length
+
+            # Base the number of stitches in each section on the _longest_ of
+            # the two beziers. Otherwise, things could get too sparse when one
+            # side is significantly longer (e.g. when going around a corner).
+            # The risk here is that we poke a hole in the fabric if we try to
+            # cram too many stitches on the short bezier.  The user will need
+            # to avoid this through careful construction of paths.
+            #
+            # TODO: some commercial machine embroidery software compensates by
+            # pulling in some of the "inner" stitches toward the center a bit.
+
+            # note, this rounds down using integer-division
+            num_points = max(len1, len2) / spacing
+
+            spacing1 = len1 / num_points
+            spacing2 = len2 / num_points
+
+            pos1 = subpath1[0]
+            index1 = 0
+
+            pos2 = subpath2[0]
+            index2 = 0
+
+            for i in xrange(int(num_points)):
+                add_pair(pos1, pos2)
+
+                pos1, index1 = self.walk(subpath1, pos1, index1, spacing1)
+                pos2, index2 = self.walk(subpath2, pos2, index2, spacing2)
+
+            if index1 < len(subpath1) - 1:
+                remainder_path1 = [pos1] + subpath1[index1 + 1:]
+            else:
+                remainder_path1 = []
+
+            if index2 < len(subpath2) - 1:
+                remainder_path2 = [pos2] + subpath2[index2 + 1:]
+            else:
+                remainder_path2 = []
+
+        # We're off by one in the algorithm above, so we need one more
+        # pair of points.  We also want to add points at the very end to
+        # make sure we match the vectors on screen as best as possible.
+        # Try to avoid doing both if they're going to stack up too
+        # closely.
+
+        end1 = remainder_path1[-1]
+        end2 = remainder_path2[-1]
+    
+        if (end1 - pos1).length() > 0.3 * spacing:
+            add_pair(pos1, pos2)
+    
+        add_pair(end1, end2)
+    
+        return points
+
+    def do_contour_underlay(self):
+        # "contour walk" underlay: do stitches up one side and down the
+        # other.
+        forward, back = self.walk_paths(self.contour_underlay_stitch_length,
+                                        -self.contour_underlay_inset)
+        return Patch(color=self.color, stitches=(forward + list(reversed(back))))
+
+    def do_center_walk(self):
+        # Center walk underlay is just a running stitch down and back on the
+        # center line between the bezier curves.
+
+        # Do it like contour underlay, but inset all the way to the center.
+        forward, back = self.walk_paths(self.center_walk_underlay_stitch_length,
+                                        -100000)
+        return Patch(color=self.color, stitches=(forward + list(reversed(back))))
+
+    def do_zigzag_underlay(self):
+        # zigzag underlay, usually done at a much lower density than the
+        # satin itself.  It looks like this:
+        #
+        # \/\/\/\/\/\/\/\/\/\/|
+        # /\/\/\/\/\/\/\/\/\/\|
+        #
+        # In combination with the "contour walk" underlay, this is the
+        # "German underlay" described here:
+        #   http://www.mrxstitch.com/underlay-what-lies-beneath-machine-embroidery/
+
+        patch = Patch(color=self.color)
+
+        sides = self.walk_paths(self.zigzag_underlay_spacing / 2.0,
+                                -self.zigzag_underlay_inset)
+
+        # This organizes the points in each side in the order that they'll be
+        # visited.
+        sides = [sides[0][::2] + list(reversed(sides[0][1::2])),
+                 sides[1][1::2] + list(reversed(sides[1][::2]))]
+
+        # This fancy bit of iterable magic just repeatedly takes a point
+        # from each side in turn.
+        for point in chain.from_iterable(izip(*sides)):
+            patch.add_stitch(point)
+
+        return patch
+
+    def do_satin(self):
+        # satin: do a zigzag pattern, alternating between the paths.  The
+        # zigzag looks like this to make the satin stitches look perpendicular
+        # to the column:
+        #
+        # /|/|/|/|/|/|/|/|
+
+        # print >> dbg, "satin", self.zigzag_spacing, self.pull_compensation
+
+        patch = Patch(color=self.color)
+
+        sides = self.walk_paths(self.zigzag_spacing, self.pull_compensation)
+
+        # Like in zigzag_underlay(): take a point from each side in turn.
+        for point in chain.from_iterable(izip(*sides)):
+            patch.add_stitch(point)
+
+        return patch
+
+    def to_patches(self):
+        # Stitch a variable-width satin column, zig-zagging between two paths.
+
+        # The algorithm will draw zigzags between each consecutive pair of
+        # beziers.  The boundary points between beziers serve as "checkpoints",
+        # allowing the user to control how the zigzags flow around corners.
+
+        # First, verify that we have valid paths.
+        self.validate_satin_column()
+
+        patches = []
+
+        if self.center_walk_underlay:
+            patches.append(self.do_center_walk())
+
+        if self.contour_underlay:
+            patches.append(self.do_contour_underlay())
+
+        if self.zigzag_underlay:
+            # zigzag underlay comes after contour walk underlay, so that the
+            # zigzags sit on the contour walk underlay like rail ties on rails.
+            patches.append(self.do_zigzag_underlay())
+
+        patches.append(self.do_satin())
+
+        return patches
+
+
+class Patch:
     def __init__(self, color=None, stitches=None):
         self.color = color
         self.stitches = stitches or []
@@ -223,7 +963,7 @@ def stitches_to_paths(stitches):
 
 def emit_inkscape(parent, stitches):
     for color, path in stitches_to_paths(stitches):
-        dbg.write('path: %s %s\n' % (color, repr(path)))
+        # dbg.write('path: %s %s\n' % (color, repr(path)))
         inkex.etree.SubElement(parent,
                                inkex.addNS('path', 'svg'),
                                {'style': simplestyle.formatStyle(
@@ -235,9 +975,7 @@ def emit_inkscape(parent, stitches):
 
 
 class Embroider(inkex.Effect):
-
     def __init__(self, *args, **kwargs):
-        # dbg.write("args: %s\n" % repr(sys.argv))
         inkex.Effect.__init__(self)
         self.OptionParser.add_option("-r", "--row_spacing_mm",
                                      action="store", type="float",
@@ -249,15 +987,15 @@ class Embroider(inkex.Effect):
                                      help="zigzag spacing (mm)")
         self.OptionParser.add_option("-l", "--max_stitch_len_mm",
                                      action="store", type="float",
-                                     dest="max_stitch_len_mm", default=3.0,
+                                     dest="max_stitch_length_mm", default=3.0,
                                      help="max stitch length (mm)")
         self.OptionParser.add_option("--running_stitch_len_mm",
                                      action="store", type="float",
-                                     dest="running_stitch_len_mm", default=3.0,
+                                     dest="running_stitch_length_mm", default=3.0,
                                      help="running stitch length (mm)")
         self.OptionParser.add_option("-c", "--collapse_len_mm",
                                      action="store", type="float",
-                                     dest="collapse_len_mm", default=0.0,
+                                     dest="collapse_length_mm", default=0.0,
                                      help="max collapse length (mm)")
         self.OptionParser.add_option("-f", "--flatness",
                                      action="store", type="float",
@@ -283,276 +1021,44 @@ class Embroider(inkex.Effect):
                                      help="Max number of backups of output files to keep.")
         self.OptionParser.add_option("-p", "--pixels_per_mm",
                                      action="store", type="int",
-                                     dest="pixels_per_millimeter", default=10,
+                                     dest="pixels_per_mm", default=10,
                                      help="Number of on-screen pixels per millimeter.")
         self.patches = []
 
-    def process_one_path(self, node, shpath, threadcolor, angle):
-        # self.add_shapely_geo_to_svg(shpath.boundary, color="#c0c000")
-
-        flip = get_boolean_param(node, "flip", False)
-        row_spacing_px = get_float_param(node, "row_spacing", self.options.row_spacing_mm) * self.options.pixels_per_millimeter
-        max_stitch_len_px = get_float_param(node, "max_stitch_length", self.options.max_stitch_len_mm) * self.options.pixels_per_millimeter
-        num_staggers = get_int_param(node, "staggers", 4)
-
-        rows_of_segments = self.intersect_region_with_grating(shpath, row_spacing_px, angle, flip)
-        groups_of_segments = self.pull_runs(rows_of_segments, shpath, row_spacing_px)
-
-        # "east" is the name of the direction that is to the right along a row
-        east = PyEmb.Point(1, 0).rotate(-angle)
-
-        # print >> sys.stderr, len(groups_of_segments)
-
-        patches = []
-        for group_of_segments in groups_of_segments:
-            patch = Patch(color=threadcolor)
-            first_segment = True
-            swap = False
-            last_end = None
-
-            for segment in group_of_segments:
-                # We want our stitches to look like this:
-                #
-                # ---*-----------*-----------
-                # ------*-----------*--------
-                # ---------*-----------*-----
-                # ------------*-----------*--
-                # ---*-----------*-----------
-                #
-                # Each successive row of stitches will be staggered, with
-                # num_staggers rows before the pattern repeats.  A value of
-                # 4 gives a nice fill while hiding the needle holes.  The
-                # first row is offset 0%, the second 25%, the third 50%, and
-                # the fourth 75%.
-                #
-                # Actually, instead of just starting at an offset of 0, we
-                # can calculate a row's offset relative to the origin.  This
-                # way if we have two abutting fill regions, they'll perfectly
-                # tile with each other.  That's important because we often get
-                # abutting fill regions from pull_runs().
-
-                (beg, end) = segment
-
-                if (swap):
-                    (beg, end) = (end, beg)
-
-                beg = PyEmb.Point(*beg)
-                end = PyEmb.Point(*end)
-
-                row_direction = (end - beg).unit()
-                segment_length = (end - beg).length()
-
-                # only stitch the first point if it's a reasonable distance away from the
-                # last stitch
-                if last_end is None or (beg - last_end).length() > 0.5 * self.options.pixels_per_millimeter:
-                    patch.add_stitch(beg)
-
-                # Now, imagine the coordinate axes rotated by 'angle' degrees, such that
-                # the rows are parallel to the X axis.  We can find the coordinates in these
-                # axes of the beginning point in this way:
-                relative_beg = beg.rotate(angle)
-
-                absolute_row_num = round(relative_beg.y / row_spacing_px)
-                row_stagger = absolute_row_num % num_staggers
-                row_stagger_offset = (float(row_stagger) / num_staggers) * max_stitch_len_px
-
-                first_stitch_offset = (relative_beg.x - row_stagger_offset) % max_stitch_len_px
-
-                first_stitch = beg - east * first_stitch_offset
-
-                # we might have chosen our first stitch just outside this row, so move back in
-                if (first_stitch - beg) * row_direction < 0:
-                    first_stitch += row_direction * max_stitch_len_px
-
-                offset = (first_stitch - beg).length()
-
-                while offset < segment_length:
-                    patch.add_stitch(beg + offset * row_direction)
-                    offset += max_stitch_len_px
-
-                if (end - patch.stitches[-1]).length() > 0.1 * self.options.pixels_per_millimeter:
-                    patch.add_stitch(end)
-
-                last_end = end
-                swap = not swap
-
-            patches.append(patch)
-        return patches
-
-    def intersect_region_with_grating(self, shpath, row_spacing_px, angle, flip=False):
-        # the max line length I'll need to intersect the whole shape is the diagonal
-        (minx, miny, maxx, maxy) = shpath.bounds
-        upper_left = PyEmb.Point(minx, miny)
-        lower_right = PyEmb.Point(maxx, maxy)
-        length = (upper_left - lower_right).length()
-        half_length = length / 2.0
-
-        # Now get a unit vector rotated to the requested angle.  I use -angle
-        # because shapely rotates clockwise, but my geometry textbooks taught
-        # me to consider angles as counter-clockwise from the X axis.
-        direction = PyEmb.Point(1, 0).rotate(-angle)
-
-        # and get a normal vector
-        normal = direction.rotate(math.pi / 2)
-
-        # I'll start from the center, move in the normal direction some amount,
-        # and then walk left and right half_length in each direction to create
-        # a line segment in the grating.
-        center = PyEmb.Point((minx + maxx) / 2.0, (miny + maxy) / 2.0)
-
-        # I need to figure out how far I need to go along the normal to get to
-        # the edge of the shape.  To do that, I'll rotate the bounding box
-        # angle degrees clockwise and ask for the new bounding box.  The max
-        # and min y tell me how far to go.
-
-        _, start, _, end = affinity.rotate(shpath, angle, origin='center', use_radians=True).bounds
-
-        # convert start and end to be relative to center (simplifies things later)
-        start -= center.y
-        end -= center.y
-
-        # offset start slightly so that rows are always an even multiple of
-        # row_spacing_px from the origin.  This makes it so that abutting
-        # fill regions at the same angle and spacing always line up nicely.
-        start -= (start + normal * center) % row_spacing_px
-
-        rows = []
-
-        while start < end:
-            p0 = center + normal.mul(start) + direction.mul(half_length)
-            p1 = center + normal.mul(start) - direction.mul(half_length)
-            endpoints = [p0.as_tuple(), p1.as_tuple()]
-            shline = shgeo.LineString(endpoints)
-
-            res = shline.intersection(shpath)
-
-            if (isinstance(res, shgeo.MultiLineString)):
-                runs = map(lambda line_string: line_string.coords, res.geoms)
-            else:
-                if res.is_empty or len(res.coords) == 1:
-                    # ignore if we intersected at a single point or no points
-                    start += row_spacing_px
-                    continue
-                runs = [res.coords]
-
-            runs.sort(key=lambda seg: (PyEmb.Point(*seg[0]) - upper_left).length())
-
-            if flip:
-                runs.reverse()
-                runs = map(lambda run: tuple(reversed(run)), runs)
-
-            rows.append(runs)
-
-            start += row_spacing_px
-
-        return rows
-
-    def pull_runs(self, rows, shpath, row_spacing_px):
-        # Given a list of rows, each containing a set of line segments,
-        # break the area up into contiguous patches of line segments.
-        #
-        # This is done by repeatedly pulling off the first line segment in
-        # each row and calling that a shape.  We have to be careful to make
-        # sure that the line segments are part of the same shape.  Consider
-        # the letter "H", with an embroidery angle of 45 degrees.  When
-        # we get to the bottom of the lower left leg, the next row will jump
-        # over to midway up the lower right leg.  We want to stop there and
-        # start a new patch.
-
-        # Segments more than this far apart are considered not to be part of
-        # the same run.
-        row_distance_cutoff = row_spacing_px * 1.1
-
-        def make_quadrilateral(segment1, segment2):
-            return shgeo.Polygon((segment1[0], segment1[1], segment2[1], segment2[0], segment1[0]))
-
-        def is_same_run(segment1, segment2):
-            if shgeo.LineString(segment1).distance(shgeo.LineString(segment1)) > row_spacing_px * 1.1:
-                return False
-
-            quad = make_quadrilateral(segment1, segment2)
-            quad_area = quad.area
-            try:
-                intersection_area = shpath.intersection(quad).area
-            except:
-                dbg.write("blowup: %s" % quad)
-                raise
-
-            return (intersection_area / quad_area) >= 0.9
-
-        # for row in rows:
-        #    print >> sys.stderr, len(row)
-
-        # print >>sys.stderr, "\n".join(str(len(row)) for row in rows)
-
-        runs = []
-        count = 0
-        while (len(rows) > 0):
-            run = []
-            prev = None
-
-            for row_num in xrange(len(rows)):
-                row = rows[row_num]
-                first, rest = row[0], row[1:]
-
-                # TODO: only accept actually adjacent rows here
-                if prev is not None and not is_same_run(prev, first):
-                    break
-
-                run.append(first)
-                prev = first
-
-                rows[row_num] = rest
-
-            # print >> sys.stderr, len(run)
-            runs.append(run)
-            rows = [row for row in rows if len(row) > 0]
-
-            count += 1
+    def handle_node(self, node):
+        print >> dbg, "handling node", node.get('id'), node.get('tag')
 
-        return runs
+        element = EmbroideryElement(node, self.options)
 
-    def handle_node(self, node):
-        if simplestyle.parseStyle(node.get("style")).get('display') == "none":
+        if element.has_style('display') and element.get_style('display') is None:
             return
 
-        if node.tag == self.svgdefs:
+        if node.tag == SVG_DEFS_TAG:
             return
 
         for child in node:
             self.handle_node(child)
 
-        if node.tag != self.svgpath:
+        if node.tag != SVG_PATH_TAG:
             return
 
         # dbg.write("Node: %s\n"%str((id, etree.tostring(node, pretty_print=True))))
 
-        if get_boolean_param(node, "satin_column"):
-            self.patch_list.extend(self.satin_column(node))
+        if element.get_boolean_param("satin_column"):
+            self.elements.append(SatinColumn(node, self.options))
         else:
-            stroke = []
-            fill = []
+            elements = []
 
-            if (self.get_style(node, "stroke") is not None):
-                stroke = self.path_to_patch_list(node)
-            if (self.get_style(node, "fill") is not None):
-                fill = self.filled_region_to_patchlist(node)
+            if element.get_style("fill"):
+                elements.append(Fill(node, self.options))
 
-            if get_boolean_param(node, "stroke_first", False):
-                self.patch_list.extend(stroke)
-                self.patch_list.extend(fill)
-            else:
-                self.patch_list.extend(fill)
-                self.patch_list.extend(stroke)
+            if element.get_style("stroke"):
+                elements.append(Stroke(node, self.options))
 
-    def get_style(self, node, style_name):
-        style = simplestyle.parseStyle(node.get("style"))
-        if (style_name not in style):
-            return None
-        value = style[style_name]
-        if (value is None or value == "none"):
-            return None
-        return value
+            if element.get_boolean_param("stroke_first", False):
+                elements.reverse()
+
+            self.elements.extend(elements)
 
     def get_output_path(self):
         svg_filename = self.document.getroot().get(inkex.addNS('docname', 'sodipodi'))
@@ -581,23 +1087,23 @@ class Embroider(inkex.Effect):
 
         return output_path
 
+    def hide_layers(self):
+        for g in self.document.getroot().findall(SVG_GROUP_TAG):
+            if g.get(inkex.addNS("groupmode", "inkscape")) == "layer":
+                g.set("style", "display:none")
+
     def effect(self):
         # Printing anything other than a valid SVG on stdout blows inkscape up.
         old_stdout = sys.stdout
         sys.stdout = sys.stderr
 
-        self.row_spacing_px = self.options.row_spacing_mm * self.options.pixels_per_millimeter
-        self.zigzag_spacing_px = self.options.zigzag_spacing_mm * self.options.pixels_per_millimeter
-        self.max_stitch_len_px = self.options.max_stitch_len_mm * self.options.pixels_per_millimeter
-        self.running_stitch_len_px = self.options.running_stitch_len_mm * self.optoins.pixels_per_millimeter
-        self.collapse_len_px = self.options.collapse_len_mm * self.options.pixels_per_millimeter
-
-        self.svgpath = inkex.addNS('path', 'svg')
-        self.svgdefs = inkex.addNS('defs', 'svg')
         self.patch_list = []
 
-        dbg.write("starting nodes: %s" % time.time())
+        print >> dbg, "starting nodes: %s\n" % time.time()
         dbg.flush()
+
+        self.elements = []
+
         if self.selected:
             # be sure to visit selected nodes in the order they're stacked in
             # the document
@@ -606,10 +1112,11 @@ class Embroider(inkex.Effect):
                     self.handle_node(node)
         else:
             self.handle_node(self.document.getroot())
-        dbg.write("finished nodes: %s" % time.time())
+
+        print >> dbg, "finished nodes: %s" % time.time()
         dbg.flush()
 
-        if not self.patch_list:
+        if not self.elements:
             if self.selected:
                 inkex.errormsg("No embroiderable paths selected.")
             else:
@@ -620,407 +1127,20 @@ class Embroider(inkex.Effect):
         if self.options.hide_layers:
             self.hide_layers()
 
-        stitches = patches_to_stitches(self.patch_list, self.collapse_len_px)
-        emb = PyEmb.Embroidery(stitches, pixels_per_millimeter)
+        patches = chain.from_iterable(element.to_patches() for element in self.elements)
+        stitches = patches_to_stitches(patches, self.options.collapse_length_mm * self.options.pixels_per_mm)
+        emb = PyEmb.Embroidery(stitches, self.options.pixels_per_mm)
         emb.export(self.get_output_path(), self.options.output_format)
 
-        new_layer = inkex.etree.SubElement(self.document.getroot(),
-                                           inkex.addNS('g', 'svg'), {})
+        new_layer = inkex.etree.SubElement(self.document.getroot(), SVG_GROUP_TAG, {})
         new_layer.set('id', self.uniqueId("embroidery"))
         new_layer.set(inkex.addNS('label', 'inkscape'), 'Embroidery')
         new_layer.set(inkex.addNS('groupmode', 'inkscape'), 'layer')
+
         emit_inkscape(new_layer, stitches)
 
         sys.stdout = old_stdout
 
-    def hide_layers(self):
-        for g in self.document.getroot().findall(inkex.addNS("g", "svg")):
-            if g.get(inkex.addNS("groupmode", "inkscape")) == "layer":
-                g.set("style", "display:none")
-
-    def path_to_patch_list(self, node):
-        threadcolor = simplestyle.parseStyle(node.get("style"))["stroke"]
-        stroke_width_str = simplestyle.parseStyle(node.get("style"))["stroke-width"]
-        if (stroke_width_str.endswith("px")):
-            # don't really know how we should be doing unit conversions.
-            # but let's hope px are kind of like pts?
-            stroke_width_str = stroke_width_str[:-2]
-        stroke_width = float(stroke_width_str)
-        dashed = self.get_style(node, "stroke-dasharray") is not None
-        # dbg.write("stroke_width is <%s>\n" % repr(stroke_width))
-        # dbg.flush()
-
-        running_stitch_len_px = get_float_param(node, "stitch_length", self.options.running_stitch_len_mm) * self.pixels_per_millimeter
-        zigzag_spacing_px = get_float_param(node, "zigzag_spacing", self.options.zigzag_spacing_mm) * self.options.pixels_per_millimeter
-        repeats = get_int_param(node, "repeats", 1)
-
-        paths = flatten(parse_path(node), self.options.flat)
-
-        # regularize the points lists.
-        # (If we're parsing beziers, there will be a list of multi-point
-        # subarrays.)
-
-        patches = []
-
-        for path in paths:
-            path = [PyEmb.Point(x, y) for x, y in path]
-            if (stroke_width <= STROKE_MIN or dashed):
-                # dbg.write("self.max_stitch_len_px = %s\n" % self.max_stitch_len_px)
-                patch = self.stroke_points(path, running_stitch_len_px, 0.0, repeats, threadcolor)
-            else:
-                patch = self.stroke_points(path, zigzag_spacing_px * 0.5, stroke_width, repeats, threadcolor)
-            patches.extend(patch)
-
-        return patches
-
-    def stroke_points(self, emb_point_list, zigzag_spacing_px, stroke_width, repeats, threadcolor):
-        patch = Patch(color=threadcolor)
-        p0 = emb_point_list[0]
-        rho = 0.0
-        fact = 1
-        last_segment_direction = None
-
-        for repeat in xrange(repeats):
-            if repeat % 2 == 0:
-                order = range(1, len(emb_point_list))
-            else:
-                order = range(-2, -len(emb_point_list) - 1, -1)
-
-            for segi in order:
-                p1 = emb_point_list[segi]
-
-                # how far we have to go along segment
-                seg_len = (p1 - p0).length()
-                if (seg_len == 0):
-                    continue
-
-                # vector pointing along segment
-                along = (p1 - p0).unit()
-                # vector pointing to edge of stroke width
-                perp = along.rotate_left().mul(stroke_width * 0.5)
-
-                if stroke_width == 0.0 and last_segment_direction is not None:
-                    if abs(1.0 - along * last_segment_direction) > 0.5:
-                        # if greater than 45 degree angle, stitch the corner
-                        # print >> sys.stderr, "corner", along * last_segment_direction
-                        rho = zigzag_spacing_px
-                        patch.add_stitch(p0)
-
-                # iteration variable: how far we are along segment
-                while (rho <= seg_len):
-                    left_pt = p0 + along.mul(rho) + perp.mul(fact)
-                    patch.add_stitch(left_pt)
-                    rho += zigzag_spacing_px
-                    fact = -fact
-
-                p0 = p1
-                last_segment_direction = along
-                rho -= seg_len
-
-            if (p0 - patch.stitches[-1]).length() > 0.1:
-                patch.add_stitch(p0)
-
-        return [patch]
-
-    def filled_region_to_patchlist(self, node):
-        angle = math.radians(float(get_float_param(node, 'angle', 0)))
-        paths = flatten(parse_path(node), self.options.flat)
-        shapelyPolygon = csp_to_shapely_polygon(paths)
-        threadcolor = simplestyle.parseStyle(node.get("style"))["fill"]
-        return self.process_one_path(
-            node,
-            shapelyPolygon,
-            threadcolor,
-            angle)
-
-    def fatal(self, message):
-        print >> sys.stderr, "error:", message
-        sys.exit(1)
-
-    def validate_satin_column(self, node, csp):
-        node_id = node.get("id")
-
-        if len(csp) != 2:
-            self.fatal("satin column: object %s invalid: expected exactly two sub-paths, but there are %s" % (node_id, len(csp)))
-
-        if self.get_style(node, "fill") is not None:
-            self.fatal("satin column: object %s has a fill (but should not)" % node_id)
-
-        if len(csp[0]) != len(csp[1]):
-            self.fatal("satin column: object %s has two paths with an unequal number of points (%s and %s)" % (node_id, len(csp[0]), len(csp[1])))
-
-    def satin_column(self, node):
-        # Stitch a variable-width satin column, zig-zagging between two paths.
-
-        # The node should have exactly two paths with no fill.  Each
-        # path should have the same number of points.  The two paths will be
-        # split into segments, and each segment will have a number of zigzags
-        # defined by the length of the longer of the two segments, divided
-        # by the zigzag spacing parameter.
-
-        id = node.get("id")
-
-        # First, verify that we have a valid node.
-        csp = parse_path(node)
-        self.validate_satin_column(node, csp)
-
-        # fetch parameters
-        zigzag_spacing_px = get_float_param(node, "zigzag_spacing", self.zigzag_spacing_mm) * self.options.pixels_per_millimeter
-        pull_compensation_px = get_float_param(node, "pull_compensation", 0) * self.options.pixels_per_millimeter
-        underlay_inset = get_float_param(node, "satin_underlay_inset", 0) * self.options.pixels_per_millimeter
-        underlay_stitch_len_px = get_float_param(node, "stitch_length", self.running_stitch_len_mm) * self.options.pixels_per_millimeter
-        underlay = get_boolean_param(node, "satin_underlay", False)
-        center_walk = get_boolean_param(node, "satin_center_walk", False)
-        zigzag_underlay_spacing = get_float_param(node, "satin_zigzag_underlay_spacing", 0) * self.options.pixels_per_millimeter
-        zigzag_underlay_inset = underlay_inset / 2.0
-
-        # A path is a collection of tuples, each of the form:
-        #
-        # (control_before, point, control_after)
-        #
-        # A bezier curve segment is defined by an endpoint, a control point,
-        # a second control point, and a final endpoint.  A path is a bunch of
-        # bezier curves strung together.  One could represent a path as a set
-        # of four-tuples, but there would be redundancy because the ending
-        # point of one bezier is the starting point of the next.  Instead, a
-        # path is a set of 3-tuples as shown above, and one must construct
-        # each bezier curve by taking the appropriate endpoints and control
-        # points.  Bleh. It should be noted that a straight segment is
-        # represented by having the control point on each end equal to that
-        # end's point.
-        #
-        # A "superpath" is a collection of paths that are all in one object.
-        # The "cubic" bit in "cubic superpath" is because the bezier curves
-        # inkscape uses involve cubic polynomials.
-        #
-        # In a path, each element in the 3-tuple is itself a tuple of (x, y).
-        # Tuples all the way down.  Hasn't anyone heard of using classes?
-
-        path1 = csp[0]
-        path2 = csp[1]
-
-        threadcolor = simplestyle.parseStyle(node.get("style"))["stroke"]
-        patch = Patch(color=threadcolor)
-
-        def offset_points(pos1, pos2, offset_px):
-            # Expand or contract points.  This is useful for pull
-            # compensation and insetting underlay.
-
-            distance = (pos1 - pos2).length()
-
-            if (pos1 - pos2).length() < 0.0001:
-                # if they're the same, we don't know which direction
-                # to offset in, so we have to just return the points
-                return pos1, pos2
-
-            # if offset is negative, don't contract so far that pos1
-            # and pos2 switch places
-            if offset_px < -distance / 2.0:
-                offset_px = -distance / 2.0
-
-            midpoint = (pos2 + pos1) * 0.5
-            pos1 = pos1 + (pos1 - midpoint).unit() * offset_px
-            pos2 = pos2 + (pos2 - midpoint).unit() * offset_px
-
-            return pos1, pos2
-
-        def walk_paths(spacing, offset):
-            # Take a bezier segment from each path in turn, and plot out an
-            # equal number of points on each side.  Later code can alternate
-            # between these points to create satin stitch, underlay, etc.
-
-            side1 = []
-            side2 = []
-
-            def add_pair(pos1, pos2):
-                # Stitches in satin tend to pull toward each other.  We can compensate
-                # by spreading the points out.
-                pos1, pos2 = offset_points(pos1, pos2, offset)
-                side1.append(pos1)
-                side2.append(pos2)
-
-            remainder_path1 = []
-            remainder_path2 = []
-
-            for segment in xrange(1, len(path1)):
-                # construct the current bezier segments
-                bezier1 = (path1[segment - 1][1],  # point from previous 3-tuple
-                           path1[segment - 1][2],  # "after" control point from previous 3-tuple
-                           path1[segment][0],  # "before" control point from this 3-tuple
-                           path1[segment][1],  # point from this 3-tuple
-                           )
-
-                bezier2 = (path2[segment - 1][1],
-                           path2[segment - 1][2],
-                           path2[segment][0],
-                           path2[segment][1],
-                           )
-
-                # Here's what I want to be able to do.  However, beziertatlength is so incredibly slow that it's unusable.
-                # for stitch in xrange(num_zigzags):
-                #    patch.add_stitch(bezierpointatt(bezier1, beziertatlength(bezier1, stitch_len1 * stitch)))
-                #    patch.add_stitch(bezierpointatt(bezier2, beziertatlength(bezier2, stitch_len2 * (stitch + 0.5))))
-
-                # Instead, flatten the beziers down to a set of line segments.
-                subpath1 = remainder_path1 + flatten([[path1[segment - 1], path1[segment]]], self.options.flat)[0]
-                subpath2 = remainder_path2 + flatten([[path2[segment - 1], path2[segment]]], self.options.flat)[0]
-
-                len1 = shgeo.LineString(subpath1).length
-                len2 = shgeo.LineString(subpath2).length
-
-                subpath1 = [PyEmb.Point(*p) for p in subpath1]
-                subpath2 = [PyEmb.Point(*p) for p in subpath2]
-
-                # Base the number of stitches in each section on the _longest_ of
-                # the two beziers. Otherwise, things could get too sparse when one
-                # side is significantly longer (e.g. when going around a corner).
-                # The risk here is that we poke a hole in the fabric if we try to
-                # cram too many stitches on the short bezier.  The user will need
-                # to avoid this through careful construction of paths.
-                num_points = max(len1, len2) / spacing
-
-                spacing1 = len1 / num_points
-                spacing2 = len2 / num_points
-
-                def walk(path, start_pos, start_index, distance):
-                    # Move <distance> pixels along <path>'s line segments.
-                    # <start_index> is the index of the line segment in <path> that
-                    # we're currently on.  <start_pos> is where along that line
-                    # segment we are.  Return a new position and index.
-
-                    pos = start_pos
-                    index = start_index
-
-                    if index >= len(path) - 1:
-                        # it's possible we'll go too far due to inaccuracy in the
-                        # bezier length calculation
-                        return start_pos, start_index
-
-                    while True:
-                        segment_end = path[index + 1]
-                        segment_remaining = (segment_end - pos)
-                        distance_remaining = segment_remaining.length()
-
-                        if distance_remaining > distance:
-                            return pos + segment_remaining.unit().mul(distance), index
-                        else:
-                            index += 1
-
-                            if index >= len(path) - 1:
-                                return segment_end, index
-
-                            distance -= distance_remaining
-                            pos = segment_end
-
-                pos1 = subpath1[0]
-                i1 = 0
-
-                pos2 = subpath2[0]
-                i2 = 0
-
-    #            if num_zigzags >= 1.0:
-    #                for stitch in xrange(int(num_zigzags) + 1):
-                for i in xrange(int(num_points)):
-                    add_pair(pos1, pos2)
-
-                    pos2, i2 = walk(subpath2, pos2, i2, spacing2)
-                    pos1, i1 = walk(subpath1, pos1, i1, spacing1)
-
-                if i1 < len(subpath1) - 1:
-                    remainder_path1 = [pos1] + subpath1[i1 + 1:]
-                else:
-                    remainder_path1 = []
-
-                if i2 < len(subpath2) - 1:
-                    remainder_path2 = [pos2] + subpath2[i2 + 1:]
-                else:
-                    remainder_path2 = []
-
-                remainder_path1 = [p.as_tuple() for p in remainder_path1]
-                remainder_path2 = [p.as_tuple() for p in remainder_path2]
-
-            # We're off by one in the algorithm above, so we need one more
-            # pair of points.  We also want to add points at the very end to
-            # make sure we match the vectors on screen as best as possible.
-            # Try to avoid doing both if they're going to stack up too
-            # closely.
-
-            end1 = PyEmb.Point(*remainder_path1[-1])
-            end2 = PyEmb.Point(*remainder_path2[-1])
-            if (end1 - pos1).length() > 0.3 * spacing:
-                add_pair(pos1, pos2)
-
-            add_pair(end1, end2)
-
-            return [side1, side2]
-
-        def calculate_underlay(inset):
-            # "contour walk" underlay: do stitches up one side and down the
-            # other.
-            forward, back = walk_paths(underlay_stitch_len_px, -inset)
-            return Patch(color=threadcolor, stitches=(forward + list(reversed(back))))
-
-        def calculate_zigzag_underlay(zigzag_spacing, inset):
-            # zigzag underlay, usually done at a much lower density than the
-            # satin itself.  It looks like this:
-            #
-            # \/\/\/\/\/\/\/\/\/\/|
-            # /\/\/\/\/\/\/\/\/\/\|
-            #
-            # In combination with the "contour walk" underlay, this is the
-            # "German underlay" described here:
-            #   http://www.mrxstitch.com/underlay-what-lies-beneath-machine-embroidery/
-
-            patch = Patch(color=threadcolor)
-
-            sides = walk_paths(zigzag_spacing / 2.0, -inset)
-            sides = [sides[0][::2] + list(reversed(sides[0][1::2])), sides[1][1::2] + list(reversed(sides[1][::2]))]
-
-            # this fancy bit of iterable magic just repeatedly takes a point
-            # from each list in turn
-            for point in chain.from_iterable(izip(*sides)):
-                patch.add_stitch(point)
-
-            return patch
-
-        def calculate_satin(zigzag_spacing, pull_compensation):
-            # satin: do a zigzag pattern, alternating between the paths.  The
-            # zigzag looks like this:
-            #
-            # /|/|/|/|/|/|/|/|
-
-            patch = Patch(color=threadcolor)
-
-            sides = walk_paths(zigzag_spacing, pull_compensation)
-
-            for point in chain.from_iterable(izip(*sides)):
-                patch.add_stitch(point)
-
-            return patch
-
-        if center_walk:
-            # Center walk is a running stitch exactly between the paths, down
-            # and back.  It comes first.
-
-            # Bit of a hack: do it just like contour walk underlay but inset it
-            # really far.  The inset will be clamped to the center between the
-            # paths.
-            patch += calculate_underlay(10000)
-
-        if underlay:
-            # Now do the contour walk underlay.
-            patch += calculate_underlay(underlay_inset)
-
-        if zigzag_underlay_spacing:
-            # zigzag underlay comes after contour walk underlay, so that the
-            # zigzags sit on the contour walk underlay like rail ties on rails.
-            patch += calculate_zigzag_underlay(zigzag_underlay_spacing, zigzag_underlay_inset)
-
-        # Finally, add the satin itself.
-        patch += calculate_satin(zigzag_spacing_px, pull_compensation_px)
-
-        return [patch]
-
 if __name__ == '__main__':
     sys.setrecursionlimit(100000)
     e = Embroider()