# Copyright 2003-2008 by Leighton Pritchard.  All rights reserved.
# Revisions copyright 2008-2012 by Peter Cock.
# This code is part of the Biopython distribution and governed by its
# license.  Please see the LICENSE file that should have been included
# as part of this package.
#
# Contact:       Leighton Pritchard, Scottish Crop Research Institute,
#                Invergowrie, Dundee, Scotland, DD2 5DA, UK
#                L.Pritchard@scri.ac.uk
################################################################################

"""CircularDrawer module for GenomeDiagram."""

# ReportLab imports
from reportlab.graphics.shapes import *
from reportlab.lib import colors
from reportlab.pdfbase import _fontdata
from reportlab.graphics.shapes import ArcPath

# GenomeDiagram imports
from _AbstractDrawer import AbstractDrawer, draw_polygon, intermediate_points
from _AbstractDrawer import _stroke_and_fill_colors
from _FeatureSet import FeatureSet
from _GraphSet import GraphSet

from math import ceil, pi, cos, sin, asin


class CircularDrawer(AbstractDrawer):
    """Object for drawing circular diagrams.

        o __init__(self, ...) Called on instantiation

        o set_page_size(self, pagesize, orientation)    Set the page size to the
                                                    passed size and orientation

        o set_margins(self, x, y, xl, xr, yt, yb)   Set the drawable area of the
                                                    page

        o set_bounds(self, start, end)  Set the bounds for the elements to be
                                        drawn

        o is_in_bounds(self, value)     Returns a boolean for whether the position
                                        is actually to be drawn

        o __len__(self)     Returns the length of sequence that will be drawn


        o draw(self)    Place the drawing elements on the diagram

        o init_fragments(self)  Calculate information
                                about sequence fragment locations on the drawing

        o set_track_heights(self)   Calculate information about the offset of
                                    each track from the fragment base

        o draw_test_tracks(self)    Add lines demarcating each track to the
                                    drawing

        o draw_track(self, track)   Return the contents of the passed track as
                                    drawing elements

        o draw_scale(self, track)   Return a scale for the passed track as
                                    drawing elements

        o draw_greytrack(self, track)   Return a grey background and superposed
                                        label for the passed track as drawing
                                        elements

        o draw_feature_set(self, set)   Return the features in the passed set as
                                        drawing elements

        o draw_feature(self, feature)   Return a single feature as drawing
                                        elements

        o get_feature_sigil(self, feature, x0, x1, fragment)    Return a single
                                        feature as its sigil in drawing elements

        o draw_graph_set(self, set)     Return the data in a set of graphs as
                                        drawing elements

        o draw_line_graph(self, graph)  Return the data in a graph as a line
                                        graph in drawing elements

        o draw_heat_graph(self, graph)  Return the data in a graph as a heat
                                        graph in drawing elements

        o draw_bar_graph(self, graph)   Return the data in a graph as a bar
                                        graph in drawing elements

        o canvas_angle(self, base)      Return the angle, and cos and sin of
                                        that angle, subtended by the passed
                                        base position at the diagram center

        o draw_arc(self, inner_radius, outer_radius, startangle, endangle,
                    color)    Return a drawable element describing an arc

        Attributes:

        o tracklines    Boolean for whether to draw lines dilineating tracks

        o pagesize      Tuple describing the size of the page in pixels

        o x0            Float X co-ord for leftmost point of drawable area

        o xlim          Float X co-ord for rightmost point of drawable area

        o y0            Float Y co-ord for lowest point of drawable area

        o ylim          Float Y co-ord for topmost point of drawable area

        o pagewidth     Float pixel width of drawable area

        o pageheight    Float pixel height of drawable area

        o xcenter       Float X co-ord of center of drawable area

        o ycenter       Float Y co-ord of center of drawable area

        o start         Int, base to start drawing from

        o end           Int, base to stop drawing at

        o length        Size of sequence to be drawn

        o track_size    Float (0->1) the proportion of the track height to
                        draw in

        o drawing       Drawing canvas

        o drawn_tracks  List of ints denoting which tracks are to be drawn

        o current_track_level   Int denoting which track is currently being
                                drawn

        o track_offsets     Dictionary of number of pixels that each track top,
                            center and bottom is offset from the base of a
                            fragment, keyed by track

        o sweep     Float (0->1) the proportion of the circle circumference to
                    use for the diagram

        o cross_track_links List of tuples each with four entries (track A,
                            feature A, track B, feature B) to be linked.
    """
    def __init__(self, parent=None, pagesize='A3', orientation='landscape',
                 x=0.05, y=0.05, xl=None, xr=None, yt=None, yb=None,
                 start=None, end=None, tracklines=0, track_size=0.75,
                 circular=1, circle_core=0.0, cross_track_links=None):
        """Create CircularDrawer object.

            o parent    Diagram object containing the data that the drawer
                        draws

            o pagesize  String describing the ISO size of the image, or a tuple
                        of pixels

            o orientation   String describing the required orientation of the
                            final drawing ('landscape' or 'portrait')

            o x         Float (0->1) describing the relative size of the X
                        margins to the page

            o y         Float (0->1) describing the relative size of the Y
                        margins to the page

            o xl        Float (0->1) describing the relative size of the left X
                        margin to the page (overrides x)

            o xl        Float (0->1) describing the relative size of the left X
                        margin to the page (overrides x)

            o xr        Float (0->1) describing the relative size of the right X
                        margin to the page (overrides x)

            o yt        Float (0->1) describing the relative size of the top Y
                        margin to the page (overrides y)

            o yb        Float (0->1) describing the relative size of the lower Y
                        margin to the page (overrides y)

            o start     Int, the position to begin drawing the diagram at

            o end       Int, the position to stop drawing the diagram at

            o tracklines    Boolean flag to show (or not) lines delineating tracks
                            on the diagram

            o track_size    The proportion of the available track height that
                            should be taken up in drawing

            o circular      Boolean flaw to show whether the passed sequence is
                            circular or not

            o circle_core   The proportion of the available radius to leave
                            empty at the center of a circular diagram (0 to 1).

            o cross_track_links List of tuples each with four entries (track A,
                                feature A, track B, feature B) to be linked.
        """
        # Use the superclass' instantiation method
        AbstractDrawer.__init__(self, parent, pagesize, orientation,
                                  x, y, xl, xr, yt, yb, start, end,
                                  tracklines, cross_track_links)

        # Useful measurements on the page
        self.track_size = track_size
        self.circle_core = circle_core
        if not circular:   # Determine the proportion of the circumference
            self.sweep = 0.9    # around which information will be drawn
        else:
            self.sweep = 1

    def set_track_heights(self):
        """Initialise track heights.

        Since tracks may not be of identical heights, the bottom and top
        radius for each track is stored in a dictionary - self.track_radii,
        keyed by track number
        """
        bot_track = min(min(self.drawn_tracks), 1)
        top_track = max(self.drawn_tracks) # The 'highest' track to draw

        trackunit_sum = 0 # Total number of 'units' taken up by all tracks
        trackunits = {} # Start and & units for each track keyed by track number
        heightholder = 0  # placeholder variable
        for track in range(bot_track, top_track+1): # track numbers to 'draw'
            try:
                trackheight = self._parent[track].height # Get track height
            except:
                trackheight = 1
            trackunit_sum += trackheight # increment total track unit height
            trackunits[track] = (heightholder, heightholder+trackheight)
            heightholder += trackheight # move to next height

        max_radius = 0.5*min(self.pagewidth, self.pageheight)
        trackunit_height = max_radius * (1 - self.circle_core) / trackunit_sum
        track_core = max_radius * self.circle_core

        # Calculate top and bottom radii for each track
        self.track_radii = {} # The inner, outer and center radii for each track
        track_crop = trackunit_height*(1-self.track_size)/2. # 'step back' in pixels
        for track in trackunits:
            top = trackunits[track][1]*trackunit_height - track_crop + track_core
            btm = trackunits[track][0]*trackunit_height + track_crop + track_core
            ctr = btm+(top-btm)/2.
            self.track_radii[track] = (btm, ctr, top)

    def draw(self):
        """Draw a circular diagram of the stored data."""
        # Instantiate the drawing canvas
        self.drawing = Drawing(self.pagesize[0], self.pagesize[1])

        feature_elements = []           # holds feature elements
        feature_labels = []             # holds feature labels
        greytrack_bgs = []              # holds track background
        greytrack_labels = []           # holds track foreground labels
        scale_axes = []                 # holds scale axes
        scale_labels = []               # holds scale axis labels

        # Get tracks to be drawn and set track sizes
        self.drawn_tracks = self._parent.get_drawn_levels()
        self.set_track_heights()

        # Go through each track in the parent (if it is to be drawn) one by
        # one and collate the data as drawing elements
        for track_level in self._parent.get_drawn_levels():
            self.current_track_level = track_level
            track = self._parent[track_level]
            gbgs, glabels = self.draw_greytrack(track)    # Greytracks
            greytrack_bgs.append(gbgs)
            greytrack_labels.append(glabels)
            features, flabels = self.draw_track(track)   # Features and graphs
            feature_elements.append(features)
            feature_labels.append(flabels)
            if track.scale:
                axes, slabels = self.draw_scale(track)       # Scale axes
                scale_axes.append(axes)
                scale_labels.append(slabels)

        feature_cross_links = []
        for cross_link_obj in self.cross_track_links:
            cross_link_elements = self.draw_cross_link(cross_link_obj)
            if cross_link_elements:
                feature_cross_links.append(cross_link_elements)

        # Groups listed in order of addition to page (from back to front)
        # Draw track backgrounds
        # Draw feature cross track links
        # Draw features and graphs
        # Draw scale axes
        # Draw scale labels
        # Draw feature labels
        # Draw track labels
        element_groups = [greytrack_bgs, feature_cross_links,
                          feature_elements,
                          scale_axes, scale_labels,
                          feature_labels, greytrack_labels
                          ]
        for element_group in element_groups:
            for element_list in element_group:
                [self.drawing.add(element) for element in element_list]

        if self.tracklines:
            # Draw test tracks over top of diagram
            self.draw_test_tracks()

    def draw_track(self, track):
        """Returns list of track elements and list of track labels."""
        track_elements = [] # Holds elements for features and graphs
        track_labels = []   # Holds labels for features and graphs

        # Distribution dictionary for dealing with different set types
        set_methods = {FeatureSet: self.draw_feature_set,
                       GraphSet: self.draw_graph_set
                       }

        for set in track.get_sets(): # Draw the feature or graph sets
            elements, labels = set_methods[set.__class__](set)
            track_elements += elements
            track_labels += labels
        return track_elements, track_labels

    def draw_feature_set(self, set):
        """Returns list of feature elements and list of labels for them."""
        #print 'draw feature set'
        feature_elements = [] # Holds diagram elements belonging to the features
        label_elements = []   # Holds diagram elements belonging to feature labels

        # Collect all the elements for the feature set
        for feature in set.get_features():
            if self.is_in_bounds(feature.start) or self.is_in_bounds(feature.end):
                features, labels = self.draw_feature(feature)
                feature_elements += features
                label_elements += labels

        return feature_elements, label_elements

    def draw_feature(self, feature):
        """Returns list of feature elements and list of labels for them."""
        feature_elements = [] # Holds drawable elements for a single feature
        label_elements = []   # Holds labels for a single feature

        if feature.hide:    # Don't show feature: return early
            return feature_elements, label_elements

        start, end = self._current_track_start_end()
        # A single feature may be split into subfeatures, so loop over them
        for locstart, locend in feature.locations:
            if locend < start:
                continue
            locstart = max(locstart, start)
            if end < locstart:
                continue
            locend = min(locend, end)
            # Get sigil for the feature/ each subfeature
            feature_sigil, label = self.get_feature_sigil(feature, locstart, locend)
            feature_elements.append(feature_sigil)
            if label is not None:   # If there's a label
                label_elements.append(label)

        return feature_elements, label_elements

    def get_feature_sigil(self, feature, locstart, locend, **kwargs):
        """Returns graphics for feature, and any required label for it.

            o feature       Feature object

            o locstart      The start position of the feature

            o locend        The end position of the feature
        """
        # Establish the co-ordinates for the sigil
        btm, ctr, top = self.track_radii[self.current_track_level]

        startangle, startcos, startsin = self.canvas_angle(locstart)
        endangle, endcos, endsin = self.canvas_angle(locend)
        midangle, midcos, midsin = self.canvas_angle(float(locend+locstart)/2)

        # Distribution dictionary for various ways of drawing the feature
        # Each method takes the inner and outer radii, the start and end angle
        # subtended at the diagram center, and the color as arguments
        draw_methods = {'BOX': self._draw_sigil_box,
                        'OCTO': self._draw_sigil_cut_corner_box,
                        'JAGGY': self._draw_sigil_jaggy,
                        'ARROW': self._draw_sigil_arrow,
                        'BIGARROW': self._draw_sigil_big_arrow,
                        }

        # Get sigil for the feature, location dependent on the feature strand
        method = draw_methods[feature.sigil]
        kwargs['head_length_ratio'] = feature.arrowhead_length
        kwargs['shaft_height_ratio'] = feature.arrowshaft_height

        #Support for clickable links... needs ReportLab 2.4 or later
        #which added support for links in SVG output.
        if hasattr(feature, "url") :
            kwargs["hrefURL"] = feature.url
            kwargs["hrefTitle"] = feature.name

        sigil = method(btm, ctr, top, startangle, endangle, feature.strand,
                       color=feature.color, border=feature.border, **kwargs)

        if feature.label:   # Feature needs a label
            #The spaces are a hack to force a little space between the label
            #and the edge of the feature
            label = String(0, 0, " %s " % feature.name.strip(),
                           fontName=feature.label_font,
                           fontSize=feature.label_size,
                           fillColor=feature.label_color)
            labelgroup = Group(label)
            if feature.label_strand:
                strand = feature.label_strand
            else:
                strand = feature.strand
            if feature.label_position in ('start', "5'", 'left'):
                # Position the label at the feature's start
                if strand != -1:
                    label_angle = startangle + 0.5 * pi # Make text radial
                    sinval, cosval = startsin, startcos
                else:
                    label_angle = endangle + 0.5 * pi # Make text radial
                    sinval, cosval = endsin, endcos
            elif feature.label_position in ('middle', 'center', 'centre'):
                # Position the label at the feature's midpoint
                label_angle = midangle + 0.5 * pi # Make text radial
                sinval, cosval = midsin, midcos
            elif feature.label_position in ('end', "3'", 'right'):
                # Position the label at the feature's end
                if strand != -1:
                    label_angle = endangle + 0.5 * pi # Make text radial
                    sinval, cosval = endsin, endcos
                else:
                    label_angle = startangle + 0.5 * pi # Make text radial
                    sinval, cosval = startsin, startcos
            elif startangle < pi:
                # Default to placing the label the bottom of the feature
                # as drawn on the page, meaning feature end on left half
                label_angle = endangle + 0.5 * pi # Make text radial
                sinval, cosval = endsin,endcos
            else:
                # Default to placing the label on the bottom of the feature,
                # which means the feature end when on right hand half
                label_angle = startangle + 0.5 * pi # Make text radial
                sinval, cosval = startsin, startcos
            if strand != -1:
                # Feature label on top
                radius = top
                if startangle < pi: # Turn text round
                    label_angle -= pi
                else:
                    labelgroup.contents[0].textAnchor = 'end'
            else:
                # Feature label on bottom
                radius = btm
                if startangle < pi: # Turn text round and anchor end
                    label_angle -= pi
                    labelgroup.contents[0].textAnchor = 'end'
            x_pos = self.xcenter + radius*sinval
            y_pos = self.ycenter + radius*cosval
            coslabel = cos(label_angle)
            sinlabel = sin(label_angle)
            labelgroup.transform = (coslabel, -sinlabel, sinlabel, coslabel,
                                    x_pos, y_pos)
        else:
            # No label required
            labelgroup = None
        #if locstart > locend:
        #    print locstart, locend, feature.strand, sigil, feature.name
        #print locstart, locend, feature.name
        return sigil, labelgroup

    def draw_cross_link(self, cross_link):
        startA = cross_link.startA
        startB = cross_link.startB
        endA = cross_link.endA
        endB = cross_link.endB

        if not self.is_in_bounds(startA) \
        and not self.is_in_bounds(endA):
            return None
        if not self.is_in_bounds(startB) \
        and not self.is_in_bounds(endB):
            return None

        if startA < self.start:
            startA = self.start
        if startB < self.start:
            startB = self.start
        if self.end < endA:
            endA = self.end
        if self.end < endB:
            endB = self.end

        trackobjA = cross_link._trackA(self._parent.tracks.values())
        trackobjB = cross_link._trackB(self._parent.tracks.values())
        assert trackobjA is not None
        assert trackobjB is not None
        if trackobjA == trackobjB:
            raise NotImplementedError()

        if trackobjA.start is not None:
            if endA < trackobjA.start:
                return
            startA = max(startA, trackobjA.start)
        if trackobjA.end is not None:
            if trackobjA.end < startA:
                return
            endA = min(endA, trackobjA.end)
        if trackobjB.start is not None:
            if endB < trackobjB.start:
                return
            startB = max(startB, trackobjB.start)
        if trackobjB.end is not None:
            if trackobjB.end < startB:
                return
            endB = min(endB, trackobjB.end)

        for track_level in self._parent.get_drawn_levels():
            track = self._parent[track_level]
            if track == trackobjA:
                trackA = track_level
            if track == trackobjB:
                trackB = track_level
        if trackA == trackB:
            raise NotImplementedError()

        startangleA, startcosA, startsinA = self.canvas_angle(startA)
        startangleB, startcosB, startsinB = self.canvas_angle(startB)
        endangleA, endcosA, endsinA = self.canvas_angle(endA)
        endangleB, endcosB, endsinB = self.canvas_angle(endB)

        btmA, ctrA, topA = self.track_radii[trackA]
        btmB, ctrB, topB = self.track_radii[trackB]

        if ctrA < ctrB:
            return [self._draw_arc_poly(topA, btmB,
                           startangleA, endangleA,
                           startangleB, endangleB,
                           cross_link.color, cross_link.border, cross_link.flip)]
        else:
            return [self._draw_arc_poly(btmA, topB,
                           startangleA, endangleA,
                           startangleB, endangleB,
                           cross_link.color, cross_link.border, cross_link.flip)]

    def draw_graph_set(self, set):
        """Returns list of graph elements and list of their labels.

            o set       GraphSet object
        """
        #print 'draw graph set'
        elements = [] # Holds graph elements

        # Distribution dictionary for how to draw the graph
        style_methods = {'line': self.draw_line_graph,
                         'heat': self.draw_heat_graph,
                         'bar': self.draw_bar_graph
                         }

        for graph in set.get_graphs():
            elements += style_methods[graph.style](graph)

        return elements, []

    def draw_line_graph(self, graph):
        """Returns line graph as list of drawable elements.

            o graph     GraphData object
        """
        line_elements = [] # holds drawable elements

        # Get graph data
        data_quartiles = graph.quartiles()
        minval, maxval = data_quartiles[0],data_quartiles[4]
        btm, ctr, top = self.track_radii[self.current_track_level]
        trackheight = 0.5*(top-btm)
        datarange = maxval - minval
        if datarange == 0:
            datarange = trackheight

        start, end = self._current_track_start_end()
        data = graph[start:end]

        if not data:
            return []

        # midval is the value at which the x-axis is plotted, and is the
        # central ring in the track
        if graph.center is None:
            midval = (maxval + minval)/2.
        else:
            midval = graph.center
        # Whichever is the greatest difference: max-midval or min-midval, is
        # taken to specify the number of pixel units resolved along the
        # y-axis
        resolution = max((midval-minval), (maxval-midval))

        # Start from first data point
        pos, val = data[0]
        lastangle, lastcos, lastsin = self.canvas_angle(pos)
        # We calculate the track height
        posheight = trackheight*(val-midval)/resolution + ctr
        lastx = self.xcenter+posheight*lastsin  # start xy coords
        lasty = self.ycenter+posheight*lastcos
        for pos, val in data:
            posangle, poscos, possin = self.canvas_angle(pos)
            posheight = trackheight*(val-midval)/resolution + ctr
            x = self.xcenter+posheight*possin   # next xy coords
            y = self.ycenter+posheight*poscos
            line_elements.append(Line(lastx, lasty, x, y,
                                      strokeColor = graph.poscolor,
                                      strokeWidth = graph.linewidth))
            lastx, lasty, = x, y
        return line_elements

    def draw_bar_graph(self, graph):
        """Returns list of drawable elements for a bar graph.

            o graph     Graph object
        """
        # At each point contained in the graph data, we draw a vertical bar
        # from the track center to the height of the datapoint value (positive
        # values go up in one color, negative go down in the alternative
        # color).
        bar_elements = []

        # Set the number of pixels per unit for the data
        data_quartiles = graph.quartiles()
        minval, maxval = data_quartiles[0],data_quartiles[4]
        btm, ctr, top = self.track_radii[self.current_track_level]
        trackheight = 0.5*(top-btm)
        datarange = maxval - minval
        if datarange == 0:
            datarange = trackheight
        data = graph[self.start:self.end]
        # midval is the value at which the x-axis is plotted, and is the
        # central ring in the track
        if graph.center is None:
            midval = (maxval + minval)/2.
        else:
            midval = graph.center

        # Convert data into 'binned' blocks, covering half the distance to the
        # next data point on either side, accounting for the ends of fragments
        # and tracks
        start, end = self._current_track_start_end()
        data = intermediate_points(start, end, graph[start:end])

        if not data:
            return []

        # Whichever is the greatest difference: max-midval or min-midval, is
        # taken to specify the number of pixel units resolved along the
        # y-axis
        resolution = max((midval-minval), (maxval-midval))
        if resolution == 0:
            resolution = trackheight

        # Create elements for the bar graph based on newdata
        for pos0, pos1, val in data:
            pos0angle, pos0cos, pos0sin = self.canvas_angle(pos0)
            pos1angle, pos1cos, pos1sin = self.canvas_angle(pos1)

            barval = trackheight*(val-midval)/resolution
            if barval >=0:
                barcolor = graph.poscolor
            else:
                barcolor = graph.negcolor

            # Draw bar
            bar_elements.append(self._draw_arc(ctr, ctr+barval, pos0angle,
                                              pos1angle, barcolor))
        return bar_elements

    def draw_heat_graph(self, graph):
        """Returns list of drawable elements for the heat graph.

            o graph     Graph object
        """
        # At each point contained in the graph data, we draw a box that is the
        # full height of the track, extending from the midpoint between the
        # previous and current data points to the midpoint between the current
        # and next data points
        heat_elements = [] # holds drawable elements

        # Get graph data
        data_quartiles = graph.quartiles()
        minval, maxval = data_quartiles[0],data_quartiles[4]
        midval = (maxval + minval)/2. # mid is the value at the X-axis
        btm, ctr, top = self.track_radii[self.current_track_level]
        trackheight = (top-btm)

        start, end = self._current_track_start_end()
        data = intermediate_points(start, end, graph[start:end])

        # Create elements on the graph, indicating a large positive value by
        # the graph's poscolor, and a large negative value by the graph's
        # negcolor attributes
        for pos0, pos1, val in data:
            pos0angle, pos0cos, pos0sin = self.canvas_angle(pos0)
            pos1angle, pos1cos, pos1sin = self.canvas_angle(pos1)

            # Calculate the heat color, based on the differential between
            # the value and the median value
            heat = colors.linearlyInterpolatedColor(graph.poscolor,
                                                    graph.negcolor,
                                                    maxval, minval, val)

            # Draw heat box
            heat_elements.append(self._draw_arc(btm, top, pos0angle, pos1angle,
                                                heat, border=heat))
        return heat_elements

    def draw_scale(self, track):
        """Returns list of elements in the scale and list of their labels.

            o track     Track object
        """
        scale_elements = [] # holds axes and ticks
        scale_labels = [] # holds labels

        if not track.scale:
            # no scale required, exit early
            return [], []

        # Get track locations
        btm, ctr, top = self.track_radii[self.current_track_level]
        trackheight = (top-ctr)

        # X-axis
        start, end = self._current_track_start_end()
        if track.start is not None or track.end is not None:
            # Draw an arc, leaving out the wedge
            p = ArcPath(strokeColor=track.scale_color, fillColor=None)
            startangle, startcos, startsin = self.canvas_angle(start)
            endangle, endcos, endsin = self.canvas_angle(end)
            p.addArc(self.xcenter, self.ycenter, ctr,
                     90 - (endangle * 180 / pi),
                     90 - (startangle * 180 / pi))
            scale_elements.append(p)
            del p
            # Y-axis start marker
            x0, y0 = self.xcenter+btm*startsin, self.ycenter+btm*startcos
            x1, y1 = self.xcenter+top*startsin, self.ycenter+top*startcos
            scale_elements.append(Line(x0, y0, x1, y1, strokeColor=track.scale_color))
            # Y-axis end marker
            x0, y0 = self.xcenter+btm*endsin, self.ycenter+btm*endcos
            x1, y1 = self.xcenter+top*endsin, self.ycenter+top*endcos
            scale_elements.append(Line(x0, y0, x1, y1, strokeColor=track.scale_color))
        elif self.sweep < 1:
            # Draw an arc, leaving out the wedge
            p = ArcPath(strokeColor=track.scale_color, fillColor=None)
            # Note reportlab counts angles anti-clockwise from the horizontal
            # (as in mathematics, e.g. complex numbers and polar coordinates)
            # in degrees.
            p.addArc(self.xcenter, self.ycenter, ctr,
                     startangledegrees=90-360*self.sweep,
                     endangledegrees=90)
            scale_elements.append(p)
            del p
            # Y-axis start marker
            x0, y0 = self.xcenter, self.ycenter+btm
            x1, y1 = self.xcenter, self.ycenter+top
            scale_elements.append(Line(x0, y0, x1, y1, strokeColor=track.scale_color))
            # Y-axis end marker
            alpha = 2*pi*self.sweep
            x0, y0 = self.xcenter+btm*sin(alpha), self.ycenter+btm*cos(alpha)
            x1, y1 = self.xcenter+top*sin(alpha), self.ycenter+top*cos(alpha)
            scale_elements.append(Line(x0, y0, x1, y1, strokeColor=track.scale_color))
        else:
            # Draw a full circle
            scale_elements.append(Circle(self.xcenter, self.ycenter, ctr,
                                         strokeColor=track.scale_color,
                                         fillColor=None))

        start, end = self._current_track_start_end()
        if track.scale_ticks: # Ticks are required on the scale
            # Draw large ticks
            # I want the ticks to be consistently positioned relative to
            # the start of the sequence (position 0), not relative to the
            # current viewpoint (self.start and self.end)

            ticklen = track.scale_largeticks * trackheight
            tickiterval = int(track.scale_largetick_interval)
            # Note that we could just start the list of ticks using
            # range(0,self.end,tickinterval) and the filter out the
            # ones before self.start - but this seems wasteful.
            # Using tickiterval * (self.start/tickiterval) is a shortcut.
            for tickpos in range(tickiterval * (self.start//tickiterval),
                                 int(self.end), tickiterval):
                if tickpos <= start or end <= tickpos:
                    continue
                tick, label = self.draw_tick(tickpos, ctr, ticklen,
                                             track,
                                             track.scale_largetick_labels)
                scale_elements.append(tick)
                if label is not None: # If there's a label, add it
                    scale_labels.append(label)
            # Draw small ticks
            ticklen = track.scale_smallticks * trackheight
            tickiterval = int(track.scale_smalltick_interval)
            for tickpos in range(tickiterval * (self.start//tickiterval),
                                 int(self.end), tickiterval):
                if tickpos <= start or end <= tickpos:
                    continue
                tick, label = self.draw_tick(tickpos, ctr, ticklen,
                                             track,
                                             track.scale_smalltick_labels)
                scale_elements.append(tick)
                if label is not None: # If there's a label, add it
                    scale_labels.append(label)

        # Check to see if the track contains a graph - if it does, get the
        # minimum and maximum values, and put them on the scale Y-axis
        # at 60 degree intervals, ordering the labels by graph_id
        startangle, startcos, startsin = self.canvas_angle(start)
        endangle, endcos, endsin = self.canvas_angle(end)
        if track.axis_labels:
            for set in track.get_sets():
                if set.__class__ is GraphSet:
                    # Y-axis
                    for n in xrange(7):
                        angle = n * 1.0471975511965976
                        if angle < startangle or endangle < angle:
                            continue
                        ticksin, tickcos = sin(angle), cos(angle)
                        x0, y0 = self.xcenter+btm*ticksin, self.ycenter+btm*tickcos
                        x1, y1 = self.xcenter+top*ticksin, self.ycenter+top*tickcos
                        scale_elements.append(Line(x0, y0, x1, y1,
                                                   strokeColor=track.scale_color))

                        graph_label_min = []
                        graph_label_max = []
                        graph_label_mid = []
                        for graph in set.get_graphs():
                            quartiles = graph.quartiles()
                            minval, maxval = quartiles[0], quartiles[4]
                            if graph.center is None:
                                midval = (maxval + minval)/2.
                                graph_label_min.append("%.3f" % minval)
                                graph_label_max.append("%.3f" % maxval)
                                graph_label_mid.append("%.3f" % midval)
                            else:
                                diff = max((graph.center-minval),
                                           (maxval-graph.center))
                                minval = graph.center-diff
                                maxval = graph.center+diff
                                midval = graph.center
                                graph_label_mid.append("%.3f" % midval)
                                graph_label_min.append("%.3f" % minval)
                                graph_label_max.append("%.3f" % maxval)
                        xmid, ymid = (x0+x1)/2., (y0+y1)/2.
                        for limit, x, y, in [(graph_label_min, x0, y0),
                                             (graph_label_max, x1, y1),
                                             (graph_label_mid, xmid, ymid)]:
                            label = String(0, 0, ";".join(limit),
                                           fontName=track.scale_font,
                                           fontSize=track.scale_fontsize,
                                           fillColor=track.scale_color)
                            label.textAnchor = 'middle'
                            labelgroup = Group(label)
                            labelgroup.transform = (tickcos, -ticksin,
                                                    ticksin, tickcos,
                                                    x, y)
                            scale_labels.append(labelgroup)

        return scale_elements, scale_labels

    def draw_tick(self, tickpos, ctr, ticklen, track, draw_label):
        """Returns drawing element for a tick on the scale.

            o tickpos   Int, position of the tick on the sequence

            o ctr       Float, Y co-ord of the center of the track

            o ticklen   How long to draw the tick

            o track     Track, the track the tick is drawn on

            o draw_label    Boolean, write the tick label?
        """
        # Calculate tick co-ordinates
        tickangle, tickcos, ticksin = self.canvas_angle(tickpos)
        x0, y0 = self.xcenter+ctr*ticksin, self.ycenter+ctr*tickcos
        x1, y1 = self.xcenter+(ctr+ticklen)*ticksin, self.ycenter+(ctr+ticklen)*tickcos
        # Calculate height of text label so it can be offset on lower half
        # of diagram
        # LP: not used, as not all fonts have ascent_descent data in reportlab.pdfbase._fontdata
        #label_offset = _fontdata.ascent_descent[track.scale_font][0]*\
        #               track.scale_fontsize/1000.
        tick = Line(x0, y0, x1, y1, strokeColor=track.scale_color)
        if draw_label:
            # Put tick position on as label
            if track.scale_format == 'SInt':
                if tickpos >= 1000000:
                    tickstring = str(tickpos//1000000) + " Mbp"
                elif tickpos >= 1000:
                    tickstring = str(tickpos//1000) + " Kbp"
                else:
                    tickstring = str(tickpos)
            else:
                tickstring = str(tickpos)
            label = String(0, 0, tickstring, # Make label string
                           fontName=track.scale_font,
                           fontSize=track.scale_fontsize,
                           fillColor=track.scale_color)
            if tickangle > pi:
                label.textAnchor = 'end'
            # LP: This label_offset depends on ascent_descent data, which is not available for all
            # fonts, so has been deprecated.
            #if 0.5*pi < tickangle < 1.5*pi:
            #    y1 -= label_offset
            labelgroup = Group(label)
            labelgroup.transform = (1,0,0,1, x1, y1)
        else:
            labelgroup = None
        return tick, labelgroup

    def draw_test_tracks(self):
        """Draw blue test tracks with grene line down their center."""
        # Add lines only for drawn tracks
        for track in self.drawn_tracks:
            btm, ctr, top = self.track_radii[track]
            self.drawing.add(Circle(self.xcenter, self.ycenter, top,
                                    strokeColor=colors.blue,
                                    fillColor=None))  # top line
            self.drawing.add(Circle(self.xcenter, self.ycenter, ctr,
                                    strokeColor=colors.green,
                                    fillColor=None))  # middle line
            self.drawing.add(Circle(self.xcenter, self.ycenter, btm,
                                    strokeColor=colors.blue,
                                    fillColor=None))  # bottom line

    def draw_greytrack(self, track):
        """Drawing element for grey background to passed track.

            o track     Track object
        """
        greytrack_bgs = [] # Holds track backgrounds
        greytrack_labels = [] # Holds track foreground labels

        if not track.greytrack: # No greytrack required, return early
            return [], []

        # Get track location
        btm, ctr, top = self.track_radii[self.current_track_level]

        start, end = self._current_track_start_end()
        startangle, startcos, startsin = self.canvas_angle(start)
        endangle, endcos, endsin = self.canvas_angle(end)

        # Make background
        if track.start is not None or track.end is not None:
            # Draw an arc, leaving out the wedge
            p = ArcPath(strokeColor=track.scale_color, fillColor=None)
            greytrack_bgs.append(self._draw_arc(btm, top, startangle, endangle,
                                 colors.Color(0.96, 0.96, 0.96)))
        elif self.sweep < 1:
            # Make a partial circle, a large arc box
            # This method assumes the correct center for us.
            greytrack_bgs.append(self._draw_arc(btm, top, 0, 2*pi*self.sweep,
                                 colors.Color(0.96, 0.96, 0.96)))
        else:
            # Make a full circle (using a VERY thick linewidth)
            greytrack_bgs.append(Circle(self.xcenter, self.ycenter, ctr,
                                 strokeColor = colors.Color(0.96, 0.96, 0.96),
                                 fillColor=None, strokeWidth=top-btm))

        if track.greytrack_labels:
            # Labels are required for this track
            labelstep = self.length//track.greytrack_labels  # label interval
            for pos in range(self.start, self.end, labelstep):
                label = String(0, 0, track.name,            # Add a new label at
                           fontName=track.greytrack_font,   # each interval
                           fontSize=track.greytrack_fontsize,
                           fillColor=track.greytrack_fontcolor)
                theta, costheta, sintheta = self.canvas_angle(pos)
                if theta < startangle or endangle < theta:
                    continue
                x,y = self.xcenter+btm*sintheta, self.ycenter+btm*costheta  # start text halfway up marker
                labelgroup = Group(label)
                labelangle = self.sweep*2*pi*(pos-self.start)/self.length - pi/2
                if theta > pi:
                    label.textAnchor = 'end'    # Anchor end of text to inner radius
                    labelangle += pi            # and reorient it
                cosA, sinA = cos(labelangle), sin(labelangle)
                labelgroup.transform = (cosA, -sinA, sinA,
                                        cosA, x, y)
                if not self.length-x <= labelstep:  # Don't overrun the circle
                    greytrack_labels.append(labelgroup)

        return greytrack_bgs, greytrack_labels

    def canvas_angle(self, base):
        """Given base-pair position, return (angle, cosine, sin)."""
        angle = self.sweep*2*pi*(base-self.start)/self.length
        return (angle, cos(angle), sin(angle))

    def _draw_sigil_box(self, bottom, center, top,
                        startangle, endangle, strand,
                        **kwargs):
        """Draw BOX sigil."""
        if strand == 1:
            inner_radius = center
            outer_radius = top
        elif strand == -1:
            inner_radius = bottom
            outer_radius = center
        else:
            inner_radius = bottom
            outer_radius = top
        return self._draw_arc(inner_radius, outer_radius, startangle, endangle, **kwargs)

    def _draw_arc(self, inner_radius, outer_radius, startangle, endangle,
                 color, border=None, colour=None, **kwargs):
        """Returns close path describing an arc box.

            o inner_radius  Float distance of inside of arc from drawing center

            o outer_radius  Float distance of outside of arc from drawing center

            o startangle    Float angle subtended by start of arc at drawing center
                            (in radians)

            o endangle      Float angle subtended by end of arc at drawing center
                            (in radians)

            o color        colors.Color object for arc (overridden by backwards
                           compatible argument with UK spelling, colour).

        Returns a closed path object describing an arced box corresponding to
        the passed values.  For very small angles, a simple four sided
        polygon is used.
        """
        # Let the UK spelling (colour) override the USA spelling (color)
        if colour is not None:
            color = colour

        strokecolor, color = _stroke_and_fill_colors(color, border)

        if abs(float(endangle - startangle))>.01:
            # Wide arc, must use full curves
            p = ArcPath(strokeColor=strokecolor,
                        fillColor=color,
                        strokewidth=0)
            # Note reportlab counts angles anti-clockwise from the horizontal
            # (as in mathematics, e.g. complex numbers and polar coordinates)
            # but we use clockwise from the vertical.  Also reportlab uses
            # degrees, but we use radians.
            p.addArc(self.xcenter, self.ycenter, inner_radius,
                     90 - (endangle * 180 / pi), 90 - (startangle * 180 / pi),
                     moveTo=True)
            p.addArc(self.xcenter, self.ycenter, outer_radius,
                     90 - (endangle * 180 / pi), 90 - (startangle * 180 / pi),
                     reverse=True)
            p.closePath()
            return p
        else:
            # Cheat and just use a four sided polygon.
            # Calculate trig values for angle and coordinates
            startcos, startsin = cos(startangle), sin(startangle)
            endcos, endsin = cos(endangle), sin(endangle)
            x0,y0 = self.xcenter, self.ycenter # origin of the circle
            x1,y1 = (x0+inner_radius*startsin, y0+inner_radius*startcos)
            x2,y2 = (x0+inner_radius*endsin, y0+inner_radius*endcos)
            x3,y3 = (x0+outer_radius*endsin, y0+outer_radius*endcos)
            x4,y4 = (x0+outer_radius*startsin, y0+outer_radius*startcos)
            return draw_polygon([(x1,y1),(x2,y2),(x3,y3),(x4,y4)], color, border)

    def _draw_arc_line(self, path, start_radius, end_radius, start_angle, end_angle,
                       move=False):
        """Adds a list of points to a path object.

        Assumes angles given are in degrees!

        Represents what would be a straight line on a linear diagram.
        """
        x0, y0 = self.xcenter, self.ycenter # origin of the circle
        radius_diff = end_radius - start_radius
        angle_diff = end_angle - start_angle
        dx = 0.01 # heuristic
        a = start_angle*pi/180
        if move:
            path.moveTo(x0+start_radius*cos(a), y0+start_radius*sin(a))
        else:
            path.lineTo(x0+start_radius*cos(a), y0+start_radius*sin(a))
        x = dx
        if 0.01 <= abs(dx):
            while x < 1:
                r = start_radius + x*radius_diff
                a = (start_angle + x * (angle_diff)) * pi / 180  # to radians for sin/cos
                #print x0+r*cos(a), y0+r*sin(a)
                path.lineTo(x0+r*cos(a), y0+r*sin(a))
                x += dx
        a = end_angle*pi/180
        path.lineTo(x0+end_radius*cos(a), y0+end_radius*sin(a))

    def _draw_arc_poly(self, inner_radius, outer_radius,
                       inner_startangle, inner_endangle,
                       outer_startangle, outer_endangle,
                       color, border=None, flip=False,
                       **kwargs):
        """Returns polygon path describing an arc."""
        strokecolor, color = _stroke_and_fill_colors(color, border)

        x0, y0 = self.xcenter, self.ycenter      # origin of the circle
        if abs(inner_endangle - outer_startangle)>0.01 \
        or abs(outer_endangle - inner_startangle)>0.01 \
        or abs(inner_startangle - outer_startangle)>0.01 \
        or abs(outer_startangle - outer_startangle)>0.01:
            # Wide arc, must use full curves
            p = ArcPath(strokeColor=strokecolor,
                        fillColor=color,
                        #default is mitre/miter which can stick out too much:
                        strokeLineJoin=1,  # 1=round
                        strokewidth=0)
            #Note reportlab counts angles anti-clockwise from the horizontal
            #(as in mathematics, e.g. complex numbers and polar coordinates)
            #but we use clockwise from the vertical.  Also reportlab uses
            #degrees, but we use radians.
            i_start = 90 - (inner_startangle * 180 / pi)
            i_end = 90 - (inner_endangle * 180 / pi)
            o_start = 90 - (outer_startangle * 180 / pi)
            o_end = 90 - (outer_endangle * 180 / pi)
            p.addArc(x0, y0, inner_radius, i_end, i_start,
                     moveTo=True, reverse=True)
            if flip:
                #Flipped, join end to start,
                self._draw_arc_line(p, inner_radius, outer_radius, i_end, o_start)
                p.addArc(x0, y0, outer_radius, o_end, o_start, reverse=True)
                self._draw_arc_line(p, outer_radius, inner_radius, o_end, i_start)
            else:
                #Not flipped, join start to start, end to end
                self._draw_arc_line(p, inner_radius, outer_radius, i_end, o_end)
                p.addArc(x0, y0, outer_radius, o_end, o_start,
                         reverse=False)
                self._draw_arc_line(p, outer_radius, inner_radius, o_start, i_start)
            p.closePath()
            return p
        else:
            #Cheat and just use a four sided polygon.
            # Calculate trig values for angle and coordinates
            inner_startcos, inner_startsin = cos(inner_startangle), sin(inner_startangle)
            inner_endcos, inner_endsin = cos(inner_endangle), sin(inner_endangle)
            outer_startcos, outer_startsin = cos(outer_startangle), sin(outer_startangle)
            outer_endcos, outer_endsin = cos(outer_endangle), sin(outer_endangle)
            x1,y1 = (x0+inner_radius*inner_startsin, y0+inner_radius*inner_startcos)
            x2,y2 = (x0+inner_radius*inner_endsin, y0+inner_radius*inner_endcos)
            x3,y3 = (x0+outer_radius*outer_endsin, y0+outer_radius*outer_endcos)
            x4,y4 = (x0+outer_radius*outer_startsin, y0+outer_radius*outer_startcos)
            return draw_polygon([(x1,y1),(x2,y2),(x3,y3),(x4,y4)], color, border,
                                #default is mitre/miter which can stick out too much:
                                strokeLineJoin=1,  # 1=round
                                )

    def _draw_sigil_cut_corner_box(self, bottom, center, top,
                          startangle, endangle, strand,
                          color, border=None, corner=0.5,
                          **kwargs):
        """Draw OCTO sigil, box with corners cut off."""
        if strand == 1:
            inner_radius = center
            outer_radius = top
        elif strand == -1:
            inner_radius = bottom
            outer_radius = center
        else:
            inner_radius = bottom
            outer_radius = top

        strokecolor, color = _stroke_and_fill_colors(color, border)

        startangle, endangle = min(startangle, endangle), max(startangle, endangle)
        angle = float(endangle - startangle)

        middle_radius = 0.5*(inner_radius+outer_radius)
        boxheight = outer_radius - inner_radius

        corner_len = min(0.5*boxheight, 0.5*boxheight*corner)
        shaft_inner_radius = inner_radius + corner_len
        shaft_outer_radius = outer_radius - corner_len

        cornerangle_delta = max(0.0,min(abs(boxheight)*0.5*corner/middle_radius, abs(angle*0.5)))
        if angle < 0:
            cornerangle_delta *= -1  # reverse it

        # Calculate trig values for angle and coordinates
        startcos, startsin = cos(startangle), sin(startangle)
        endcos, endsin = cos(endangle), sin(endangle)
        x0, y0 = self.xcenter, self.ycenter      # origin of the circle
        p = ArcPath(strokeColor=strokecolor,
                    fillColor=color,
                    strokeLineJoin=1,  # 1=round
                    strokewidth=0,
                    **kwargs)
        #Inner curved edge
        p.addArc(self.xcenter, self.ycenter, inner_radius,
                 90 - ((endangle-cornerangle_delta) * 180 / pi),
                 90 - ((startangle+cornerangle_delta) * 180 / pi),
                 moveTo=True)
        #Corner edge - straight lines assumes small angle!
        #TODO - Use self._draw_arc_line(p, ...) here if we expose corner setting
        p.lineTo(x0+shaft_inner_radius*startsin, y0+shaft_inner_radius*startcos)
        p.lineTo(x0+shaft_outer_radius*startsin, y0+shaft_outer_radius*startcos)
        #Outer curved edge
        p.addArc(self.xcenter, self.ycenter, outer_radius,
                 90 - ((endangle-cornerangle_delta) * 180 / pi),
                 90 - ((startangle+cornerangle_delta) * 180 / pi),
                 reverse=True)
        #Corner edges
        p.lineTo(x0+shaft_outer_radius*endsin, y0+shaft_outer_radius*endcos)
        p.lineTo(x0+shaft_inner_radius*endsin, y0+shaft_inner_radius*endcos)
        p.closePath()
        return p

    def _draw_sigil_arrow(self, bottom, center, top,
                          startangle, endangle, strand,
                          **kwargs):
        """Draw ARROW sigil."""
        if strand == 1:
            inner_radius = center
            outer_radius = top
            orientation = "right"
        elif strand == -1:
            inner_radius = bottom
            outer_radius = center
            orientation = "left"
        else:
            inner_radius = bottom
            outer_radius = top
            orientation = "right"  # backwards compatibility
        return self._draw_arc_arrow(inner_radius, outer_radius, startangle, endangle,
                                    orientation=orientation, **kwargs)

    def _draw_sigil_big_arrow(self, bottom, center, top,
                              startangle, endangle, strand,
                              **kwargs):
        """Draw BIGARROW sigil, like ARROW but straddles the axis."""
        if strand == -1:
            orientation = "left"
        else:
            orientation = "right"
        return self._draw_arc_arrow(bottom, top, startangle, endangle,
                                    orientation=orientation, **kwargs)

    def _draw_arc_arrow(self, inner_radius, outer_radius, startangle, endangle,
                  color, border=None,
                  shaft_height_ratio=0.4, head_length_ratio=0.5, orientation='right',
                  colour=None, **kwargs):
        """Draw an arrow along an arc."""
        #Let the UK spelling (colour) override the USA spelling (color)
        if colour is not None:
            color = colour

        strokecolor, color = _stroke_and_fill_colors(color, border)

        #if orientation == 'right':
        #    startangle, endangle = min(startangle, endangle), max(startangle, endangle)
        #elif orientation == 'left':
        #    startangle, endangle = max(startangle, endangle), min(startangle, endangle)
        #else:
        startangle, endangle = min(startangle, endangle), max(startangle, endangle)
        if orientation != "left" and orientation != "right":
            raise ValueError("Invalid orientation %s, should be 'left' or 'right'"
                             % repr(orientation))

        angle = float(endangle - startangle)    # angle subtended by arc
        middle_radius = 0.5*(inner_radius+outer_radius)
        boxheight = outer_radius - inner_radius
        shaft_height = boxheight*shaft_height_ratio
        shaft_inner_radius = middle_radius - 0.5*shaft_height
        shaft_outer_radius = middle_radius + 0.5*shaft_height
        headangle_delta = max(0.0,min(abs(boxheight)*head_length_ratio/middle_radius, abs(angle)))
        if angle < 0:
            headangle_delta *= -1  # reverse it
        if orientation=="right":
            headangle = endangle-headangle_delta
        else:
            headangle = startangle+headangle_delta
        if startangle <= endangle:
            headangle = max(min(headangle, endangle), startangle)
        else:
            headangle = max(min(headangle, startangle), endangle)
        assert startangle <= headangle <= endangle \
            or endangle <= headangle <= startangle, \
            (startangle, headangle, endangle, angle)

        # Calculate trig values for angle and coordinates
        startcos, startsin = cos(startangle), sin(startangle)
        headcos, headsin = cos(headangle), sin(headangle)
        endcos, endsin = cos(endangle), sin(endangle)
        x0,y0 = self.xcenter, self.ycenter      # origin of the circle
        if 0.5 >= abs(angle) and abs(headangle_delta) >= abs(angle):
            #If the angle is small, and the arrow is all head,
            #cheat and just use a triangle.
            if orientation=="right":
                x1,y1 = (x0+inner_radius*startsin, y0+inner_radius*startcos)
                x2,y2 = (x0+outer_radius*startsin, y0+outer_radius*startcos)
                x3,y3 = (x0+middle_radius*endsin, y0+middle_radius*endcos)
            else:
                x1,y1 = (x0+inner_radius*endsin, y0+inner_radius*endcos)
                x2,y2 = (x0+outer_radius*endsin, y0+outer_radius*endcos)
                x3,y3 = (x0+middle_radius*startsin, y0+middle_radius*startcos)
            #return draw_polygon([(x1,y1),(x2,y2),(x3,y3)], color, border,
            #                    stroke_line_join=1)
            return Polygon([x1,y1,x2,y2,x3,y3],
                           strokeColor=border or color,
                           fillColor=color,
                           strokeLineJoin=1,  # 1=round, not mitre!
                           strokewidth=0)
        elif orientation=="right":
            p = ArcPath(strokeColor=strokecolor,
                        fillColor=color,
                        #default is mitre/miter which can stick out too much:
                        strokeLineJoin=1,  # 1=round
                        strokewidth=0,
                        **kwargs)
            #Note reportlab counts angles anti-clockwise from the horizontal
            #(as in mathematics, e.g. complex numbers and polar coordinates)
            #but we use clockwise from the vertical.  Also reportlab uses
            #degrees, but we use radians.
            p.addArc(self.xcenter, self.ycenter, shaft_inner_radius,
                     90 - (headangle * 180 / pi), 90 - (startangle * 180 / pi),
                     moveTo=True)
            p.addArc(self.xcenter, self.ycenter, shaft_outer_radius,
                     90 - (headangle * 180 / pi), 90 - (startangle * 180 / pi),
                     reverse=True)
            if abs(angle) < 0.5:
                p.lineTo(x0+outer_radius*headsin, y0+outer_radius*headcos)
                p.lineTo(x0+middle_radius*endsin, y0+middle_radius*endcos)
                p.lineTo(x0+inner_radius*headsin, y0+inner_radius*headcos)
            else:
                self._draw_arc_line(p, outer_radius, middle_radius,
                                    90 - (headangle * 180 / pi),
                                    90 - (endangle * 180 / pi))
                self._draw_arc_line(p, middle_radius, inner_radius,
                                    90 - (endangle * 180 / pi),
                                    90 - (headangle * 180 / pi))
            p.closePath()
            return p
        else:
            p = ArcPath(strokeColor=strokecolor,
                        fillColor=color,
                        #default is mitre/miter which can stick out too much:
                        strokeLineJoin=1,  # 1=round
                        strokewidth=0,
                        **kwargs)
            #Note reportlab counts angles anti-clockwise from the horizontal
            #(as in mathematics, e.g. complex numbers and polar coordinates)
            #but we use clockwise from the vertical.  Also reportlab uses
            #degrees, but we use radians.
            p.addArc(self.xcenter, self.ycenter, shaft_inner_radius,
                     90 - (endangle * 180 / pi), 90 - (headangle * 180 / pi),
                     moveTo=True, reverse=True)
            p.addArc(self.xcenter, self.ycenter, shaft_outer_radius,
                     90 - (endangle * 180 / pi), 90 - (headangle * 180 / pi),
                     reverse=False)
            #Note - two staight lines is only a good approximation for small
            #head angle, in general will need to curved lines here:
            if abs(angle) < 0.5:
                p.lineTo(x0+outer_radius*headsin, y0+outer_radius*headcos)
                p.lineTo(x0+middle_radius*startsin, y0+middle_radius*startcos)
                p.lineTo(x0+inner_radius*headsin, y0+inner_radius*headcos)
            else:
                self._draw_arc_line(p, outer_radius, middle_radius,
                                    90 - (headangle * 180 / pi),
                                    90 - (startangle * 180 / pi))
                self._draw_arc_line(p, middle_radius, inner_radius,
                                    90 - (startangle * 180 / pi),
                                    90 - (headangle * 180 / pi))
            p.closePath()
            return p

    def _draw_sigil_jaggy(self, bottom, center, top,
                          startangle, endangle, strand,
                          color, border=None,
                          **kwargs):
        """Draw JAGGY sigil.

        Although we may in future expose the head/tail jaggy lengths, for now
        both the left and right edges are drawn jagged.
        """
        if strand == 1:
            inner_radius = center
            outer_radius = top
            teeth = 2
        elif strand == -1:
            inner_radius = bottom
            outer_radius = center
            teeth = 2
        else:
            inner_radius = bottom
            outer_radius = top
            teeth = 4

        #TODO, expose these settings?
        tail_length_ratio = 1.0
        head_length_ratio = 1.0

        strokecolor, color = _stroke_and_fill_colors(color, border)

        startangle, endangle = min(startangle, endangle), max(startangle, endangle)
        angle = float(endangle - startangle)    # angle subtended by arc
        height = outer_radius - inner_radius

        assert startangle <= endangle and angle >= 0
        if head_length_ratio and tail_length_ratio:
            headangle = max(endangle - min(height*head_length_ratio/(center*teeth), angle*0.5), startangle)
            tailangle = min(startangle + min(height*tail_length_ratio/(center*teeth), angle*0.5), endangle)
            #With very small features, can due to floating point calculations
            #violate the assertion below that start <= tail <= head <= end
            tailangle = min(tailangle, headangle)
        elif head_length_ratio:
            headangle = max(endangle - min(height*head_length_ratio/(center*teeth), angle), startangle)
            tailangle = startangle
        else:
            headangle = endangle
            tailangle = min(startangle + min(height*tail_length_ratio/(center*teeth), angle), endangle)

        assert startangle <= tailangle <= headangle <= endangle, \
            (startangle, tailangle, headangle, endangle, angle)

        # Calculate trig values for angle and coordinates
        startcos, startsin = cos(startangle), sin(startangle)
        headcos, headsin = cos(headangle), sin(headangle)
        endcos, endsin = cos(endangle), sin(endangle)
        x0,y0 = self.xcenter, self.ycenter      # origin of the circle

        p = ArcPath(strokeColor=strokecolor,
                    fillColor=color,
                    #default is mitre/miter which can stick out too much:
                    strokeLineJoin=1,  # 1=round
                    strokewidth=0,
                    **kwargs)
        #Note reportlab counts angles anti-clockwise from the horizontal
        #(as in mathematics, e.g. complex numbers and polar coordinates)
        #but we use clockwise from the vertical.  Also reportlab uses
        #degrees, but we use radians.
        p.addArc(self.xcenter, self.ycenter, inner_radius,
                 90 - (headangle * 180 / pi), 90 - (tailangle * 180 / pi),
                 moveTo=True)
        for i in range(0, teeth):
            p.addArc(self.xcenter, self.ycenter, inner_radius+i*height/teeth,
                     90 - (tailangle * 180 / pi), 90 - (startangle * 180 / pi))
            #Curved line needed when drawing long jaggies
            self._draw_arc_line(p,
                                inner_radius+i*height/teeth,
                                inner_radius+(i+1)*height/teeth,
                                90 - (startangle * 180 / pi),
                                90 - (tailangle * 180 / pi))
        p.addArc(self.xcenter, self.ycenter, outer_radius,
                 90 - (headangle * 180 / pi), 90 - (tailangle * 180 / pi),
                 reverse=True)
        for i in range(0, teeth):
            p.addArc(self.xcenter, self.ycenter, outer_radius-i*height/teeth,
                     90 - (endangle * 180 / pi), 90 - (headangle * 180 / pi),
                     reverse=True)
            #Curved line needed when drawing long jaggies
            self._draw_arc_line(p,
                                outer_radius-i*height/teeth,
                                outer_radius-(i+1)*height/teeth,
                                90 - (endangle * 180 / pi),
                                90 - (headangle * 180 / pi))
        p.closePath()
        return p
