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391 lines
16 KiB
Python
391 lines
16 KiB
Python
'''
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Given an svg.path.Path object representing a glyph, a StrokeExtractor instance
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will break it down into a list of svg.path.Path objects, one for each stroke.
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The algorithm we currently use is a 'corner-and-bridge' algorithm. First, we
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detect possible corners in the path object. 'Corners' are points where the
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derivative of the curve angle is sharply negative - that is, points at which
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the curve is very non-convex. If two strokes cross eachother, we should detect
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four corners, one at each place at the outline of the intersection.
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(Note that much more complex configurations are possible - for example a stroke
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may end at the middle of another stroke, or many strokes may intersect to form
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a star shape.)
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We then detect 'bridges', which are edges between corners where the stroke
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entering one corner may continue to the stroke exiting the other corner. In our
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two-strokes-crossing example, we should detect four bridges connecting the four
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corners to form a simple quadrilateral.
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Finally, we traverse the path, usually following SVG path elements, but taking
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bridges when they are inline with the previously traversed path element. The
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output of this traversal is our final stroke decomposition.
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At many points during this algorithm we may detect various anomalies. We log
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these anomalies so that they can be reviewed manually.
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'''
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import collections
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import math
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import svg.path
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MAX_BRIDGE_DISTANCE = 128
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MAX_CORNER_MERGE_DISTANCE = 16
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MIN_CORNER_ANGLE = 0.1*math.pi
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MIN_CORNER_TANGENT_DISTANCE = 4
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def area(path):
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'''
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Returns the area of the path. The result is positive iff the path winds in
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the counter-clockwise direction.
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'''
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def area_under_curve(x):
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return (x.start.real - x.end.real)*(x.start.imag + x.end.imag)
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return int(sum(map(area_under_curve, path))/2)
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def split_and_orient_path(path):
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'''
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Takes a non-empty svg.path.Path object that may contain multiple closed loops.
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Returns a list of svg.path.Path objects that are all minimal closed curve.
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The returned paths will be the way a TTF glyph should be: exterior curves
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will be counter-clockwise and interior curves will be clockwise.
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'''
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paths = [[path[0]]]
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for element in path[1:]:
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if element.start == element.end:
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continue
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if element.start != paths[-1][-1].end:
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paths.append([])
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paths[-1].append(element)
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# Determine if this glyph is oriented in the wrong direction by computing the
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# area of each glyph. The glyph with maximum |area| should have positive area,
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# because it must be an exterior path.
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def reverse(path):
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for element in path:
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(element.start, element.end) = (element.end, element.start)
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return reversed(path)
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areas = [area(path) for path in paths]
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max_area = max((abs(area), area) for area in areas)[1]
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if max_area < 0:
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paths = map(reverse, paths)
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return [svg.path.Path(*path) for path in paths]
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class Corner(object):
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def __init__(self, paths, index):
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self.index = index
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(i, j) = index
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self.path = paths[i]
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self.point = paths[i][j].start
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(self.tangent1, self.tangent2) = self._get_tangents()
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self.angle = self._get_angle(self.tangent1, self.tangent2)
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def bridge(self, other):
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'''
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Returns true if a stroke continues from this corner point to the other.
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Internally, this function builds a 7-dimensional feature vector and then
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calls a classifier. The 7 features are:
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features[0]: The angle between the edge in and the bridge
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features[1]: The angle between the bridge and the edge out
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features[2]: The angle between the cross stroke out and the bridge
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features[3]: The angle between the cross stroke in and the bridge
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features[4]: The angle at this corner
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features[5]: The angle at the other corner
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features[6]: The length of the bridge
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At an ideal bridge, features[0] and features[1] should be very close to 0,
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meaning that the stroke can continue smoothly from this corner to the other.
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features[2] + features[3] is close to pi, meaning that the stroke in
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is straight, and features[6], the distance, is small.
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This ideal configuration might look like this diagram:
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/ ^
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/ /
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<-O S--
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where S is this corner and O is the other and the arrows indicate the
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direction of the curve.
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'''
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diff = other.point - self.point
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length = abs(diff)
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if length == 0 or length > MAX_BRIDGE_DISTANCE:
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return False
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# NOTE: These angle features make sense even if points are on different
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# subpaths of the glyph path! Because of our preprocessing, exterior glyph
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# paths are clockwise while interior paths are counter-clockwise, so angle
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# features around a bridge are the same whether or not the two sides of
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# the bridge are on the same path.
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features = (
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self._get_angle(self.tangent1, diff),
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self._get_angle(diff, other.tangent2),
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self._get_angle(diff, self.tangent2),
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self._get_angle(other.tangent1, diff),
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self.angle,
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other.angle,
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length,
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)
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# TODO(skishore): Log this sample and use it to train the classifier.
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result = self._run_classifier(features)
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return result
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def merge_into(self, other):
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'''
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Merges this corner into the other corner, updating the other's data.
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The merged corner takes the position of the sharper corner of the two.
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Because the path curves slightly in the positive direction on average, a
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curve is sharper if its angle is more negative.
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'''
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if self.angle < other.angle:
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other.index = self.index
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other.point = self.point
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other.tangent1 = self.tangent1
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other.angle = other._get_angle(other.tangent1, other.tangent2)
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def should_merge(self, other):
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'''
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Returns true if this corner point is close enough to the next one that
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they should be combined into one corner point. Note that the next corner
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should have an index that occurs soon after this corner's.
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'''
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assert other.index[0] == self.index[0], \
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'merge called for corners on different curves!'
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if abs(other.point - self.point) > MAX_CORNER_MERGE_DISTANCE:
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return False
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distance = 0
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j = self.index[1]
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while j != other.index[1]:
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distance += abs(self.path[j].end - self.path[j].start)
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j = (j + 1) % len(self.path)
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return distance < MAX_CORNER_MERGE_DISTANCE
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def _get_angle(self, vector1, vector2):
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ratio = vector2/vector1 if vector1 else 0
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return math.atan2(ratio.imag, ratio.real)
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def _get_tangents(self):
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segment1 = self.path[self.index[1] - 1]
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tangent1 = segment1.end - segment1.start
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if (type(segment1) == svg.path.QuadraticBezier and
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abs(segment1.end - segment1.control) > MIN_CORNER_TANGENT_DISTANCE):
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tangent1 = segment1.end - segment1.control
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segment2 = self.path[self.index[1]]
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tangent2 = segment2.end - segment2.start
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if (type(segment2) == svg.path.QuadraticBezier and
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abs(segment2.control - segment2.start) > MIN_CORNER_TANGENT_DISTANCE):
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tangent2 = segment2.control - segment2.start
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return (tangent1, tangent2)
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def _run_classifier(self, features):
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# TODO(skishore): Replace these inequalities with a trained classifier.
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alignment = abs(features[0]) + abs(features[1])
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incidence = abs(features[2] + features[3] + math.pi)
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short = features[6] < MAX_BRIDGE_DISTANCE/2
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clean = alignment < 0.1*math.pi or alignment + incidence < 0.2*math.pi
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cross = all([
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features[0] > 0,
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features[1] > 0,
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features[2] + features[3] < -0.5*math.pi,
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])
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result = 0
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if features[2] < 0 and features[3] < 0 and (clean or (short and cross)):
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result = (1 if short else 0.75) if clean else 0.5
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return result
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class StrokeExtractor(object):
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def __init__(self, name, d):
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self.name = name
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self.messages = []
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self.paths = split_and_orient_path(svg.path.parse_path(d))
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self.corners = self.get_corners()
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self.bridges = self.get_bridges()
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(self.strokes, self.stroke_adjacency) = self.extract_strokes()
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def extract_stroke(self, extracted, start):
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'''
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Given a path, a list of corners, and an adjacency list representation of
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bridges between then, extract a stroke that starts at the given index
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and add the indices of all elements on that stroke to extracted.
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This method will return a pair (path, corners), where the first element is
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an svg.path.Path object representing the stroke and the second is a list of
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corners that appear on that stroke. The corners list will have duplicates if
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the stroke loops back on itself, which indicates a mistake somewhere.
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This method will fail if, when following edges the the initial path element,
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we cross a bridge and enter a stroke that has already been extracted. If so,
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the path we return will be None.
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NOTE: We deliberately avoid using bridge directionality in this algorithm
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so that we can handle manually added bridges.
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'''
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current = start
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corners = []
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path = svg.path.Path()
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visited = set()
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def advance(index):
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return (index[0], (index[1] + 1) % len(self.paths[index[0]]))
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def angle(index, bridge):
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tangent = self.corners[index].tangent1
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ratio = (self.corners[bridge].point - self.corners[index].point)/tangent
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return abs(math.atan2(ratio.imag, ratio.real))
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while True:
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# Add the current stroke element to the path and advance along it.
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path.append(self.paths[current[0]][current[1]])
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visited.add(current)
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current = advance(current)
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# If there is a bridge aligned with the stroke element that we advanced
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# over, advance over that bridge as well. If there are multiple bridges,
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# choose the one that is most aligned.
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if current in self.bridges:
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next = sorted(self.bridges[current], key=lambda x: angle(current, x))[0]
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corners.extend([self.corners[current], self.corners[next]])
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path.append(svg.path.Line(
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start=self.corners[current].point, end=self.corners[next].point))
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current = next
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# Check if we either closed the loop or hit an already extracted stroke.
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if current == start:
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extracted.update(visited)
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return (path, corners)
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elif current in visited or current in extracted:
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return (None, [])
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def extract_strokes(self):
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'''
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Returns a pair (strokes, stroke_adjacency), where the first element is a
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list of svg.path.Path objects that decompose this glyph into strokes and the
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second is an adjacency-list representation of the indices of strokes which
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share corner points.
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This method will log if some path elements do not appear on any stroke.
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'''
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extracted = set()
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strokes = []
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stroke_adjacency = collections.defaultdict(set)
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corner_adjacency = collections.defaultdict(set)
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for i, path in enumerate(self.paths):
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for j, element in enumerate(path):
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index = (i, j)
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if index not in extracted:
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(stroke, corners) = self.extract_stroke(extracted, index)
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if stroke is None:
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self.log('Stroke extraction missed some path elements!')
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continue
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stroke_index = len(strokes)
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strokes.append(stroke)
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corner_indices = set(corner.index for corner in corners)
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if len(corner_indices) < len(corners):
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self.log('Stroke {0} is self-intersecting!'.format(stroke_index))
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for corner_index in corner_indices:
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for other_index in corner_adjacency[corner_index]:
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stroke_adjacency[other_index].add(stroke_index)
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stroke_adjacency[stroke_index].add(other_index)
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corner_adjacency[corner_index].add(stroke_index)
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return (strokes, stroke_adjacency)
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def get_bridges(self):
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'''
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Returns an adjacency list of bridges. A bridge is a pair of corner indices
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through which a stroke continues. The adjacency list is undirected: for any
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two corner indices a and b, if b in result[a], a in result[b].
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'''
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# Collect bridge candidates scored by our bridge classifier.
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candidates = []
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for corner in self.corners.itervalues():
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for other in self.corners.itervalues():
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confidence = corner.bridge(other)
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if confidence > 0:
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candidates.append((confidence, corner.index, other.index))
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candidates.sort(reverse=True)
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# Add bridges to the set of bridges in order of decreasing confidence.
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# However, we do NOT add bridges that would either a) form a triangle with
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# an existing bridge, or b) that are long and should be multiple bridges.
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bridges = set()
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for (confidence, index1, index2) in candidates:
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other1 = set(b for (a, b) in bridges if a == index1)
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other2 = set(b for (a, b) in bridges if a == index2)
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if (other1.intersection(other2) or
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self.should_split_bridge((index1, index2))):
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continue
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bridges.add((index1, index2))
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bridges.add((index2, index1))
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# Convert the result to an adjacency list. Having more than two bridges at
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# any given corner results in a warning.
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result = collections.defaultdict(list)
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for (index1, index2) in bridges:
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result[index1].append(index2)
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if len(result[index1]) == 3:
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self.log('More than two bridges at corner {0}'.format(
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self.corners[index1].point))
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return result
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def get_corners(self):
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'''
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Returns a dict mapping indices to corners at that index. Each corner is a
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point on the curve where the path makes a sharp negative angle. Since the
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path has a small positive average angle, it is non-convex at these corners.
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'''
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result = {}
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for i, path in enumerate(self.paths):
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candidates = [Corner(self.paths, (i, j)) for j in xrange(len(path))]
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j = 0
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while j < len(candidates):
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next_j = (j + 1) % len(candidates)
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if candidates[j].should_merge(candidates[next_j]):
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candidates[j].merge_into(candidates[next_j])
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candidates.pop(j)
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else:
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j += 1
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for corner in filter(lambda x: x.angle < -MIN_CORNER_ANGLE, candidates):
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result[corner.index] = corner
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return result
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def get_data(self):
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'''
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Returns a representation of the data extracted from this glyph that can be
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serialized to JSON. The result is a dictionary with the following keys:
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- points: list of [x, y] pairs of endpoints on the glyph's SVG path
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- corners: list of [x, y] pairs of points that are also corners
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- bridges: list of pairs of corners [[x1, y1], [x2, y2]] that are bridges
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- strokes: list of SVG path data strings for the extracted strokes
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'''
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pair = lambda point: [int(point.real), int(point.imag)]
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return {
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'points': [pair(element.end) for path in self.paths for element in path],
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'corners': [pair(corner.point) for corner in self.corners.itervalues()],
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'bridges': [
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[pair(self.corners[index1].point), pair(self.corners[index2].point)]
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for (index1, others) in self.bridges.iteritems() for index2 in others
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if index1 < index2
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],
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'strokes': [stroke.d() for stroke in self.strokes],
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}
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def log(self, message):
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self.messages.append(message)
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def should_split_bridge(self, bridge):
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'''
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Returns true if there is some corner that is too close to the middle of the
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given bridge. When this occurs, the gap between these indices should usually
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be spanned by multiple bridges instead.
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'''
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(index1, index2) = bridge
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base = self.corners[index1].point
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diff = self.corners[index2].point - base
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for corner in self.corners.itervalues():
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if corner.index in bridge:
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continue
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t = ((corner.point.real - base.real)*diff.real +
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(corner.point.imag - base.imag)*diff.imag)/(abs(diff)**2)
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distance_to_line = abs(self.corners[index1].point + t*diff - corner.point)
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if 0 < t < 1 and distance_to_line < MAX_CORNER_MERGE_DISTANCE:
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return True
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return False
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