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|
from __future__ import print_function, division, absolute_import
import math
from fontTools.misc import bezierTools
from fontTools.pens.basePen import decomposeQuadraticSegment
import pyclipper
from .exceptions import OpenContourError
"""
To Do:
- the stuff listed below
- need to know what kind of curves should be used for
curve fit--curve or qcurve
- false curves and duplicate points need to be filtered early on
notes:
- the flattened segments *must* be cyclical.
if they aren't, matching is almost impossible.
optimization ideas:
- the flattening of the output segment in the full contour
matching is probably expensive.
- there should be a way to flag an input contour as
entirely used so that it isn't tried and tried and
tried for segment matches.
- do a faster test when matching segments: when a end
match is found, jump back input length and grab the
output segment. test for match with the input.
- cache input contour objects. matching these to incoming
will be a little difficult because of point names and
identifiers. alternatively, deal with those after the fact.
- some tests on input before conversion to input objects
could yield significant speedups. would need to check
each contour for self intersection and each
non-self-intersectingcontour for collision with other
contours. and contours that don't have a hit could be
skipped. this cound be done roughly with bounds.
this should probably be done by extenal callers.
- set a proper starting points of the output segments based on known points
known points are:
input oncurve points
if nothing found intersection points (only use this is in the final curve fitting stage)
test cases:
- untouched contour: make clockwise and counter-clockwise tests
of the same contour
"""
epsilon = 1e-8
# factors for transferring coordinates to and from Clipper
clipperScale = 1 << 17
inverseClipperScale = 1.0 / clipperScale
# approximateSegmentLength setting
_approximateSegmentLength = 5.3
# -------------
# Input Objects
# -------------
# Input
class InputContour(object):
def __init__(self, contour):
# gather the point data
pointPen = ContourPointDataPen()
contour.drawPoints(pointPen)
points = pointPen.getData()
reversedPoints = _reversePoints(points)
# gather segments
self.segments = _convertPointsToSegments(points)
# only calculate once all the flat points.
# it seems to have some tiny difference and its a lot faster
# if the flat points are calculated from the reversed input points.
self.reversedSegments = _convertPointsToSegments(reversedPoints, willBeReversed=True)
# simple reverse the flat points and store them in the reversedSegments
index = 0
for segment in self.segments:
otherSegment = self.reversedSegments[index]
otherSegment.flat = segment.getReversedFlatPoints()
index -= 1
# get the direction; returns True if counter-clockwise, False otherwise
self.clockwise = not pyclipper.Orientation(points)
# store the gathered data
if self.clockwise:
self.clockwiseSegments = self.segments
self.counterClockwiseSegments = self.reversedSegments
else:
self.clockwiseSegments = self.reversedSegments
self.counterClockwiseSegments = self.segments
# flag indicating if the contour has been used
self.used = False
# ----------
# Attributes
# ----------
# the original direction in flat segments
def _get_originalFlat(self):
if self.clockwise:
return self.clockwiseFlat
else:
return self.counterClockwiseFlat
originalFlat = property(_get_originalFlat)
# the clockwise direction in flat segments
def _get_clockwiseFlat(self):
flat = []
segments = self.clockwiseSegments
for segment in segments:
flat.extend(segment.flat)
return flat
clockwiseFlat = property(_get_clockwiseFlat)
# the counter-clockwise direction in flat segments
def _get_counterClockwiseFlat(self):
flat = []
segments = self.counterClockwiseSegments
for segment in segments:
flat.extend(segment.flat)
return flat
counterClockwiseFlat = property(_get_counterClockwiseFlat)
def hasOnCurve(self):
for inputSegment in self.segments:
if not inputSegment.used and inputSegment.segmentType != "line":
return True
return False
class InputSegment(object):
# __slots__ = ["points", "previousOnCurve", "scaledPreviousOnCurve", "flat", "used"]
def __init__(self, points=None, previousOnCurve=None, willBeReversed=False):
if points is None:
points = []
self.points = points
self.previousOnCurve = previousOnCurve
self.scaledPreviousOnCurve = _scaleSinglePoint(previousOnCurve, scale=clipperScale)
self.used = False
self.flat = []
# if the bcps are equal to the oncurves convert the segment to a line segment.
# otherwise this causes an error when flattening.
if self.segmentType == "curve":
if previousOnCurve == points[0].coordinates and points[1].coordinates == points[-1].coordinates:
oncurve = points[-1]
oncurve.segmentType = "line"
self.points = points = [oncurve]
elif previousOnCurve[0] == points[0].coordinates[0] == points[1].coordinates[0] == points[-1].coordinates[0]:
oncurve = points[-1]
oncurve.segmentType = "line"
self.points = points = [oncurve]
elif previousOnCurve[1] == points[0].coordinates[1] == points[1].coordinates[1] == points[-1].coordinates[1]:
oncurve = points[-1]
oncurve.segmentType = "line"
self.points = points = [oncurve]
# its a reversed segment the flat points will be set later on in the InputContour
if willBeReversed:
return
pointsToFlatten = []
if self.segmentType == "qcurve":
assert len(points) >= 0
flat = []
currentOnCurve = previousOnCurve
pointCoordinates = [point.coordinates for point in points]
for pt1, pt2 in decomposeQuadraticSegment(pointCoordinates[1:]):
pt0x, pt0y = currentOnCurve
pt1x, pt1y = pt1
pt2x, pt2y = pt2
mid1x = pt0x + 0.66666666666666667 * (pt1x - pt0x)
mid1y = pt0y + 0.66666666666666667 * (pt1y - pt0y)
mid2x = pt2x + 0.66666666666666667 * (pt1x - pt2x)
mid2y = pt2y + 0.66666666666666667 * (pt1y - pt2y)
convertedQuadPointToFlatten = [currentOnCurve, (mid1x, mid1y), (mid2x, mid2y), pt2]
flat.extend(_flattenSegment(convertedQuadPointToFlatten))
currentOnCurve = pt2
self.flat = flat
# this shoudl be easy.
# copy the quad to cubic from fontTools.pens.basePen
elif self.segmentType == "curve":
pointsToFlatten = [previousOnCurve] + [point.coordinates for point in points]
else:
assert len(points) == 1
self.flat = [point.coordinates for point in points]
if pointsToFlatten:
self.flat = _flattenSegment(pointsToFlatten)
# if len(self.flat) == 1 and self.segmentType == "curve":
# oncurve = self.points[-1]
# oncurve.segmentType = "line"
# self.points = [oncurve]
self.flat = _scalePoints(self.flat, scale=clipperScale)
self.flat = _checkFlatPoints(self.flat)
self.used = False
def _get_segmentType(self):
return self.points[-1].segmentType
segmentType = property(_get_segmentType)
def getReversedFlatPoints(self):
reversedFlatPoints = [self.scaledPreviousOnCurve] + self.flat[:-1]
reversedFlatPoints.reverse()
return reversedFlatPoints
def split(self, tValues):
"""
Split the segment according the t values
"""
if self.segmentType == "curve":
on1 = self.previousOnCurve
off1 = self.points[0].coordinates
off2 = self.points[1].coordinates
on2 = self.points[2].coordinates
return bezierTools.splitCubicAtT(on1, off1, off2, on2, *tValues)
elif self.segmentType == "line":
segments = []
x1, y1 = self.previousOnCurve
x2, y2 = self.points[0].coordinates
dx = x2 - x1
dy = y2 - y1
pp = x1, y1
for t in tValues:
np = (x1+dx*t, y1+dy*t)
segments.append([pp, np])
pp = np
segments.append([pp, (x2, y2)])
return segments
elif self.segmentType == "qcurve":
raise NotImplementedError
else:
raise NotImplementedError
def tValueForPoint(self, point):
"""
get a t values for a given point
required:
the point must be a point on the curve.
in an overlap cause the point will be an intersection points wich is alwasy a point on the curve
"""
if self.segmentType == "curve":
on1 = self.previousOnCurve
off1 = self.points[0].coordinates
off2 = self.points[1].coordinates
on2 = self.points[2].coordinates
return _tValueForPointOnCubicCurve(point, (on1, off1, off2, on2))
elif self.segmentType == "line":
return _tValueForPointOnLine(point, (self.previousOnCurve, self.points[0].coordinates))
elif self.segmentType == "qcurve":
raise NotImplementedError
else:
raise NotImplementedError
class InputPoint(object):
__slots__ = ["coordinates", "segmentType", "smooth", "name", "kwargs"]
def __init__(self, coordinates, segmentType=None, smooth=False, name=None, kwargs=None):
x, y = coordinates
self.coordinates = coordinates
self.segmentType = segmentType
self.smooth = smooth
self.name = name
self.kwargs = kwargs
def __getitem__(self, i):
return self.coordinates[i]
def copy(self):
copy = self.__class__(
coordinates=self.coordinates,
segmentType=self.segmentType,
smooth=self.smooth,
name=self.name,
kwargs=self.kwargs
)
return copy
def __str__(self):
return "%s %s" % (self.segmentType, self.coordinates)
def __repr__(self):
return self.__str__()
# -------------
# Input Support
# -------------
class ContourPointDataPen:
"""
Point pen for gathering raw contour data.
An instance of this pen may only be used for one contour.
"""
def __init__(self):
self._points = None
self._foundStartingPoint = False
def getData(self):
"""
Return a list of normalized InputPoint objects
for the contour drawn with this pen.
"""
# organize the points into segments
# 1. make sure there is an on curve
haveOnCurve = False
for point in self._points:
if point.segmentType is not None:
haveOnCurve = True
break
# 2. move the off curves to front of the list
if haveOnCurve:
_prepPointsForSegments(self._points)
# 3. ignore double points on start and end
firstPoint = self._points[0]
lastPoint = self._points[-1]
if firstPoint.segmentType is not None and lastPoint.segmentType is not None:
if firstPoint.coordinates == lastPoint.coordinates:
if (firstPoint.segmentType in ["line", "move"]):
del self._points[0]
else:
raise AssertionError("Unhandled point type sequence")
# done
return self._points
def beginPath(self):
assert self._points is None
self._points = []
def endPath(self):
pass
def addPoint(self, pt, segmentType=None, smooth=False, name=None, **kwargs):
if segmentType == "move":
raise OpenContourError("Unhandled open contour")
if not self._foundStartingPoint and segmentType is not None:
kwargs['startingPoint'] = self._foundStartingPoint = True
data = InputPoint(
coordinates=pt,
segmentType=segmentType,
smooth=smooth,
name=name,
kwargs=kwargs
)
self._points.append(data)
def addComponent(self, baseGlyphName, transformation):
raise NotImplementedError
def _prepPointsForSegments(points):
"""
Move any off curves at the end of the contour
to the beginning of the contour. This makes
segmentation easier.
"""
while 1:
point = points[-1]
if point.segmentType:
break
else:
point = points.pop()
points.insert(0, point)
continue
def _copyPoints(points):
"""
Make a shallow copy of the points.
"""
copied = [point.copy() for point in points]
return copied
def _reversePoints(points):
"""
Reverse the points. This differs from the
reversal point pen in RoboFab in that it doesn't
worry about maintaing the start point position.
That has no benefit within the context of this module.
"""
# copy the points
points = _copyPoints(points)
# find the first on curve type and recycle
# it for the last on curve type
firstOnCurve = None
for index, point in enumerate(points):
if point.segmentType is not None:
firstOnCurve = index
break
lastSegmentType = points[firstOnCurve].segmentType
# reverse the points
points = reversed(points)
# work through the reversed remaining points
final = []
for point in points:
segmentType = point.segmentType
if segmentType is not None:
point.segmentType = lastSegmentType
lastSegmentType = segmentType
final.append(point)
# move any offcurves at the end of the points
# to the start of the points
_prepPointsForSegments(final)
# done
return final
def _convertPointsToSegments(points, willBeReversed=False):
"""
Compile points into InputSegment objects.
"""
# get the last on curve
previousOnCurve = None
for point in reversed(points):
if point.segmentType is not None:
previousOnCurve = point.coordinates
break
assert previousOnCurve is not None
# gather the segments
offCurves = []
segments = []
for point in points:
# off curve, hold.
if point.segmentType is None:
offCurves.append(point)
else:
segment = InputSegment(
points=offCurves + [point],
previousOnCurve=previousOnCurve,
willBeReversed=willBeReversed
)
segments.append(segment)
offCurves = []
previousOnCurve = point.coordinates
assert not offCurves
return segments
# --------------
# Output Objects
# --------------
class OutputContour(object):
def __init__(self, pointList):
if pointList[0] == pointList[-1]:
del pointList[-1]
self.clockwise = not pyclipper.Orientation(pointList)
self.segments = [
OutputSegment(
segmentType="flat",
points=[point]
) for point in pointList
]
def _scalePoint(self, point):
x, y = point
x = x * inverseClipperScale
if int(x) == x:
x = int(x)
y = y * inverseClipperScale
if int(y) == y:
y = int(y)
return x, y
# ----------
# Attributes
# ----------
def _get_final(self):
# XXX this could be optimized:
# store a fixed value after teh contour is finalized
# don't do the dymanic searching if that flag is set to True
for segment in self.segments:
if not segment.final:
return False
return True
final = property(_get_final)
# --------------------------
# Re-Curve and Curve Fitting
# --------------------------
def reCurveFromEntireInputContour(self, inputContour):
"""
Match if entire input contour matches entire output contour,
allowing for different start point.
"""
if self.clockwise:
inputFlat = inputContour.clockwiseFlat
else:
inputFlat = inputContour.counterClockwiseFlat
outputFlat = []
for segment in self.segments:
# XXX this could be expensive
assert segment.segmentType == "flat"
outputFlat += segment.points
# test lengths
haveMatch = False
if len(inputFlat) == len(outputFlat):
if inputFlat == outputFlat:
haveMatch = True
else:
inputStart = inputFlat[0]
if inputStart in outputFlat:
# there should be only one occurance of the point
# but handle it just in case
if outputFlat.count(inputStart) > 1:
startIndexes = [index for index, point in enumerate(outputFlat) if point == inputStart]
else:
startIndexes = [outputFlat.index(inputStart)]
# slice and dice to test possible orders
for startIndex in startIndexes:
test = outputFlat[startIndex:] + outputFlat[:startIndex]
if inputFlat == test:
haveMatch = True
break
if haveMatch:
# clear out the flat points
self.segments = []
# replace with the appropriate points from the input
if self.clockwise:
inputSegments = inputContour.clockwiseSegments
else:
inputSegments = inputContour.counterClockwiseSegments
for inputSegment in inputSegments:
self.segments.append(
OutputSegment(
segmentType=inputSegment.segmentType,
points=[
OutputPoint(
coordinates=point.coordinates,
segmentType=point.segmentType,
smooth=point.smooth,
name=point.name,
kwargs=point.kwargs
)
for point in inputSegment.points
],
final=True
)
)
inputSegment.used = True
# reset the direction of the final contour
self.clockwise = inputContour.clockwise
return True
return False
def reCurveFromInputContourSegments(self, inputContour):
return
# match individual segments
if self.clockwise:
inputSegments = inputContour.clockwiseSegments
else:
inputSegments = inputContour.counterClockwiseSegments
for inputSegment in inputSegments:
# skip used
if inputSegment.used:
continue
# skip if the input contains more points than the entire output contour
if len(inputSegment.flat) > len(self.segments):
continue
# skip if the input end is not in the contour
inputSegmentLastPoint = inputSegment.flat[-1]
outputFlat = [segment.points[-1] for segment in self.segments]
if inputSegmentLastPoint not in outputFlat:
continue
# work through all output segments
for outputSegmentIndex, outputSegment in enumerate(self.segments):
# skip finalized
if outputSegment.final:
continue
# skip if the output point doesn't match the input end
if outputSegment.points[-1] != inputSegmentLastPoint:
continue
# make a set of ranges for slicing the output into a testable list of points
inputLength = len(inputSegment.flat)
outputRanges = []
outputSegmentIndex += 1
if outputSegmentIndex - inputLength < 0:
r1 = (len(self.segments) + outputSegmentIndex - inputLength, len(self.segments))
outputRanges.append(r1)
r2 = (0, outputSegmentIndex)
outputRanges.append(r2)
else:
outputRanges.append((outputSegmentIndex - inputLength, outputSegmentIndex))
# gather the output segments
testableOutputSegments = []
for start, end in outputRanges:
testableOutputSegments += self.segments[start:end]
# create a list of points
test = []
for s in testableOutputSegments:
# stop if a segment is final
if s.final:
test = None
break
test.append(s.points[-1])
if test == inputSegment.flat and inputSegment.segmentType != "line":
# insert new segment
newSegment = OutputSegment(
segmentType=inputSegment.segmentType,
points=[
OutputPoint(
coordinates=point.coordinates,
segmentType=point.segmentType,
smooth=point.smooth,
name=point.name,
kwargs=point.kwargs
)
for point in inputSegment.points
],
final=True
)
self.segments.insert(outputSegmentIndex, newSegment)
# remove old segments
# XXX this is sloppy
for start, end in outputRanges:
if start > outputSegmentIndex:
start += 1
end += 1
del self.segments[start:end]
# flag the original as used
inputSegment.used = True
break
# ? match line start points (to prevent curve fit in shortened line)
return False
def reCurveSubSegmentsCheckInputContoursOnHasCurve(self, inputContours):
# test is the remaining input contours contains only lineTo points
# XXX could be cached
return True
# for inputContour in inputContours:
# if inputContour.used:
# continue
# if inputContour.hasOnCurve():
# return True
# return False
def reCurveSubSegments(self, inputContours):
if not self.segments:
# its all done
return
# the inputContours has some curved segments
# if not it all the segments will be converted at the end
if self.reCurveSubSegmentsCheckInputContoursOnHasCurve(inputContours):
# collect all flat points in a dict of unused inputContours
# collect both clockwise segment and counterClockwise segments
# it happens a lot that the directions turns around
# the clockwise attribute can help but testing the directions is always needed
# collect all oncurve points as well
flatInputPointsSegmentDict = dict()
reversedFlatInputPointsSegmentDict = dict()
flatIntputOncurves = set()
for inputContour in inputContours:
if inputContour.used:
continue
if self.clockwise:
inputSegments = inputContour.clockwiseSegments
reversedSegments = inputContour.counterClockwiseSegments
else:
inputSegments = inputContour.counterClockwiseSegments
reversedSegments = inputContour.clockwiseSegments
for inputSegment in inputSegments:
if inputSegment.used:
continue
for p in inputSegment.flat:
flatInputPointsSegmentDict[p] = inputSegment
flatIntputOncurves.add(inputSegment.scaledPreviousOnCurve)
for inputSegment in reversedSegments:
if inputSegment.used:
continue
for p in inputSegment.flat:
reversedFlatInputPointsSegmentDict[p] = inputSegment
flatIntputOncurves.add(inputSegment.scaledPreviousOnCurve)
flatInputPoints = set(flatInputPointsSegmentDict.keys())
# reset the starting point to a known point.
# not somewhere in the middle of a flatten point list
firstSegment = self.segments[0]
foundStartingPoint = True
if firstSegment.segmentType == "flat":
foundStartingPoint = False
for index, segment in enumerate(self.segments):
if segment.segmentType in ["line", "curve", "qcurve"]:
foundStartingPoint = True
break
if foundStartingPoint:
# if found re index the segments
# if there is no known starting point found do it later based on the intersection points
self.segments = self.segments[index:] + self.segments[:index]
# collect all flat points in a intersect segment
remainingSubSegment = OutputSegment(segmentType="intersect", points=[])
# store all segments in one big temp list
newSegments = []
for index, segment in enumerate(self.segments):
if segment.segmentType != "flat":
# when the segment contains only one points its a line cause it is a single intersection point
if len(remainingSubSegment.points) == 1:
remainingSubSegment.segmentType = "line"
remainingSubSegment.final = True
remainingSubSegment.points = [
OutputPoint(
coordinates=self._scalePoint(point),
segmentType="line",
smooth=point.smooth,
name=point.name,
kwargs=point.kwargs
)
for point in remainingSubSegment.points
]
newSegments.append(remainingSubSegment)
remainingSubSegment = OutputSegment(segmentType="intersect", points=[])
newSegments.append(segment)
continue
remainingSubSegment.points.extend(segment.points)
newSegments.append(remainingSubSegment)
# loop over all segments
for segment in newSegments:
# handle only segments tagged as intersect
if segment.segmentType != "intersect":
continue
# skip empty segments
if not segment.points:
continue
# get al inputSegments, this is an unorderd list of all points no in the the flatInputPoints
segmentPointsSet = set(segment.points)
intersectionPoints = segmentPointsSet - flatInputPoints
# merge both oncurves and intersectionPoints as known points
possibleStartingPoints = flatIntputOncurves | intersectionPoints
hasOncurvePoints = segmentPointsSet & flatIntputOncurves
# if not starting point is found earlier do it here
foundStartingPointIndex = None
if not foundStartingPoint:
for index, p in enumerate(segment.points):
if p in flatIntputOncurves:
foundStartingPointIndex = index
break
if foundStartingPointIndex is None:
for index, p in enumerate(segment.points):
if p in intersectionPoints:
foundStartingPointIndex = index
break
segment.points = segment.points[foundStartingPointIndex:] + segment.points[:foundStartingPointIndex]
# split list based on oncurvepoints and intersection points, aka possibleStartingPoints.
segmentedFlatPoints = [[]]
for p in segment.points:
segmentedFlatPoints[-1].append(p)
if p in possibleStartingPoints:
segmentedFlatPoints.append([])
if not segmentedFlatPoints[-1]:
segmentedFlatPoints.pop(-1)
if len(segmentedFlatPoints) > 1 and len(segmentedFlatPoints[0]) == 1:
# if last segment is a curve, the start point may be last point on the last segment. If so, merge them.
# check if they both have the same inputSegment or reversedInputSegment
fp = segmentedFlatPoints[0][0]
lp = segmentedFlatPoints[-1][-1]
mergeFirstSegments = False
if fp in flatInputPoints and lp in flatInputPoints:
firstInputSegment = flatInputPointsSegmentDict[fp]
lastInputSegment = flatInputPointsSegmentDict[lp]
reversedFirstInputSegment = reversedFlatInputPointsSegmentDict[fp]
reversedLastInputSegment = reversedFlatInputPointsSegmentDict[lp]
if (firstInputSegment.segmentType == reversedFirstInputSegment.segmentType == "curve") or (lastInputSegment.segmentType == reversedLastInputSegment.segmentType == "curve"):
if firstInputSegment == lastInputSegment or reversedFirstInputSegment == reversedLastInputSegment:
mergeFirstSegments = True
# elif len(firstInputSegment.points) > 1 and len(lastInputSegment.points) > 1:
elif fp == lastInputSegment.scaledPreviousOnCurve:
mergeFirstSegments = True
elif lp == firstInputSegment.scaledPreviousOnCurve:
mergeFirstSegments = True
elif fp == reversedLastInputSegment.scaledPreviousOnCurve:
mergeFirstSegments = True
elif lp == reversedFirstInputSegment.scaledPreviousOnCurve:
mergeFirstSegments = True
elif not hasOncurvePoints and _distance(fp, lp):
# Merge last segment with first segment if the distance between the last point and the first
# point is less than the step distance between the last two points. _approximateSegmentLength
# can be significantly smaller than this step size.
if len(segmentedFlatPoints[-1]) > 1:
f1 = segmentedFlatPoints[-1][-2]
f2 = segmentedFlatPoints[-1][-1]
stepLen = _distance(f1, f2)
else:
stepLen = _approximateSegmentLength*clipperScale
if _distance(fp, lp) <= stepLen:
mergeFirstSegments = True
if mergeFirstSegments:
segmentedFlatPoints[0] = segmentedFlatPoints[-1] + segmentedFlatPoints[0]
segmentedFlatPoints.pop(-1)
mergeFirstSegments = False
convertedSegments = []
previousIntersectionPoint = None
if segmentedFlatPoints[-1][-1] in intersectionPoints:
previousIntersectionPoint = self._scalePoint(segmentedFlatPoints[-1][-1])
elif segmentedFlatPoints[0][0] in intersectionPoints:
previousIntersectionPoint = self._scalePoint(segmentedFlatPoints[0][0])
for flatSegment in segmentedFlatPoints:
# search two points in the flat segment that is not an inputOncurve or intersection point
# to get a proper direction of the flatSegment
# based on these two points pick a inputSegment
fp = ep = None
for p in flatSegment:
if p in possibleStartingPoints:
continue
elif fp is None:
fp = p
elif ep is None:
ep = p
else:
break
canDoFastLine = True
if ep is None and ((fp is None) or (len(flatSegment) == 2)):
# if fp is not None, then it is a flattened part of a curve, and should be used to derive the input segment.
# It may be either the first or second point.
# If fp is None, I use the original logic.
if fp is None:
fp = flatSegment[-1]
# flat segment only contains two intersection points or one intersection point and one input oncurve point
# this can be ignored cause this is a very small line
# and will be converted to a simple line
if self.clockwise:
inputSegment = reversedFlatInputPointsSegmentDict.get(fp)
else:
inputSegment = flatInputPointsSegmentDict.get(fp)
else:
# get inputSegment based on the clockwise settings
inputSegment = flatInputPointsSegmentDict[fp]
if ep is not None and ep in inputSegment.flat:
# if two points are found get indexes
fi = inputSegment.flat.index(fp)
ei = inputSegment.flat.index(ep)
if fi > ei:
# if the start index is bigger
# get the reversed inputSegment
inputSegment = reversedFlatInputPointsSegmentDict[fp]
else:
# if flat segment is short and has only one point not in intersections and input oncurves
# test it against the reversed inputSegment
reversedInputSegment = reversedFlatInputPointsSegmentDict[fp]
if flatSegment[0] == reversedInputSegment.flat[0] and flatSegment[-1] == reversedInputSegment.flat[-1]:
inputSegment = reversedInputSegment
elif flatSegment[0] in intersectionPoints and flatSegment[-1] == reversedInputSegment.flat[-1]:
inputSegment = reversedInputSegment
elif flatSegment[-1] in intersectionPoints and flatSegment[0] == reversedInputSegment.flat[0]:
inputSegment = reversedInputSegment
canDoFastLine = False
# if there is only one point in a flat segment
# this is a single intersection points (two crossing lineTo's)
if inputSegment.segmentType == "curve":
canDoFastLine = False
if (len(flatSegment) == 1 or inputSegment is None) and canDoFastLine:
# p = flatSegment[0]
for p in flatSegment:
previousIntersectionPoint = self._scalePoint(p)
pointInfo = dict()
kwargs = dict()
if p in flatInputPointsSegmentDict:
lineSegment = flatInputPointsSegmentDict[p]
segmentPoint = lineSegment.points[-1]
pointInfo["smooth"] = segmentPoint.smooth
pointInfo["name"] = segmentPoint.name
kwargs.update(segmentPoint.kwargs)
convertedSegments.append(OutputPoint(coordinates=previousIntersectionPoint, segmentType="line", kwargs=kwargs, **pointInfo))
continue
tValues = None
lastPointWithAttributes = None
if flatSegment[0] == inputSegment.flat[0] and flatSegment[-1] != inputSegment.flat[-1]:
# needed the first part of the segment
# if previousIntersectionPoint is None:
# previousIntersectionPoint = self._scalePoint(flatSegment[-1])
searchPoint = self._scalePoint(flatSegment[-1])
tValues = inputSegment.tValueForPoint(searchPoint)
curveNeeded = 0
replacePointOnNewCurve = [(3, searchPoint)]
previousIntersectionPoint = searchPoint
elif flatSegment[-1] == inputSegment.flat[-1] and flatSegment[0] != inputSegment.flat[0]:
# needed the end of the segment
if previousIntersectionPoint is None:
previousIntersectionPoint = self._scalePoint(flatSegment[0])
convertedSegments.append(OutputPoint(
coordinates=previousIntersectionPoint,
segmentType="line",
))
tValues = inputSegment.tValueForPoint(previousIntersectionPoint)
curveNeeded = -1
replacePointOnNewCurve = [(0, previousIntersectionPoint)]
previousIntersectionPoint = None
lastPointWithAttributes = inputSegment.points[-1]
elif flatSegment[0] != inputSegment.flat[0] and flatSegment[-1] != inputSegment.flat[-1]:
# needed the a middle part of the segment
if previousIntersectionPoint is None:
previousIntersectionPoint = self._scalePoint(flatSegment[0])
tValues = inputSegment.tValueForPoint(previousIntersectionPoint)
searchPoint = self._scalePoint(flatSegment[-1])
tValues.extend(inputSegment.tValueForPoint(searchPoint))
curveNeeded = 1
replacePointOnNewCurve = [(0, previousIntersectionPoint), (3, searchPoint)]
previousIntersectionPoint = searchPoint
else:
# take the whole segments as is
newCurve = [
OutputPoint(
coordinates=point.coordinates,
segmentType=point.segmentType,
smooth=point.smooth,
name=point.name,
kwargs=point.kwargs
)
for point in inputSegment.points
]
convertedSegments.extend(newCurve)
previousIntersectionPoint = None
# if we found some tvalue, split the curve and get the requested parts of the splitted curves
if tValues:
newCurve = inputSegment.split(tValues)
newCurve = list(newCurve[curveNeeded])
for i, replace in replacePointOnNewCurve:
newCurve[i] = replace
newCurve = [OutputPoint(coordinates=p, segmentType=None) for p in newCurve[1:]]
newCurve[-1].segmentType = inputSegment.segmentType
if lastPointWithAttributes is not None:
newCurve[-1].smooth = lastPointWithAttributes.smooth
newCurve[-1].name = lastPointWithAttributes.name
newCurve[-1].kwargs = lastPointWithAttributes.kwargs
convertedSegments.extend(newCurve)
# replace the the points with the converted segments
segment.points = convertedSegments
segment.segmentType = "reCurved"
self.segments = newSegments
# XXX convert all of the remaining segments to lines
for segment in self.segments:
if not segment.points:
continue
if segment.segmentType not in ["intersect", "flat"]:
continue
segment.segmentType = "line"
segment.points = [
OutputPoint(
coordinates=self._scalePoint(point),
segmentType="line",
# smooth=point.smooth,
# name=point.name,
# kwargs=point.kwargs
)
for point in segment.points
]
# ----
# Draw
# ----
def drawPoints(self, pointPen):
pointPen.beginPath()
points = []
for segment in self.segments:
points.extend(segment.points)
hasOnCurve = False
originalStartingPoints = []
for index, point in enumerate(points):
if point.segmentType is not None:
hasOnCurve = True
if point.kwargs is not None and point.kwargs.get("startingPoint"):
distanceFromOrigin = math.hypot(*point)
originalStartingPoints.append((distanceFromOrigin, index))
if originalStartingPoints:
# use the original starting point that is closest to the origin
startingPointIndex = sorted(originalStartingPoints)[0][1]
points = points[startingPointIndex:] + points[:startingPointIndex]
elif hasOnCurve:
while points[0].segmentType is None:
p = points.pop(0)
points.append(p)
previousPointCoordinates = None
for point in points:
if previousPointCoordinates is not None and point.segmentType and tuple(point.coordinates) == previousPointCoordinates:
continue
kwargs = {}
if point.kwargs is not None:
kwargs = point.kwargs
pointPen.addPoint(
point.coordinates,
segmentType=point.segmentType,
smooth=point.smooth,
name=point.name,
**kwargs
)
if point.segmentType:
previousPointCoordinates = tuple(point.coordinates)
else:
previousPointCoordinates = None
pointPen.endPath()
class OutputSegment(object):
__slots__ = ["segmentType", "points", "final"]
def __init__(self, segmentType=None, points=None, final=False):
self.segmentType = segmentType
if points is None:
points = []
self.points = points
self.final = final
class OutputPoint(InputPoint):
pass
# ----------
# Misc. Math
# ----------
def _tValueForPointOnCubicCurve(point, cubicCurve, isHorizontal=0):
"""
Finds a t value on a curve from a point.
The points must be originaly be a point on the curve.
This will only back trace the t value, needed to split the curve in parts
"""
pt1, pt2, pt3, pt4 = cubicCurve
a, b, c, d = bezierTools.calcCubicParameters(pt1, pt2, pt3, pt4)
solutions = bezierTools.solveCubic(a[isHorizontal], b[isHorizontal], c[isHorizontal],
d[isHorizontal] - point[isHorizontal])
solutions = [t for t in solutions if 0 <= t < 1]
if not solutions and not isHorizontal:
# can happen that a horizontal line doens intersect, try the vertical
return _tValueForPointOnCubicCurve(point, (pt1, pt2, pt3, pt4), isHorizontal=1)
if len(solutions) > 1:
intersectionLenghts = {}
for t in solutions:
tp = _getCubicPoint(t, pt1, pt2, pt3, pt4)
dist = _distance(tp, point)
intersectionLenghts[dist] = t
minDist = min(intersectionLenghts.keys())
solutions = [intersectionLenghts[minDist]]
return solutions
def _tValueForPointOnQuadCurve(point, pts, isHorizontal=0):
quadSegments = decomposeQuadraticSegment(pts[1:])
previousOnCurve = pts[0]
solutionsDict = dict()
for index, (pt1, pt2) in enumerate(quadSegments):
a, b, c = bezierTools.calcQuadraticParameters(previousOnCurve, pt1, pt2)
subSolutions = bezierTools.solveQuadratic(a[isHorizontal], b[isHorizontal], c[isHorizontal] - point[isHorizontal])
subSolutions = [t for t in subSolutions if 0 <= t < 1]
for t in subSolutions:
solutionsDict[(t, index)] = _getQuadPoint(t, previousOnCurve, pt1, pt2)
previousOnCurve = pt2
solutions = list(solutionsDict.keys())
if not solutions and not isHorizontal:
return _tValueForPointOnQuadCurve(point, pts, isHorizontal=1)
if len(solutions) > 1:
intersectionLenghts = {}
for t in solutions:
tp = solutionsDict[t]
dist = _distance(tp, point)
intersectionLenghts[dist] = t
minDist = min(intersectionLenghts.keys())
solutions = [intersectionLenghts[minDist]]
return solutions
def _tValueForPointOnLine(point, line):
pt1, pt2 = line
dist = _distance(pt1, point)
totalDist = _distance(pt1, pt2)
return [dist / totalDist]
def _scalePoints(points, scale=1, convertToInteger=True):
"""
Scale points and optionally convert them to integers.
"""
if convertToInteger:
points = [
(int(round(x * scale)), int(round(y * scale)))
for (x, y) in points
]
else:
points = [(x * scale, y * scale) for (x, y) in points]
return points
def _scaleSinglePoint(point, scale=1, convertToInteger=True):
"""
Scale a single point
"""
x, y = point
if convertToInteger:
return int(round(x * scale)), int(round(y * scale))
else:
return (x * scale, y * scale)
def _intPoint(pt):
return int(round(pt[0])), int(round(pt[1]))
def _checkFlatPoints(points):
_points = []
previousX = previousY = None
for x, y in points:
if x == previousX:
continue
elif y == previousY:
continue
if (x, y) not in _points:
# is it possible that two flat point are on top of eachother???
_points.append((x, y))
previousX, previousY = x, y
if _points[-1] != points[-1]:
_points[-1] = points[-1]
return _points
"""
The curve flattening code was forked and modified from RoboFab's FilterPen.
That code was written by Erik van Blokland.
"""
def _flattenSegment(segment, approximateSegmentLength=_approximateSegmentLength):
"""
Flatten the curve segment int a list of points.
The first and last points in the segment must be
on curves. The returned list of points will not
include the first on curve point.
false curves (where the off curves are not any
different from the on curves) must not be sent here.
duplicate points must not be sent here.
"""
onCurve1, offCurve1, offCurve2, onCurve2 = segment
if _pointOnLine(onCurve1, onCurve2, offCurve1) and _pointOnLine(onCurve1, onCurve2, offCurve2):
return [onCurve2]
est = _estimateCubicCurveLength(onCurve1, offCurve1, offCurve2, onCurve2) / approximateSegmentLength
flat = []
minStep = 0.1564
step = 1.0 / est
if step > .3:
step = minStep
t = step
while t < 1:
pt = _getCubicPoint(t, onCurve1, offCurve1, offCurve2, onCurve2)
# ignore when point is in the same direction as the on - off curve line
if not _pointOnLine(offCurve2, onCurve2, pt) and not _pointOnLine(onCurve1, offCurve1, pt):
flat.append(pt)
t += step
flat.append(onCurve2)
return flat
def _distance(pt1, pt2):
return math.sqrt((pt1[0] - pt2[0]) ** 2 + (pt1[1] - pt2[1]) ** 2)
def _pointOnLine(pt1, pt2, a):
return abs(_distance(pt1, a) + _distance(a, pt2) - _distance(pt1, pt2)) < epsilon
def _estimateCubicCurveLength(pt0, pt1, pt2, pt3, precision=10):
"""
Estimate the length of this curve by iterating
through it and averaging the length of the flat bits.
"""
points = []
length = 0
step = 1.0 / precision
factors = range(0, precision + 1)
for i in factors:
points.append(_getCubicPoint(i * step, pt0, pt1, pt2, pt3))
for i in range(len(points) - 1):
pta = points[i]
ptb = points[i + 1]
length += _distance(pta, ptb)
return length
def _mid(pt1, pt2):
"""
(Point, Point) -> Point
Return the point that lies in between the two input points.
"""
(x0, y0), (x1, y1) = pt1, pt2
return 0.5 * (x0 + x1), 0.5 * (y0 + y1)
def _getCubicPoint(t, pt0, pt1, pt2, pt3):
if t == 0:
return pt0
if t == 1:
return pt3
if t == 0.5:
a = _mid(pt0, pt1)
b = _mid(pt1, pt2)
c = _mid(pt2, pt3)
d = _mid(a, b)
e = _mid(b, c)
return _mid(d, e)
else:
cx = (pt1[0] - pt0[0]) * 3.0
cy = (pt1[1] - pt0[1]) * 3.0
bx = (pt2[0] - pt1[0]) * 3.0 - cx
by = (pt2[1] - pt1[1]) * 3.0 - cy
ax = pt3[0] - pt0[0] - cx - bx
ay = pt3[1] - pt0[1] - cy - by
t3 = t ** 3
t2 = t * t
x = ax * t3 + bx * t2 + cx * t + pt0[0]
y = ay * t3 + by * t2 + cy * t + pt0[1]
return x, y
def _getQuadPoint(t, pt0, pt1, pt2):
if t == 0:
return pt0
if t == 1:
return pt2
else:
cx = pt0[0]
cy = pt0[1]
bx = (pt1[0] - cx) * 2.0
by = (pt1[1] - cy) * 2.0
ax = pt2[0] - cx - bx
ay = pt2[1] - cy - by
x = ax * t**2 + bx * t + cx
y = ay * t**2 + by * t + cy
return x, y
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