def windingNumberOfPoint(self, pt):
bounds = self.bounds()
bounds.addMargin(10)
ray1 = Line(Point(bounds.left, pt.y), pt)
ray2 = Line(Point(bounds.right, pt.y), pt)
leftIntersections = {}
rightIntersections = {}
leftWinding = 0
rightWinding = 0
for s in self.asSegments():
for i in s.intersections(ray1):
# print("Found left intersection with %s: %s" % (ray1, i.point))
leftIntersections[i.point] = i
for i in s.intersections(ray2):
rightIntersections[i.point] = i
for i in leftIntersections.values():
# XXX tangents here are all positive? Really?
# print(i.seg1, i.t1, i.point)
tangent = s.tangentAtTime(i.t1)
# print("Tangent at left intersection %s is %f" % (i.point,tangent.y))
leftWinding += int(math.copysign(1, tangent.y))
for i in rightIntersections.values():
tangent = s.tangentAtTime(i.t1)
# print("Tangent at right intersection %s is %f" % (i.point,tangent.y))
rightWinding += int(math.copysign(1, tangent.y))
# print("Left winding: %i right winding: %i " % (leftWinding,rightWinding))
return max(abs(leftWinding), abs(rightWinding))
def thicknessAtX(path, x):
"""Returns the thickness of the path at x-coordinate ``x``."""
bounds = path.bounds()
bounds.addMargin(10)
ray = Line(Point(x - 0.1, bounds.bottom), Point(x + 0.1, bounds.top))
intersections = []
for seg in path.asSegments():
intersections.extend(seg.intersections(ray))
if len(intersections) < 2:
return None
intersections = list(sorted(intersections, key=lambda i: i.point.y))
i1, i2 = intersections[0:2]
inorm1 = i1.seg1.normalAtTime(i1.t1)
ray1 = Line(i1.point + (inorm1 * 1000), i1.point + (inorm1 * -1000))
iii = i2.seg1.intersections(ray1)
if iii:
ll1 = i1.point.distanceFrom(iii[0].point)
else:
# Simple, vertical version
return abs(i1.point.y - i2.point.y)
inorm2 = i2.seg1.normalAtTime(i2.t1)
ray2 = Line(i2.point + (inorm2 * 1000), i2.point + (inorm2 * -1000))
iii = i1.seg1.intersections(ray2)
if iii:
ll2 = i2.point.distanceFrom(iii[0].point)
return (ll1 + ll2) * 0.5
else:
return ll1
def flatten(self, degree=8):
samples = self.regularSample(self.length/degree)
ss = []
for i in range(1,len(samples)):
l = Line(samples[i-1], samples[i])
l._orig = self
ss.append(l)
return ss
def flatten(self, degree=8):
samples = self.sample(self.length / degree)
ss = []
for i in range(1, len(samples)):
l = Line(samples[i - 1], samples[i])
l._orig = self
ss.append(l)
return ss
def drawWithBrush(self, other):
"""Assuming that `other` is a closed Bezier path representing a pen or
brush of a certain shape and that `self` is an open path, this method
traces the brush along the path, returning an array of Bezier paths.
`other` may also be a function which, given a time `t` (0-1), returns a closed
path representing the shape of the brush at the given time.
This requires the `shapely` library to be installed.
"""
from shapely.geometry import Polygon
from shapely.ops import unary_union
polys = []
samples = self.sample(self.length / 2)
def constantBrush(t):
return other
brush = other
if not callable(brush):
brush = constantBrush
c = brush(0).centroid
from itertools import tee
def pairwise(iterable):
"s -> (s0,s1), (s1,s2), (s2, s3), ..."
a, b = tee(iterable)
next(b, None)
return zip(a, b)
t = 0
for n in samples:
brushHere = brush(t).clone().flatten()
brushHere.translate(n - brushHere.centroid)
polys.append(
Polygon([(x[0].x, x[0].y) for x in brushHere.asSegments()]))
t = t + 1.0 / len(samples)
concave_hull = unary_union(polys)
ll = []
for x, y in pairwise(concave_hull.exterior.coords):
l = Line(Point(x[0], x[1]), Point(y[0], y[1]))
ll.append(l)
paths = [BezierPath.fromSegments(ll)]
for interior in concave_hull.interiors:
ll = []
for x, y in pairwise(interior.coords):
l = Line(Point(x[0], x[1]), Point(y[0], y[1]))
ll.append(l)
paths.append(BezierPath.fromSegments(ll))
return paths
def tunniPoint(self):
"""Returns the Tunni point of this Bezier (the intersection of
the handles)."""
h1 = Line(self[0], self[1])
h2 = Line(self[2], self[3])
i = h1.intersections(h2, limited = False)
if len(i)<1: return
i = i[0].point
if i.distanceFrom(self[0]) > 5 * self.length:
return
else:
return i
def tunniPoint(self):
"""Returns the Tunni point of this Bezier (the intersection of
the handles)."""
h1 = Line(self[0], self[1])
h2 = Line(self[2], self[3])
i = h1.intersections(h2, limited=False)
if len(i) < 1: return
i = i[0].point
if i.distanceFrom(self[0]) > 5 * self.length:
return
else:
return i
def Rectangle(width, height, origin=None):
"""Returns a path representing an rectangle of given width and height.
You can specify the `origin` as a Point."""
if not origin:
origin = Point(0, 0)
tl = origin + west * width / 2.0 + north * height / 2.0
tr = origin + east * width / 2.0 + north * height / 2.0
bl = origin + west * width / 2.0 + south * height / 2.0
br = origin + east * width / 2.0 + south * height / 2.0
return BezierPath.fromSegments(
[Line(tl, tr), Line(tr, br),
Line(br, bl), Line(bl, tl)])
def harmonize(self, seg1, seg2):
if seg1.end.x != seg2.start.x or seg1.end.y != seg2.start.y: return
a1, a2 = seg1[1], seg1[2]
b1, b2 = seg2[1], seg2[2]
intersections = Line(a1, a2).intersections(Line(b1, b2), limited=False)
if not intersections[0]: return
p0 = a1.distanceFrom(a2) / a2.distanceFrom(intersections[0].point)
p1 = b1.distanceFrom(intersections[0].point) / b1.distanceFrom(b2)
r = math.sqrt(p0 * p1)
t = r / (r + 1)
newA3 = a2.lerp(b1, t)
fixup = seg2.start - newA3
seg1[2] += fixup
seg2[1] += fixup
def test_cubic_line_2(self):
s1 = CubicBezier.fromRepr(
"B<<584.0,126.03783241124995>-<402.0,163.0378324112499>-<220.00000000000003,200.03783241124995>-<38.0,237.03783241124995>>"
),
ray = Line.fromRepr(
"L<<357.4,-9.99999999999999>--<357.6,250.2692949284206>>")
assert (s1[0].intersections(ray))
def append(self, other, joinType="line"):
"""Append another path to this one. If the end point of the first
path is not the same as the start point of the other path, a line
will be drawn between them."""
segs1 = self.asSegments()
segs2 = other.asSegments()
if len(segs1) < 1:
self.activeRepresentation = SegmentRepresentation(self, segs2)
return
if len(segs2) < 1:
self.activeRepresentation = SegmentRepresentation(self, segs1)
return
# Which way around should they go?
dist1 = segs1[-1].end.distanceFrom(segs2[0].start)
dist2 = segs1[-1].end.distanceFrom(segs2[-1].end)
if dist2 > 2 * dist1:
segs2 = list(reversed([x.reversed() for x in segs2]))
# Add a line between if they don't match up
if segs1[-1].end != segs2[0].start:
segs1.append(Line(segs1[-1].end, segs2[0].start))
# XXX Check for discontinuities and harmonize if needed
segs1.extend(segs2)
self.activeRepresentation = SegmentRepresentation(self, segs1)
return self
def appendSegment(self, seg):
seg = [Point(n[0], n[1]) for n in seg]
if len(seg) == 2:
self.segments.append(Line(*seg))
elif len(seg) == 3:
self.segments.append(QuadraticBezier(*seg))
elif len(seg) == 4:
self.segments.append(CubicBezier(*seg))
else:
raise ValueError("Unknown segment type")
def thickness_at_x(path, x):
"""Find the path thickness at a given X coordinate
This measure the thickness of the lowest horizontal stem at the given
coordinate. If there is no stem at this X coordinate, ``None`` is
returned.
Args:
path: A ``beziers.path.BezierPath`` object
x: X coordinate to search
Returns:
The thickness of the path at this point, in font units.
"""
bounds = path.bounds()
bounds.addMargin(10)
ray = Line(Point(x - 0.1, bounds.bottom), Point(x + 0.1, bounds.top))
intersections = []
for seg in path.asSegments():
intersections.extend(seg.intersections(ray))
if len(intersections) < 2:
return None
intersections = list(sorted(intersections, key=lambda i: i.point.y))
i1, i2 = intersections[0:2]
inorm1 = i1.seg1.normalAtTime(i1.t1)
ray1 = Line(i1.point + (inorm1 * 1000), i1.point + (inorm1 * -1000))
iii = i2.seg1.intersections(ray1)
if iii:
ll1 = i1.point.distanceFrom(iii[0].point)
else:
# Simple, vertical version
return abs(i1.point.y - i2.point.y)
inorm2 = i2.seg1.normalAtTime(i2.t1)
ray2 = Line(i2.point + (inorm2 * 1000), i2.point + (inorm2 * -1000))
iii = i1.seg1.intersections(ray2)
if iii:
ll2 = i2.point.distanceFrom(iii[0].point)
return (ll1 + ll2) * 0.5
else:
return ll1
def test_cubic_line(self):
q = CubicBezier(Point(100, 240), Point(30, 60), Point(210, 230),
Point(160, 30))
l = Line(Point(25, 260), Point(230, 20))
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, [q])
i = q.intersections(l)
self.assertEqual(len(i), 3)
self.assertEqual(i[0].point, q.pointAtTime(0.117517031451))
self.assertEqual(i[1].point, q.pointAtTime(0.518591792307))
self.assertEqual(i[2].point, q.pointAtTime(0.867886610031))
def get_yb_clearance(self, parser, bariye):
font = parser.font
paths = get_bezier_paths(font, bariye)
path = paths[0]
bounds = path.bounds()
x_of_tail = get_rise(font.font, bariye)
ray = Line(
Point(x_of_tail - 0.1, bounds.bottom - 5),
Point(x_of_tail + 0.1, bounds.top + 5),
)
intersections = []
for seg in path.asSegments():
intersections.extend(seg.intersections(ray))
intersections = list(sorted(intersections, key=lambda i: i.point.y))
i = intersections[-1]
return i.point.y
def xheight_intersections(ttFont, glyph):
glyphset = ttFont.getGlyphSet()
if glyph not in glyphset:
return []
paths = BezierPath.fromFonttoolsGlyph(ttFont, glyph)
if len(paths) != 1:
return []
path = paths[0]
xheight = ttFont["OS/2"].sxHeight
bounds = path.bounds()
bounds.addMargin(10)
ray = Line(Point(bounds.left, xheight), Point(bounds.right, xheight))
intersections = []
for seg in path.asSegments():
intersections.extend(seg.intersections(ray))
return sorted(intersections, key=lambda i: i.point.x)
def bestcut(self, args=None):
""" Find the best line that cuts this octabox and its segments so that the
resulting two bounding octaboxes (of the two sets of segments) is minimised."""
currbest = OctaScore(self, None, self.area)
for x, d in enumerate(((1, 0), (0, 1), (-1, 1), (1, 1))):
splitline = Line(Point(d[0] * self.xi, d[1] * self.yi),
Point(d[0] * self.xa, d[1] * self.ya))
for sl in findshifts(self.segs, splitline):
r, l = splitWith(self.segs, sl)
rightbox = Octabox(r)
leftbox = Octabox(l)
score = rightbox.area + leftbox.area
if args is not None and args.detail & 8:
print(" {}:L[{}, {}], R[{}, {}]".format(
"xysd"[x], leftbox.area,
sum(s.area for s in leftbox.segs), rightbox.area,
sum(s.area for s in rightbox.segs)))
if score < currbest.score:
currbest = OctaScore(leftbox, rightbox, score)
return currbest
def test_intercept(self): l = Line(Point(0,10),Point(20,20.4)) self.assertAlmostEqual(l.intercept, 10)
def test_slope(self): l = Line(Point(0,10),Point(20,20.4)) self.assertAlmostEqual(l.slope, 0.52)
def clip(self, clip, cliptype, flat=False):
splitlist1 = []
splitlist2 = []
intersections = {}
cloned = self.clone()
clip = clip.clone()
# Split all segments at intersections
for s1 in self.asSegments():
for s2 in clip.asSegments():
for i in s1.intersections(s2):
if i.t1 > 1e-8 and i.t1 < 1 - 1e-8:
if i.seg1 == s1:
splitlist1.append((i.seg1, i.t1))
splitlist2.append((i.seg2, i.t2))
else:
splitlist2.append((i.seg1, i.t1))
splitlist1.append((i.seg2, i.t2))
intersections[i.point] = i
logging.debug("Split list: %s" % splitlist1)
logging.debug("Split list 2: %s" % splitlist2)
cloned.splitAtPoints(splitlist1)
clip.splitAtPoints(splitlist2)
logging.debug("Self:")
logging.debug(cloned.asSegments())
logging.debug("Clip:")
logging.debug(clip.asSegments())
segs1unflattened = cloned.asSegments()
segs2unflattened = clip.asSegments()
# Replace with flattened versions, building a dictionary of originals
segs1 = []
reconstructionLUT = {}
precision = 100.
def fillLUT(flats):
for line in flats:
key = ((line.start * precision).rounded(),
(line.end * precision).rounded())
reconstructionLUT[key] = (line._orig or line)
key2 = ((line.end * precision).rounded(),
(line.start * precision).rounded())
reconstructionLUT[key2] = (line._orig or line).reversed()
for s in segs1unflattened:
flats = s.flatten(2)
fillLUT(flats)
segs1.extend(flats)
segs2 = []
for s in segs2unflattened:
flats = s.flatten(2)
fillLUT(flats)
segs2.extend(flats)
# Leave it to the professionals
subj = [(s[0].x * precision, s[0].y * precision) for s in segs1]
clip = [(s[0].x * precision, s[0].y * precision) for s in segs2]
pc = pyclipper.Pyclipper()
pc.AddPath(clip, pyclipper.PT_CLIP, True)
pc.AddPath(subj, pyclipper.PT_SUBJECT, True)
paths = pc.Execute(cliptype, pyclipper.PFT_EVENODD,
pyclipper.PFT_EVENODD)
outpaths = []
# Now reconstruct Bezier segments from flattened paths
def pairwise(points):
a = (p for p in points)
b = (p for p in points)
next(b)
for curpoint, nextpoint in zip(a, b):
yield curpoint, nextpoint
newpaths = []
from beziers.path import BezierPath
for p in paths:
newpath = []
for scaledstart, scaledend in pairwise(p):
key = (Point(*scaledstart), Point(*scaledend))
if key in reconstructionLUT and not flat:
orig = reconstructionLUT[key]
if len(newpath) == 0 or newpath[-1] != orig:
newpath.append(orig)
else:
newpath.append(Line(key[0] / precision,
key[1] / precision))
outpaths.append(BezierPath.fromSegments(newpath))
return outpaths
def test_cubic_line_3(self):
seg = CubicBezier.fromRepr(
"B<<320.0,454.0>-<277.0,454.0>-<230.0,439.0>-<189.0,417.0>>")
ray = Line.fromRepr(
"L<<254.5,221.5>--<254.5000000000001,887.6681469418963>>")
assert seg.intersections(ray)
# Subdivision
r1 = self.minDist(uinterval=(umin, newuMid), vinterval=(vmin, newvMid))
r2 = self.minDist(uinterval=(umin, newuMid), vinterval=(newvMid, vmax))
r3 = self.minDist(uinterval=(newuMid, umax), vinterval=(vmin, newvMid))
r4 = self.minDist(uinterval=(newuMid, umax), vinterval=(newvMid, vmax))
results = min([r1, r2, r3, r4], key=lambda x: x[0])
return results
def curveDistance(bez1, bez2):
"""Find the distance between two curves."""
c = MinimumCurveDistanceFinder(bez1, bez2)
dist, t1, t2 = c.minDist()
return math.sqrt(dist), t1, t2
if __name__ == "__main__":
bez1 = CubicBezier(Point(129, 139), Point(190, 139), Point(201, 364),
Point(90, 364))
bez2 = CubicBezier(Point(309, 159), Point(178, 159), Point(215, 408),
Point(309, 408))
bez3 = Line(Point(309, 159), Point(309, 408))
c = MinimumCurveDistanceFinder(bez1, bez3)
dist, t1, t2 = c.minDist()
print(bez1.pointAtTime(t1))
print(bez3.pointAtTime(t2))
print(math.sqrt(dist))
print(c.iterations)
def derivative(self):
"""Returns a `Line` representing the derivative of this curve."""
return Line((self[1] - self[0]) * 2, (self[2] - self[1]) * 2)
def splitWith(segs, splitline, args=None):
""" Splits a list of segments given a straight splitting line. Returns
2 lists of segments such that the resulting segments are closed paths. """
trans = splitline.alignmentTransformation()
lefts = []
rights = []
splits = []
for _s in segs:
# transform so splitline is horizontal and is y=0
s = _s.transformed(trans)
roots = s._findRoots("y")
# does y=0 cut this segment?
if len(roots) == 2:
# chop a quadratic cuver and put parts in left and right collection
l, r = s.splitAtTime(roots[0])
(rights if s.start.y < 0 else lefts).append(l)
l, r = r.splitAtTime(roots[1])
(rights if s.end.y < 0 else lefts).append(r)
# keep split points so we can add joinup lines later
splits.append(
(l.start.x, (l.start.x < s.start.x) ^ (s.start.y < 0)))
splits.append((l.end.x, (l.end.x > s.end.x) ^ (s.start.y < 0)))
elif len(roots) == 1:
# chop a straight line
l, r = s.splitAtTime(roots[0])
if s.start.y < 0:
rights.append(l)
lefts.append(r)
splits.append((r.start.x, True))
else:
lefts.append(l)
rights.append(r)
splits.append((r.start.x, False))
# otherwise no cut and simply allocate the segment
elif s.start.y < 0 or s.end.y < 0:
rights.append(s)
else:
lefts.append(s)
# to convert from y=0 back to original co-ordinates
backt = AffineTransformation()
backt.apply_backwards(trans)
backt.invert()
if args is not None and args.detail & 8:
print(" ", [(Point(s[0], 0).transformed(backt), s[1])
for s in sorted(splits)])
curr = False
lastP = None
# find adjacent pairs of bounding points on the splitline and join them up on either side
# thus making closed paths, even if the segments aren't end to start all the way round.
for x, d in sorted(splits):
newP = Point(x, 0)
if d != curr:
curr = d
if lastP is None:
lastP = newP
continue
l = Line(lastP, newP)
r = Line(newP, lastP)
if not d:
rights.append(l)
lefts.append(r)
lastP = newP
rights = [s.transformed(backt) for s in rights]
lefts = [s.transformed(backt) for s in lefts]
return (rights, lefts)
def test_line_line(self):
l1 = Line(Point(310, 389), Point(453, 222))
l2 = Line(Point(289, 251), Point(447, 367))
# Sanity check
self.assertEqual(len(l1.intersections(l2)), 1)
