def fromSegments(klass, array):
"""Construct a path from an array of Segment objects."""
self = klass()
for a in array:
assert (isinstance(a, Segment))
self.activeRepresentation = SegmentRepresentation(self, array)
return self
def removeIrrelevantSegments(self, relLength=1 / 50000, absLength=0):
"""Removes small and collinear line segments. Collinear line
segments are adjacent line segments which are heading in the same
direction, and hence can be collapsed into a single segment.
Small segments (those less than ``absLength`` units, or less than
``relLength`` as a fraction of the path's total length) are
removed entirely."""
segs = self.asSegments()
newsegs = [segs[0]]
smallLength = self.length * relLength
for i in range(1, len(segs)):
prev = newsegs[-1]
this = segs[i]
if this.length < smallLength or this.length < absLength:
this[0] = prev[0]
newsegs[-1] = this
continue
if len(prev) == 2 and len(this) == 2:
if math.isclose(
prev.tangentAtTime(0).angle,
this.tangentAtTime(0).angle):
this[0] = prev[0]
newsegs[-1] = this
continue
newsegs.append(this)
self.activeRepresentation = SegmentRepresentation(self, newsegs)
return self
def test_cubic_cubic(self):
# q1 = Bezier(10,100, 90,30, 40,140, 220,220)
# q2 = Bezier(5,150, 180,20, 80,250, 210,190)
# console.log(q1.intersects(q2))
q1 = CubicBezier(Point(10, 100), Point(90, 30), Point(40, 140),
Point(220, 220))
q2 = CubicBezier(Point(5, 150), Point(180, 20), Point(80, 250),
Point(210, 190))
i = q1.intersections(q2)
# self.assertEqual(len(i),3)
# self.assertAlmostEqual(i[0].point.x,81.7904225873)
# self.assertAlmostEqual(i[0].point.y,109.899396337)
# self.assertAlmostEqual(i[1].point.x,133.186831292)
# self.assertAlmostEqual(i[1].point.y,167.148173322)
# self.assertAlmostEqual(i[2].point.x,179.869157678)
# self.assertAlmostEqual(i[2].point.y,199.661989162)
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, [q1])
path.plot(ax)
path.activeRepresentation = SegmentRepresentation(path, [q2])
path.plot(ax)
for n in i:
circle = plt.Circle((n.point.x, n.point.y),
2,
fill=True,
color="red")
ax.add_artist(circle)
def splitAtPoints(self, splitlist):
def mapx(v, ds):
return (v - ds) / (1 - ds)
segs = self.asSegments()
newsegs = []
# Cluster splitlist by seg
newsplitlist = {}
for (seg, t) in splitlist:
if not seg in newsplitlist: newsplitlist[seg] = []
newsplitlist[seg].append(t)
for k in newsplitlist:
newsplitlist[k] = sorted(newsplitlist[k])
# Now walk the path
for seg in segs:
if seg in newsplitlist:
tList = newsplitlist[seg]
while len(tList) > 0:
t = tList.pop(0)
if t < 1e-8: continue
seg1, seg2 = seg.splitAtTime(t)
newsegs.append(seg1)
seg = seg2
for i in range(0, len(tList)):
tList[i] = mapx(tList[i], t)
newsegs.append(seg)
self.activeRepresentation = SegmentRepresentation(self, newsegs)
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)
def balance(self):
"""Performs Tunni balancing on the path."""
segs = self.asSegments()
for x in segs:
if isinstance(x, CubicBezier): x.balance()
self.activeRepresentation = SegmentRepresentation(self, segs)
return self
def removeOverlap(self):
"""Resolves a path's self-intersections by 'walking around the outside'."""
if not self.closed:
raise "Can only remove overlap on closed paths"
splitlist = []
splitpoints = {}
def roundoff(point):
return (int(point.x * 1), int(point.y * 1))
for i in self.getSelfIntersections():
splitlist.append((i.seg1, i.t1))
splitlist.append((i.seg2, i.t2))
splitpoints[roundoff(i.point)] = {"in": [], "out": []}
self.splitAtPoints(splitlist)
# Trace path
segs = self.asSegments()
for i in range(0, len(segs)):
seg = segs[i]
if i < len(segs) - 1:
seg.next = segs[i + 1]
else:
seg.next = segs[0]
seg.visited = False
segWinding = self.windingNumberOfPoint(seg.pointAtTime(0.5))
seg.windingNumber = segWinding
if roundoff(seg.end) in splitpoints:
splitpoints[roundoff(seg.end)]["in"].append(seg)
if roundoff(seg.start) in splitpoints:
splitpoints[roundoff(seg.start)]["out"].append(seg)
newsegs = []
copying = True
logging.debug("Split points:", splitpoints)
seg = segs[0]
while not seg.visited:
logging.debug("Starting at %s, visiting %s" % (seg.start, seg))
newsegs.append(seg)
seg.visited = True
if roundoff(seg.end) in splitpoints and len(splitpoints[roundoff(
seg.end)]["out"]) > 0:
logging.debug("\nI am at %s and have a decision: " % seg.end)
inAngle = seg.tangentAtTime(1).angle
logging.debug("My angle is %s" % inAngle)
# logging.debug("Options are: ")
# for s in splitpoints[roundoff(seg.end)]["out"]:
# logging.debug(s.end, s.tangentAtTime(0).angle, self.windingNumberOfPoint(s.pointAtTime(0.5)))
# Filter out the inside points
splitpoints[roundoff(seg.end)]["out"] = [
o for o in splitpoints[roundoff(seg.end)]["out"]
if o.windingNumber < 2
]
splitpoints[roundoff(seg.end)]["out"].sort(
key=lambda x: x.tangentAtTime(0).angle - inAngle)
seg = splitpoints[roundoff(seg.end)]["out"].pop(-1)
# seg = seg.next
# logging.debug("I chose %s\n" % seg)
else:
seg = seg.next
self.activeRepresentation = SegmentRepresentation(self, newsegs)
def asNodelist(self):
"""Return the path as an array of Node objects."""
if not isinstance(self.activeRepresentation, NodelistRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = NodelistRepresentation(self,nl)
return self.activeRepresentation.data()
def fromPoints(self,
points,
error=50.0,
cornerTolerance=20.0,
maxSegments=20):
"""Fit a poly-bezier curve to the points given. This operation should be familiar
from 'pencil' tools in a vector drawing application: the application samples points
where your mouse pointer has been dragged, and then turns the sketch into a Bezier
path. The goodness of fit can be controlled by tuning the `error` parameter. Corner
detection can be controlled with `cornerTolerance`.
Here are some points fit with `error=100.0`:
.. figure:: curvefit1.png
:scale: 75 %
:alt: curvefit1
And with `error=10.0`:
.. figure:: curvefit2.png
:scale: 75 %
:alt: curvefit1
"""
from beziers.utils.curvefitter import CurveFit
segs = CurveFit.fitCurve(points, error, cornerTolerance, maxSegments)
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, segs)
return path
def asNodelist(self):
"""Return the path as an array of Node objects."""
if not isinstance(self.activeRepresentation, NodelistRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = NodelistRepresentation(self, nl)
return self.activeRepresentation.data()
def fromNodelist(klass, array, closed=True): """Construct a path from an array of Node objects.""" self = klass() for a in array: assert(isinstance(a, Node)) self.closed = closed self.activeRepresentation = NodelistRepresentation(self,array) self.asSegments() # Resolves a few problems return self
def asSegments(self):
"""Return the path as an array of segments (either Line, CubicBezier,
or, if you are exceptionally unlucky, QuadraticBezier objects)."""
if not isinstance(self.activeRepresentation, SegmentRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = SegmentRepresentation.fromNodelist(self,nl)
return self.activeRepresentation.data()
def smooth(self, maxCollectionSize=30, lengthLimit=20, cornerTolerance=10):
"""Smooths a curve, by collating lists of small (at most ``lengthLimit``
units long) segments at most ``maxCollectionSize`` segments at a time,
and running them through a curve fitting algorithm. The list collation
also stops when one segment turns more than ``cornerTolerance`` degrees
away from the previous one, so that corners are not smoothed."""
smallLineLength = lengthLimit
segs = self.asSegments()
i = 0
collection = []
while i < len(segs):
s = segs[i]
if s.length < smallLineLength and len(
collection) <= maxCollectionSize:
collection.append(s)
else:
corner = False
if len(collection) > 1:
last = collection[-1]
if abs(
last.tangentAtTime(1).angle -
s.tangentAtTime(0).angle) > math.radians(
cornerTolerance):
corner = True
if len(collection
) > maxCollectionSize or corner or i == len(segs) - 2:
points = [x.start for x in collection]
bp = BezierPath.fromPoints(points)
if len(bp.asSegments()) > 0:
segs[i - len(collection):i] = bp.asSegments()
i -= len(collection)
collection = []
i += 1
if len(collection) > 0:
points = [x.start for x in collection]
bp = BezierPath.fromPoints(points)
if len(bp.asSegments()) > 0:
segs[i - (1 + len(collection)):i - 1] = bp.asSegments()
self.activeRepresentation = SegmentRepresentation(self, segs)
return self
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 test_addextremes(self):
q = CubicBezier(Point(42, 135), Point(129, 242), Point(167, 77),
Point(65, 59))
ex = q.findExtremes()
self.assertEqual(len(ex), 2)
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, [q])
path.addExtremes()
path.balance()
segs = path.asSegments()
self.assertEqual(len(segs), 3)
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 offset(self, vector, rotateVector=True):
"""Returns a new BezierPath which approximates offsetting the
current Bezier path by the given vector. Note that the vector
will be rotated around the normal of the curve so that the
offsetting always happens on the same 'side' of the curve:
.. figure:: offset1.png
:scale: 75 %
:alt: offset1
If you don't want that and you want 'straight' offsetting instead
(which may intersect with the original curve), pass
`rotateVector=False`:
.. figure:: offset2.png
:scale: 75 %
:alt: offset1
"""
# Method 1 - curve fit
newsegs = []
points = []
def finishPoints(newsegs, points):
if len(points) > 0:
bp = BezierPath.fromPoints(points,
error=0.1,
cornerTolerance=1)
newsegs.extend(bp.asSegments())
while len(points) > 0:
points.pop()
for seg in self.asSegments():
if isinstance(seg, Line):
finishPoints(newsegs, points)
newsegs.append(seg.translated(vector))
else:
t = 0.0
while t < 1.0:
if rotateVector:
points.append(
seg.pointAtTime(t) +
vector.rotated(Point(0, 0),
seg.normalAtTime(t).angle))
else:
points.append(seg.pointAtTime(t) + vector)
step = max(abs(seg.curvatureAtTime(t)), 0.1)
t = t + min(seg.length / step, 0.1)
finishPoints(newsegs, points)
newpath = BezierPath()
newpath.activeRepresentation = SegmentRepresentation(newpath, newsegs)
return newpath
def splitAtPoints(self,splitlist):
def mapx(v,ds): return (v-ds)/(1-ds)
segs = self.asSegments()
newsegs = []
# Cluster splitlist by seg
newsplitlist = {}
for (seg,t) in splitlist:
if not seg in newsplitlist: newsplitlist[seg] = []
newsplitlist[seg].append(t)
for k in newsplitlist:
newsplitlist[k] = sorted(newsplitlist[k])
# Now walk the path
for seg in segs:
if seg in newsplitlist:
tList = newsplitlist[seg]
while len(tList) > 0:
t = tList.pop(0)
if t < 1e-8: continue
seg1,seg2 = seg.splitAtTime(t)
newsegs.append(seg1)
seg = seg2
for i in range(0,len(tList)): tList[i] = mapx(tList[i],t)
newsegs.append(seg)
self.activeRepresentation = SegmentRepresentation(self,newsegs)
def translate(self, vector):
"""Translates the path by a given vector."""
seg2 = [x.translated(vector) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def reverse(self):
"""Reverse this path (mutates path)."""
seg2 = [x.reversed() for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(
self, list(reversed(seg2)))
return self
def round(self):
"""Rounds the points of this path to integer coordinates."""
segs = self.asSegments()
for s in segs:
s.round()
self.activeRepresentation = SegmentRepresentation(self, segs)
def translate(self, vector): """Translates the path by a given vector.""" seg2 = [ x.translated(vector) for x in self.asSegments()] self.activeRepresentation = SegmentRepresentation(self, seg2)
class BezierPath(BooleanOperationsMixin,SampleMixin,object):
"""`BezierPath` represents a collection of `Segment` objects - the
curves and lines that make up a path.
One of the really fiddly things about manipulating Bezier paths in
a computer is that there are various ways to represent them.
Different applications prefer different representations. For instance,
when you're drawing a path on a canvas, you often want a list of nodes
like so::
{ "x":255.0, "y":20.0, "type":"curve"},
{ "x":385.0, "y":20.0, "type":"offcurve"},
{ "x":526.0, "y":79.0, "type":"offcurve"},
{ "x":566.0, "y":135.0, "type":"curve"},
{ "x":585.0, "y":162.0, "type":"offcurve"},
{ "x":566.0, "y":260.0, "type":"offcurve"},
{ "x":484.0, "y":281.0, "type":"curve"},
...
But when you're doing Clever Bezier Mathematics, you generally want
a list of segments instead::
[ (255.0,20.0), (385.0,20.0), (526.0,79.0), (566.0,135.0)],
[ (566.0,135.0), (585.0,162.0), (566.0,260.0), (484.0,281.0)],
The Beziers module is designed to allow you to move fluidly between these
different representations depending on what you're wanting to do.
"""
def __init__(self):
self.activeRepresentation = None
self.closed = True
@classmethod
def fromPoints(self, points, error = 50.0, cornerTolerance = 20.0, maxSegments = 20):
"""Fit a poly-bezier curve to the points given. This operation should be familiar
from 'pencil' tools in a vector drawing application: the application samples points
where your mouse pointer has been dragged, and then turns the sketch into a Bezier
path. The goodness of fit can be controlled by tuning the `error` parameter. Corner
detection can be controlled with `cornerTolerance`.
Here are some points fit with `error=100.0`:
.. figure:: curvefit1.png
:scale: 75 %
:alt: curvefit1
And with `error=10.0`:
.. figure:: curvefit2.png
:scale: 75 %
:alt: curvefit1
"""
from beziers.utils.curvefitter import CurveFit
segs = CurveFit.fitCurve(points, error, cornerTolerance, maxSegments)
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path,segs)
return path
@classmethod
def fromSegments(klass, array):
"""Construct a path from an array of Segment objects."""
self = klass()
for a in array: assert(isinstance(a, Segment))
self.activeRepresentation = SegmentRepresentation(self,array)
return self
@classmethod
def fromNodelist(klass, array, closed=True):
"""Construct a path from an array of Node objects."""
self = klass()
for a in array: assert(isinstance(a, Node))
self.closed = closed
self.activeRepresentation = NodelistRepresentation(self,array)
self.asSegments() # Resolves a few problems
return self
@classmethod
def fromFonttoolsGlyph(klass, glyph, glyphset, glyfTable):
"""Returns an *array of BezierPaths* from a FontTools glyph object.
You must also provide the glyphset and glyf table objects to allow glyph decomposition."""
from fontTools.pens.basePen import BasePen
class MyPen(BasePen):
def __init__(self, glyphSet=None):
super(MyPen, self).__init__(glyphSet)
self.paths = []
self.path = BezierPath()
self.nodeList = []
def _moveTo(self, p):
self.nodeList = [Node(p[0], p[1], "move")]
def _lineTo(self, p):
self.nodeList.append(Node(p[0], p[1], "line"))
def _curveToOne(self, p1, p2, p3):
self.nodeList.append(Node(p1[0], p1[1], "offcurve"))
self.nodeList.append(Node(p2[0], p2[1], "offcurve"))
self.nodeList.append(Node(p3[0], p3[1], "curve"))
def _qCurveToOne(self, p1, p2):
self.nodeList.append(Node(p1[0], p1[1], "offcurve"))
self.nodeList.append(Node(p2[0], p2[1], "curve"))
def _closePath(self):
self.path.closed = True
self.path.activeRepresentation = NodelistRepresentation(self.path, self.nodeList)
self.paths.append(self.path)
self.path = BezierPath()
pen = MyPen(glyphset)
glyph.draw(pen, glyfTable)
return pen.paths
def asSegments(self):
"""Return the path as an array of segments (either Line, CubicBezier,
or, if you are exceptionally unlucky, QuadraticBezier objects)."""
if not isinstance(self.activeRepresentation, SegmentRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = SegmentRepresentation.fromNodelist(self,nl)
return self.activeRepresentation.data()
def asNodelist(self):
"""Return the path as an array of Node objects."""
if not isinstance(self.activeRepresentation, NodelistRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = NodelistRepresentation(self,nl)
return self.activeRepresentation.data()
def asMatplot(self):
from matplotlib.path import Path
nl = self.asNodelist()
verts = [(nl[0].x,nl[0].y)]
codes = [Path.MOVETO]
for i in range(1,len(nl)):
n = nl[i]
verts.append((n.x,n.y))
if n.type == "offcurve":
if nl[i+1].type == "offcurve" or nl[i-1].type == "offcurve":
codes.append(Path.CURVE4)
else:
codes.append(Path.CURVE3)
elif n.type == "curve":
if nl[i-1].type == "offcurve" and i >2 and nl[i-2].type == "offcurve":
codes.append(Path.CURVE4)
else:
codes.append(Path.CURVE3)
elif n.type == "line":
codes.append(Path.LINETO)
else:
raise "Unknown node type"
if self.closed:
verts.append((nl[0].x,nl[0].y))
codes.append(Path.CLOSEPOLY)
return Path(verts, codes)
def plot(self,ax, **kwargs):
"""Plot the path on a Matplot subplot which you supply
::
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
path.plot(ax)
"""
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from matplotlib.path import Path
import matplotlib.patches as patches
path = self.asMatplot()
if not "lw" in kwargs:
kwargs["lw"] = 2
if not "fill" in kwargs:
kwargs["fill"] = False
drawNodes = (not("drawNodes" in kwargs) or kwargs["drawNodes"] != False)
if "drawNodes" in kwargs:
kwargs.pop("drawNodes")
patch = patches.PathPatch(path, **kwargs)
ax.add_patch(patch)
left, right = ax.get_xlim()
top, bottom = ax.get_ylim()
bounds = self.bounds()
bounds.addMargin(5)
if not (left == 0.0 and right == 1.0 and top == 0.0 and bottom == 1.0):
bounds.extend(Point(left,top))
bounds.extend(Point(right,bottom))
ax.set_xlim(bounds.left,bounds.right)
ax.set_ylim(bounds.bottom,bounds.top)
if drawNodes:
nl = self.asNodelist()
for i in range(0,len(nl)):
n = nl[i]
if n.type =="offcurve":
circle = plt.Circle((n.x, n.y), 1, fill=False)
ax.add_artist(circle)
if i+1 < len(nl) and nl[i+1].type != "offcurve":
l = Line2D([n.x, nl[i+1].x], [n.y, nl[i+1].y])
ax.add_artist(l)
if i-0 >= 0 and nl[i-1].type != "offcurve":
l = Line2D([n.x, nl[i-1].x], [n.y, nl[i-1].y])
ax.add_artist(l)
else:
circle = plt.Circle((n.x, n.y), 2)
ax.add_artist(circle)
def clone(self):
"""Return a new path which is an exact copy of this one"""
return BezierPath.fromSegments(self.asSegments())
def round(self):
"""Rounds the points of this path to integer coordinates."""
segs = self.asSegments()
for s in segs: s.round()
self.activeRepresentation = SegmentRepresentation(self,segs)
def bounds(self):
"""Determine the bounding box of the path, returned as a
`BoundingBox` object."""
bbox = BoundingBox()
for seg in self.asSegments():
bbox.extend(seg)
return bbox
def splitAtPoints(self,splitlist):
def mapx(v,ds): return (v-ds)/(1-ds)
segs = self.asSegments()
newsegs = []
# Cluster splitlist by seg
newsplitlist = {}
for (seg,t) in splitlist:
if not seg in newsplitlist: newsplitlist[seg] = []
newsplitlist[seg].append(t)
for k in newsplitlist:
newsplitlist[k] = sorted(newsplitlist[k])
# Now walk the path
for seg in segs:
if seg in newsplitlist:
tList = newsplitlist[seg]
while len(tList) > 0:
t = tList.pop(0)
if t < 1e-8: continue
seg1,seg2 = seg.splitAtTime(t)
newsegs.append(seg1)
seg = seg2
for i in range(0,len(tList)): tList[i] = mapx(tList[i],t)
newsegs.append(seg)
self.activeRepresentation = SegmentRepresentation(self,newsegs)
def addExtremes(self):
"""Add extreme points to the path."""
def mapx(v,ds): return (v-ds)/(1-ds)
segs = self.asSegments()
splitlist = []
for seg in segs:
for t in seg.findExtremes():
splitlist.append((seg,t))
self.splitAtPoints(splitlist)
@property
def length(self):
"""Returns the length of the whole path."""
segs = self.asSegments()
length = 0
for s in segs: length += s.length
return length
def pointAtTime(self,t):
"""Returns the point at time t (0->1) along the curve, where 1 is the end of the whole curve."""
segs = self.asSegments()
if t == 1.0:
return segs[-1].pointAtTime(1)
t *= len(segs)
seg = segs[int(math.floor(t))]
return seg.pointAtTime(t-math.floor(t))
def lengthAtTime(self,t):
"""Returns the length of the subset of the path from the start
up to the point t (0->1), where 1 is the end of the whole curve."""
segs = self.asSegments()
t *= len(segs)
length = 0
for s in segs[:int(math.floor(t))]: length += s.length
seg = segs[int(math.floor(t))]
s1,s2 = seg.splitAtTime(t-math.floor(t))
length += s1.length
return length
def offset(self, vector, rotateVector = True):
"""Returns a new BezierPath which approximates offsetting the
current Bezier path by the given vector. Note that the vector
will be rotated around the normal of the curve so that the
offsetting always happens on the same 'side' of the curve:
.. figure:: offset1.png
:scale: 75 %
:alt: offset1
If you don't want that and you want 'straight' offsetting instead
(which may intersect with the original curve), pass
`rotateVector=False`:
.. figure:: offset2.png
:scale: 75 %
:alt: offset1
"""
# Method 1 - curve fit
newsegs = []
points = []
def finishPoints(newsegs, points):
if len(points) > 0:
bp = BezierPath.fromPoints(points, error=0.1, cornerTolerance= 1)
newsegs.extend(bp.asSegments())
while len(points)>0:points.pop()
for seg in self.asSegments():
if isinstance(seg,Line):
finishPoints(newsegs,points)
newsegs.append(seg.translated(vector))
else:
t = 0.0
while t <1.0:
if rotateVector:
points.append( seg.pointAtTime(t) + vector.rotated(Point(0,0), seg.normalAtTime(t).angle))
else:
points.append( seg.pointAtTime(t) + vector)
step = max(abs(seg.curvatureAtTime(t)),0.1)
t = t + min(seg.length / step,0.1)
finishPoints(newsegs,points)
newpath = BezierPath()
newpath.activeRepresentation = SegmentRepresentation(newpath, newsegs)
return newpath
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)
def reverse(self):
"""Reverse this path (mutates path)."""
seg2 = [ x.reversed() for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, list(reversed(seg2)))
def translate(self, vector):
"""Translates the path by a given vector."""
seg2 = [ x.translated(vector) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
def rotate(self, about, angle):
"""Rotate the path by a given vector."""
seg2 = [ x.rotated(about, angle) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
def scale(self, by):
"""Scales the path by a given magnitude."""
seg2 = [ x.scaled(by) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
def balance(self):
"""Performs Tunni balancing on the path."""
segs = self.asSegments()
for x in segs:
if isinstance(x, CubicBezier): x.balance()
self.activeRepresentation = SegmentRepresentation(self, segs)
def findDiscontinuities(self):
"""Not implemented yet"""
def harmonize(self):
"""Not implemented yet"""
def roundCorners(self):
"""Not implemented yet"""
def dash(self, lineLength = 50, gapLength = None):
"""Returns a list of BezierPath objects created by chopping
this path into a dashed line::
paths = path.dash(lineLength = 20, gapLength = 50)
.. figure:: dash.png
:scale: 75 %
:alt: path.dash(lineLength = 20, gapLength = 50)
"""
if not gapLength:
gapLength = lineLength
granularity = self.length
newpaths = []
points = []
for t in self.regularSampleTValue(granularity):
lenSoFar = self.lengthAtTime(t) # Super inefficient. But simple!
lenSoFar = lenSoFar % (lineLength + gapLength)
if lenSoFar >= lineLength and len(points) > 0:
# When all you have is a hammer...
bp = BezierPath.fromPoints(points, error=1, cornerTolerance= 1)
points = []
if len(bp.asSegments()) > 0: newpaths.append(bp)
elif lenSoFar <= lineLength:
points.append(self.pointAtTime(t))
return newpaths
def segpairs(self):
segs = self.asSegments()
for i in range(0,len(segs)-1):
yield (segs[i],segs[i+1])
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 flatten(self,degree=8):
segs = []
for s in self.asSegments():
segs.extend(s.flatten(degree))
return BezierPath.fromSegments(segs)
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 pointIsInside(self,pt):
"""Returns true if the given point lies on the "inside" of the path,
assuming an 'even-odd' winding rule where self-intersections are considered
outside."""
li = self.windingNumberOfPoint(pt)
return li % 2 == 1
@property
def area(self):
"""Approximates the area under a closed path by flattening and treating as a polygon."""
flat = self.flatten()
area = 0
for s in flat.asSegments():
area = area + (s.start.x+s.end.x) * (s.end.y - s.start.y)
area = area / 2.0
return abs(area)
def fromSegments(klass, array): """Construct a path from an array of Segment objects.""" self = klass() for a in array: assert(isinstance(a, Segment)) self.activeRepresentation = SegmentRepresentation(self,array) return self
def rotate(self, about, angle): """Rotate the path by a given vector.""" seg2 = [ x.rotated(about, angle) for x in self.asSegments()] self.activeRepresentation = SegmentRepresentation(self, seg2)
def rotate(self, about, angle):
"""Rotate the path by a given vector."""
seg2 = [x.rotated(about, angle) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def round(self): """Rounds the points of this path to integer coordinates.""" segs = self.asSegments() for s in segs: s.round() self.activeRepresentation = SegmentRepresentation(self,segs)
def scale(self, by):
"""Scales the path by a given magnitude."""
seg2 = [x.scaled(by) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def reverse(self): """Reverse this path (mutates path).""" seg2 = [ x.reversed() for x in self.asSegments()] self.activeRepresentation = SegmentRepresentation(self, list(reversed(seg2)))
def scale(self, by): """Scales the path by a given magnitude.""" seg2 = [ x.scaled(by) for x in self.asSegments()] self.activeRepresentation = SegmentRepresentation(self, seg2)
class BezierPath(BooleanOperationsMixin, SampleMixin, object):
"""`BezierPath` represents a collection of `Segment` objects - the
curves and lines that make up a path.
One of the really fiddly things about manipulating Bezier paths in
a computer is that there are various ways to represent them.
Different applications prefer different representations. For instance,
when you're drawing a path on a canvas, you often want a list of nodes
like so::
{ "x":255.0, "y":20.0, "type":"curve"},
{ "x":385.0, "y":20.0, "type":"offcurve"},
{ "x":526.0, "y":79.0, "type":"offcurve"},
{ "x":566.0, "y":135.0, "type":"curve"},
{ "x":585.0, "y":162.0, "type":"offcurve"},
{ "x":566.0, "y":260.0, "type":"offcurve"},
{ "x":484.0, "y":281.0, "type":"curve"},
...
But when you're doing Clever Bezier Mathematics, you generally want
a list of segments instead::
[ (255.0,20.0), (385.0,20.0), (526.0,79.0), (566.0,135.0)],
[ (566.0,135.0), (585.0,162.0), (566.0,260.0), (484.0,281.0)],
The Beziers module is designed to allow you to move fluidly between these
different representations depending on what you're wanting to do.
"""
def __init__(self):
self.activeRepresentation = None
self.closed = True
@classmethod
def fromPoints(self,
points,
error=50.0,
cornerTolerance=20.0,
maxSegments=20):
"""Fit a poly-bezier curve to the points given. This operation should be familiar
from 'pencil' tools in a vector drawing application: the application samples points
where your mouse pointer has been dragged, and then turns the sketch into a Bezier
path. The goodness of fit can be controlled by tuning the `error` parameter. Corner
detection can be controlled with `cornerTolerance`.
Here are some points fit with `error=100.0`:
.. figure:: curvefit1.png
:scale: 75 %
:alt: curvefit1
And with `error=10.0`:
.. figure:: curvefit2.png
:scale: 75 %
:alt: curvefit1
"""
from beziers.utils.curvefitter import CurveFit
segs = CurveFit.fitCurve(points, error, cornerTolerance, maxSegments)
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, segs)
return path
@classmethod
def fromSegments(klass, array):
"""Construct a path from an array of Segment objects."""
self = klass()
for a in array:
assert (isinstance(a, Segment))
self.activeRepresentation = SegmentRepresentation(self, array)
return self
@classmethod
def fromNodelist(klass, array, closed=True):
"""Construct a path from an array of Node objects."""
self = klass()
for a in array:
assert (isinstance(a, Node))
self.closed = closed
self.activeRepresentation = NodelistRepresentation(self, array)
self.asSegments() # Resolves a few problems
return self
@classmethod
def fromFonttoolsGlyph(klass, font, glyphname):
"""Returns an *array of BezierPaths* from a FontTools font object and glyph name."""
glyphset = font.getGlyphSet()
from fontTools.pens.basePen import BasePen
class MyPen(BasePen):
def __init__(self, glyphSet=None):
super(MyPen, self).__init__(glyphSet)
self.paths = []
self.path = BezierPath()
self.nodeList = []
def _moveTo(self, p):
self.nodeList = [Node(p[0], p[1], "move")]
def _lineTo(self, p):
self.nodeList.append(Node(p[0], p[1], "line"))
def _curveToOne(self, p1, p2, p3):
self.nodeList.append(Node(p1[0], p1[1], "offcurve"))
self.nodeList.append(Node(p2[0], p2[1], "offcurve"))
self.nodeList.append(Node(p3[0], p3[1], "curve"))
def _qCurveToOne(self, p1, p2):
self.nodeList.append(Node(p1[0], p1[1], "offcurve"))
self.nodeList.append(Node(p2[0], p2[1], "curve"))
def _closePath(self):
self.path.closed = True
self.path.activeRepresentation = NodelistRepresentation(
self.path, self.nodeList)
self.paths.append(self.path)
self.path = BezierPath()
pen = MyPen(glyphset)
_glyph = font.getGlyphSet()[glyphname]._glyph
if "glyf" in font:
_glyph.draw(pen, font["glyf"])
else:
_glyph.draw(pen)
return pen.paths
def asSegments(self):
"""Return the path as an array of segments (either Line, CubicBezier,
or, if you are exceptionally unlucky, QuadraticBezier objects)."""
if not isinstance(self.activeRepresentation, SegmentRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = SegmentRepresentation.fromNodelist(
self, nl)
return self.activeRepresentation.data()
def asNodelist(self):
"""Return the path as an array of Node objects."""
if not isinstance(self.activeRepresentation, NodelistRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = NodelistRepresentation(self, nl)
return self.activeRepresentation.data()
def asSVGPath(self):
"""Return the path as a string suitable for a SVG <path d="..."? element."""
segs = self.asSegments()
pathParts = ["M %f %f" % (segs[0][0].x, segs[0][0].y)]
operators = "xxLQC"
for s in segs:
op = operators[len(s)] + " "
for pt in s[1:]:
op = op + "%f %f " % (pt.x, pt.y)
pathParts.append(op)
if self.closed:
pathParts.append("Z")
return " ".join(pathParts)
def asMatplot(self):
from matplotlib.path import Path
nl = self.asNodelist()
verts = [(nl[0].x, nl[0].y)]
codes = [Path.MOVETO]
for i in range(1, len(nl)):
n = nl[i]
verts.append((n.x, n.y))
if n.type == "offcurve":
if nl[i + 1].type == "offcurve" or nl[i -
1].type == "offcurve":
codes.append(Path.CURVE4)
else:
codes.append(Path.CURVE3)
elif n.type == "curve":
if nl[i - 1].type == "offcurve" and i > 2 and nl[
i - 2].type == "offcurve":
codes.append(Path.CURVE4)
else:
codes.append(Path.CURVE3)
elif n.type == "line":
codes.append(Path.LINETO)
else:
raise "Unknown node type"
if self.closed:
verts.append((nl[0].x, nl[0].y))
codes.append(Path.CLOSEPOLY)
return Path(verts, codes)
def plot(self, ax, **kwargs):
"""Plot the path on a Matplot subplot which you supply
::
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
path.plot(ax)
"""
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from matplotlib.path import Path
import matplotlib.patches as patches
path = self.asMatplot()
if not "lw" in kwargs:
kwargs["lw"] = 2
if not "fill" in kwargs:
kwargs["fill"] = False
drawNodes = (not ("drawNodes" in kwargs)
or kwargs["drawNodes"] != False)
if "drawNodes" in kwargs:
kwargs.pop("drawNodes")
patch = patches.PathPatch(path, **kwargs)
ax.add_patch(patch)
left, right = ax.get_xlim()
top, bottom = ax.get_ylim()
bounds = self.bounds()
bounds.addMargin(50)
if not (left == 0.0 and right == 1.0 and top == 0.0 and bottom == 1.0):
bounds.extend(Point(left, top))
bounds.extend(Point(right, bottom))
ax.set_xlim(bounds.left, bounds.right)
ax.set_ylim(bounds.bottom, bounds.top)
if drawNodes:
nl = self.asNodelist()
for i in range(0, len(nl)):
n = nl[i]
if n.type == "offcurve":
circle = plt.Circle((n.x, n.y),
2,
fill=True,
color="black",
alpha=0.5)
ax.add_artist(circle)
if i + 1 < len(nl) and nl[i + 1].type != "offcurve":
l = Line2D([n.x, nl[i + 1].x], [n.y, nl[i + 1].y],
linewidth=2,
color="black",
alpha=0.3)
ax.add_artist(l)
if i - 0 >= 0 and nl[i - 1].type != "offcurve":
l = Line2D([n.x, nl[i - 1].x], [n.y, nl[i - 1].y],
linewidth=2,
color="black",
alpha=0.3)
ax.add_artist(l)
else:
circle = plt.Circle((n.x, n.y),
3,
color="black",
alpha=0.3)
ax.add_artist(circle)
def clone(self):
"""Return a new path which is an exact copy of this one"""
p = BezierPath.fromSegments(self.asSegments())
p.closed = self.closed
return p
def round(self):
"""Rounds the points of this path to integer coordinates."""
segs = self.asSegments()
for s in segs:
s.round()
self.activeRepresentation = SegmentRepresentation(self, segs)
def bounds(self):
"""Determine the bounding box of the path, returned as a
`BoundingBox` object."""
bbox = BoundingBox()
for seg in self.asSegments():
bbox.extend(seg)
return bbox
def splitAtPoints(self, splitlist):
def mapx(v, ds):
return (v - ds) / (1 - ds)
segs = self.asSegments()
newsegs = []
# Cluster splitlist by seg
newsplitlist = {}
for (seg, t) in splitlist:
if not seg in newsplitlist: newsplitlist[seg] = []
newsplitlist[seg].append(t)
for k in newsplitlist:
newsplitlist[k] = sorted(newsplitlist[k])
# Now walk the path
for seg in segs:
if seg in newsplitlist:
tList = newsplitlist[seg]
while len(tList) > 0:
t = tList.pop(0)
if t < 1e-8: continue
seg1, seg2 = seg.splitAtTime(t)
newsegs.append(seg1)
seg = seg2
for i in range(0, len(tList)):
tList[i] = mapx(tList[i], t)
newsegs.append(seg)
self.activeRepresentation = SegmentRepresentation(self, newsegs)
def addExtremes(self):
"""Add extreme points to the path."""
def mapx(v, ds):
return (v - ds) / (1 - ds)
segs = self.asSegments()
splitlist = []
for seg in segs:
for t in seg.findExtremes():
splitlist.append((seg, t))
self.splitAtPoints(splitlist)
@property
def length(self):
"""Returns the length of the whole path."""
segs = self.asSegments()
length = 0
for s in segs:
length += s.length
return length
def pointAtTime(self, t):
"""Returns the point at time t (0->1) along the curve, where 1 is the end of the whole curve."""
segs = self.asSegments()
if t == 1.0:
return segs[-1].pointAtTime(1)
t *= len(segs)
seg = segs[int(math.floor(t))]
return seg.pointAtTime(t - math.floor(t))
def lengthAtTime(self, t):
"""Returns the length of the subset of the path from the start
up to the point t (0->1), where 1 is the end of the whole curve."""
segs = self.asSegments()
t *= len(segs)
length = 0
for s in segs[:int(math.floor(t))]:
length += s.length
seg = segs[int(math.floor(t))]
s1, s2 = seg.splitAtTime(t - math.floor(t))
length += s1.length
return length
def offset(self, vector, rotateVector=True):
"""Returns a new BezierPath which approximates offsetting the
current Bezier path by the given vector. Note that the vector
will be rotated around the normal of the curve so that the
offsetting always happens on the same 'side' of the curve:
.. figure:: offset1.png
:scale: 75 %
:alt: offset1
If you don't want that and you want 'straight' offsetting instead
(which may intersect with the original curve), pass
`rotateVector=False`:
.. figure:: offset2.png
:scale: 75 %
:alt: offset1
"""
# Method 1 - curve fit
newsegs = []
points = []
def finishPoints(newsegs, points):
if len(points) > 0:
bp = BezierPath.fromPoints(points,
error=0.1,
cornerTolerance=1)
newsegs.extend(bp.asSegments())
while len(points) > 0:
points.pop()
for seg in self.asSegments():
if isinstance(seg, Line):
finishPoints(newsegs, points)
newsegs.append(seg.translated(vector))
else:
t = 0.0
while t < 1.0:
if rotateVector:
points.append(
seg.pointAtTime(t) +
vector.rotated(Point(0, 0),
seg.normalAtTime(t).angle))
else:
points.append(seg.pointAtTime(t) + vector)
step = max(abs(seg.curvatureAtTime(t)), 0.1)
t = t + min(seg.length / step, 0.1)
finishPoints(newsegs, points)
newpath = BezierPath()
newpath.activeRepresentation = SegmentRepresentation(newpath, newsegs)
return newpath
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 reverse(self):
"""Reverse this path (mutates path)."""
seg2 = [x.reversed() for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(
self, list(reversed(seg2)))
return self
def translate(self, vector):
"""Translates the path by a given vector."""
seg2 = [x.translated(vector) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def rotate(self, about, angle):
"""Rotate the path by a given vector."""
seg2 = [x.rotated(about, angle) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def scale(self, by):
"""Scales the path by a given magnitude."""
seg2 = [x.scaled(by) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def balance(self):
"""Performs Tunni balancing on the path."""
segs = self.asSegments()
for x in segs:
if isinstance(x, CubicBezier): x.balance()
self.activeRepresentation = SegmentRepresentation(self, segs)
return self
def findDiscontinuities(self):
"""Not implemented yet"""
def harmonize(self):
"""Not implemented yet"""
def roundCorners(self):
"""Not implemented yet"""
def dash(self, lineLength=50, gapLength=None):
"""Returns a list of BezierPath objects created by chopping
this path into a dashed line::
paths = path.dash(lineLength = 20, gapLength = 50)
.. figure:: dash.png
:scale: 75 %
:alt: path.dash(lineLength = 20, gapLength = 50)
"""
if not gapLength:
gapLength = lineLength
granularity = self.length
newpaths = []
points = []
for t in self.regularSampleTValue(granularity):
lenSoFar = self.lengthAtTime(t) # Super inefficient. But simple!
lenSoFar = lenSoFar % (lineLength + gapLength)
if lenSoFar >= lineLength and len(points) > 0:
# When all you have is a hammer...
bp = BezierPath.fromPoints(points, error=1, cornerTolerance=1)
points = []
if len(bp.asSegments()) > 0: newpaths.append(bp)
elif lenSoFar <= lineLength:
points.append(self.pointAtTime(t))
return newpaths
def segpairs(self):
segs = self.asSegments()
for i in range(0, len(segs) - 1):
yield (segs[i], segs[i + 1])
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 flatten(self, degree=8):
segs = []
for s in self.asSegments():
segs.extend(s.flatten(degree))
return BezierPath.fromSegments(segs)
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 pointIsInside(self, pt):
"""Returns true if the given point lies on the "inside" of the path,
assuming an 'even-odd' winding rule where self-intersections are considered
outside."""
li = self.windingNumberOfPoint(pt)
return li % 2 == 1
@property
def area(self):
"""Approximates the area under a closed path by flattening and treating as a polygon."""
flat = self.flatten()
area = 0
for s in flat.asSegments():
area = area + (s.start.x * s.end.y) - (s.start.y * s.end.x)
area = area / 2.0
return abs(area)
@property
def centroid(self):
if not self.closed: return None
return self.bounds().centroid # Really?
def drawWithBrush(self,
other,
pathSmoothness=50,
brushSmoothness=20,
alpha=0.15):
"""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` and `scipy` libraries to be installed, and is very,
very slow.
"""
samples = self.sample(int(self.length * (pathSmoothness / 100.0)))
self.closed = False
def constantBrush(t):
return other
brush = other
if not callable(brush):
brush = constantBrush
c = brush(0).centroid
points = []
from shapely.geometry import Point as ShapelyPoint
t = 0
for n in samples:
brushHere = brush(t).clone()
brushHere.translate(n - brushHere.centroid)
brushsamples = brushHere.sample(
int(brushHere.length * (brushSmoothness / 100.0)))
points.extend([ShapelyPoint(s.x, s.y) for s in brushsamples])
t = t + 1.0 / len(samples)
from beziers.utils.alphashape import alpha_shape
concave_hull, edge_points = alpha_shape(points, alpha=alpha)
points = [Point(p[0], p[1]) for p in concave_hull.exterior.coords]
path = BezierPath.fromPoints(points, error=5, maxSegments=100)
return path
def quadraticsToCubics(self):
"""Converts all quadratic segments in the path to cubic Beziers."""
segs = self.asSegments()
for i, s in enumerate(segs):
if len(s) == 3:
segs[i] = s.toCubicBezier()
return self
def balance(self):
"""Performs Tunni balancing on the path."""
segs = self.asSegments()
for x in segs:
if isinstance(x, CubicBezier): x.balance()
self.activeRepresentation = SegmentRepresentation(self, segs)
class BezierPath(BooleanOperationsMixin, SampleMixin, object):
"""`BezierPath` represents a collection of `Segment` objects - the
curves and lines that make up a path.
One of the really fiddly things about manipulating Bezier paths in
a computer is that there are various ways to represent them.
Different applications prefer different representations. For instance,
when you're drawing a path on a canvas, you often want a list of nodes
like so::
{ "x":255.0, "y":20.0, "type":"curve"},
{ "x":385.0, "y":20.0, "type":"offcurve"},
{ "x":526.0, "y":79.0, "type":"offcurve"},
{ "x":566.0, "y":135.0, "type":"curve"},
{ "x":585.0, "y":162.0, "type":"offcurve"},
{ "x":566.0, "y":260.0, "type":"offcurve"},
{ "x":484.0, "y":281.0, "type":"curve"},
...
But when you're doing Clever Bezier Mathematics, you generally want
a list of segments instead::
[ (255.0,20.0), (385.0,20.0), (526.0,79.0), (566.0,135.0)],
[ (566.0,135.0), (585.0,162.0), (566.0,260.0), (484.0,281.0)],
The Beziers module is designed to allow you to move fluidly between these
different representations depending on what you're wanting to do.
"""
def __init__(self):
self.activeRepresentation = None
self.closed = True
@classmethod
def fromPoints(self,
points,
error=50.0,
cornerTolerance=20.0,
maxSegments=20):
"""Fit a poly-bezier curve to the points given. This operation should be familiar
from 'pencil' tools in a vector drawing application: the application samples points
where your mouse pointer has been dragged, and then turns the sketch into a Bezier
path. The goodness of fit can be controlled by tuning the `error` parameter. Corner
detection can be controlled with `cornerTolerance`.
Here are some points fit with `error=100.0`:
.. figure:: curvefit1.png
:scale: 75 %
:alt: curvefit1
And with `error=10.0`:
.. figure:: curvefit2.png
:scale: 75 %
:alt: curvefit1
"""
from beziers.utils.curvefitter import CurveFit
segs = CurveFit.fitCurve(points, error, cornerTolerance, maxSegments)
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, segs)
return path
@classmethod
def fromSegments(klass, array):
"""Construct a path from an array of Segment objects."""
self = klass()
for a in array:
assert (isinstance(a, Segment))
self.activeRepresentation = SegmentRepresentation(self, array)
return self
@classmethod
def fromNodelist(klass, array, closed=True):
"""Construct a path from an array of Node objects."""
self = klass()
for a in array:
assert (isinstance(a, Node))
self.closed = closed
self.activeRepresentation = NodelistRepresentation(self, array)
self.asSegments() # Resolves a few problems
return self
@classmethod
def fromGlyphsLayer(klass, layer):
"""Returns an *array of BezierPaths* from a Glyphs GSLayer object."""
from beziers.path.representations.GSPath import GSPathRepresentation
bezpaths = []
for p in layer.paths:
path = BezierPath()
path.activeRepresentation = GSPathRepresentation(path, p)
bezpaths.append(path)
return bezpaths
@classmethod
def fromDrawable(klass, layer, *penArgs, **penKwargs):
"""Returns an *array of BezierPaths* from any object conforming to the pen protocol."""
from beziers.utils.pens import BezierPathCreatingPen
pen = BezierPathCreatingPen(*penArgs, **penKwargs)
layer.draw(pen)
return pen.paths
@classmethod
def fromFonttoolsGlyph(klass, font, glyphname):
"""Returns an *array of BezierPaths* from a FontTools font object and glyph name."""
glyphset = font.getGlyphSet()
from beziers.utils.pens import BezierPathCreatingPen
pen = BezierPathCreatingPen(glyphset)
_glyph = font.getGlyphSet()[glyphname]._glyph
if "glyf" in font:
_glyph.draw(pen, font["glyf"])
else:
_glyph.draw(pen)
return pen.paths
def asSegments(self):
"""Return the path as an array of segments (either Line, CubicBezier,
or, if you are exceptionally unlucky, QuadraticBezier objects)."""
if not isinstance(self.activeRepresentation, SegmentRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = SegmentRepresentation.fromNodelist(
self, nl)
return self.activeRepresentation.data()
def asNodelist(self):
"""Return the path as an array of Node objects."""
if not isinstance(self.activeRepresentation, NodelistRepresentation):
nl = self.activeRepresentation.toNodelist()
assert isinstance(nl, list)
self.activeRepresentation = NodelistRepresentation(self, nl)
return self.activeRepresentation.data()
def asSVGPath(self):
"""Return the path as a string suitable for a SVG <path d="..."? element."""
segs = self.asSegments()
pathParts = ["M %f %f" % (segs[0][0].x, segs[0][0].y)]
operators = "xxLQC"
for s in segs:
op = operators[len(s)] + " "
for pt in s[1:]:
op = op + "%f %f " % (pt.x, pt.y)
pathParts.append(op)
if self.closed:
pathParts.append("Z")
return " ".join(pathParts)
def asMatplot(self):
from matplotlib.path import Path
nl = self.asNodelist()
verts = [(nl[0].x, nl[0].y)]
codes = [Path.MOVETO]
for i in range(1, len(nl)):
n = nl[i]
verts.append((n.x, n.y))
if n.type == "offcurve":
if nl[i + 1].type == "offcurve" or nl[i -
1].type == "offcurve":
codes.append(Path.CURVE4)
else:
codes.append(Path.CURVE3)
elif n.type == "curve":
if nl[i - 1].type == "offcurve" and i > 2 and nl[
i - 2].type == "offcurve":
codes.append(Path.CURVE4)
else:
codes.append(Path.CURVE3)
elif n.type == "line":
codes.append(Path.LINETO)
else:
raise "Unknown node type"
if self.closed:
verts.append((nl[0].x, nl[0].y))
codes.append(Path.CLOSEPOLY)
return Path(verts, codes)
def plot(self, ax, **kwargs):
"""Plot the path on a Matplot subplot which you supply
::
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
path.plot(ax)
"""
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from matplotlib.path import Path
import matplotlib.patches as patches
path = self.asMatplot()
if not "lw" in kwargs:
kwargs["lw"] = 2
if not "fill" in kwargs:
kwargs["fill"] = False
drawNodes = (not ("drawNodes" in kwargs)
or kwargs["drawNodes"] != False)
if "drawNodes" in kwargs:
kwargs.pop("drawNodes")
patch = patches.PathPatch(path, **kwargs)
ax.add_patch(patch)
left, right = ax.get_xlim()
top, bottom = ax.get_ylim()
bounds = self.bounds()
bounds.addMargin(50)
if not (left == 0.0 and right == 1.0 and top == 0.0 and bottom == 1.0):
bounds.extend(Point(left, top))
bounds.extend(Point(right, bottom))
ax.set_xlim(bounds.left, bounds.right)
ax.set_ylim(bounds.bottom, bounds.top)
if drawNodes:
nl = self.asNodelist()
for i in range(0, len(nl)):
n = nl[i]
if n.type == "offcurve":
circle = plt.Circle((n.x, n.y),
2,
fill=True,
color="black",
alpha=0.5)
ax.add_artist(circle)
if i + 1 < len(nl) and nl[i + 1].type != "offcurve":
l = Line2D([n.x, nl[i + 1].x], [n.y, nl[i + 1].y],
linewidth=2,
color="black",
alpha=0.3)
ax.add_artist(l)
if i - 0 >= 0 and nl[i - 1].type != "offcurve":
l = Line2D([n.x, nl[i - 1].x], [n.y, nl[i - 1].y],
linewidth=2,
color="black",
alpha=0.3)
ax.add_artist(l)
else:
circle = plt.Circle((n.x, n.y),
3,
color="black",
alpha=0.3)
ax.add_artist(circle)
def clone(self):
"""Return a new path which is an exact copy of this one"""
p = BezierPath.fromSegments(self.asSegments())
p.closed = self.closed
return p
def round(self):
"""Rounds the points of this path to integer coordinates."""
segs = self.asSegments()
for s in segs:
s.round()
self.activeRepresentation = SegmentRepresentation(self, segs)
def bounds(self):
"""Determine the bounding box of the path, returned as a
`BoundingBox` object."""
bbox = BoundingBox()
for seg in self.asSegments():
bbox.extend(seg)
return bbox
def splitAtPoints(self, splitlist):
def mapx(v, ds):
return (v - ds) / (1 - ds)
segs = self.asSegments()
newsegs = []
# Cluster splitlist by seg
newsplitlist = {}
for (seg, t) in splitlist:
if not seg in newsplitlist: newsplitlist[seg] = []
newsplitlist[seg].append(t)
for k in newsplitlist:
newsplitlist[k] = sorted(newsplitlist[k])
# Now walk the path
for seg in segs:
if seg in newsplitlist:
tList = newsplitlist[seg]
while len(tList) > 0:
t = tList.pop(0)
if t < 1e-8: continue
seg1, seg2 = seg.splitAtTime(t)
newsegs.append(seg1)
seg = seg2
for i in range(0, len(tList)):
tList[i] = mapx(tList[i], t)
newsegs.append(seg)
self.activeRepresentation = SegmentRepresentation(self, newsegs)
def addExtremes(self):
"""Add extreme points to the path."""
def mapx(v, ds):
return (v - ds) / (1 - ds)
segs = self.asSegments()
splitlist = []
for seg in segs:
for t in seg.findExtremes():
splitlist.append((seg, t))
self.splitAtPoints(splitlist)
return self
@property
def length(self):
"""Returns the length of the whole path."""
segs = self.asSegments()
length = 0
for s in segs:
length += s.length
return length
def pointAtTime(self, t):
"""Returns the point at time t (0->1) along the curve, where 1 is the end of the whole curve."""
segs = self.asSegments()
if t == 1.0:
return segs[-1].pointAtTime(1)
t *= len(segs)
seg = segs[int(math.floor(t))]
return seg.pointAtTime(t - math.floor(t))
def lengthAtTime(self, t):
"""Returns the length of the subset of the path from the start
up to the point t (0->1), where 1 is the end of the whole curve."""
segs = self.asSegments()
t *= len(segs)
length = 0
for s in segs[:int(math.floor(t))]:
length += s.length
seg = segs[int(math.floor(t))]
s1, s2 = seg.splitAtTime(t - math.floor(t))
length += s1.length
return length
def offset(self, vector, rotateVector=True):
"""Returns a new BezierPath which approximates offsetting the
current Bezier path by the given vector. Note that the vector
will be rotated around the normal of the curve so that the
offsetting always happens on the same 'side' of the curve:
.. figure:: offset1.png
:scale: 75 %
:alt: offset1
If you don't want that and you want 'straight' offsetting instead
(which may intersect with the original curve), pass
`rotateVector=False`:
.. figure:: offset2.png
:scale: 75 %
:alt: offset1
"""
# Method 1 - curve fit
newsegs = []
points = []
def finishPoints(newsegs, points):
if len(points) > 0:
bp = BezierPath.fromPoints(points,
error=0.1,
cornerTolerance=1)
newsegs.extend(bp.asSegments())
while len(points) > 0:
points.pop()
for seg in self.asSegments():
if isinstance(seg, Line):
finishPoints(newsegs, points)
newsegs.append(seg.translated(vector))
else:
t = 0.0
while t < 1.0:
if rotateVector:
points.append(
seg.pointAtTime(t) +
vector.rotated(Point(0, 0),
seg.normalAtTime(t).angle))
else:
points.append(seg.pointAtTime(t) + vector)
step = max(abs(seg.curvatureAtTime(t)), 0.1)
t = t + min(seg.length / step, 0.1)
finishPoints(newsegs, points)
newpath = BezierPath()
newpath.activeRepresentation = SegmentRepresentation(newpath, newsegs)
return newpath
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 reverse(self):
"""Reverse this path (mutates path)."""
seg2 = [x.reversed() for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(
self, list(reversed(seg2)))
return self
def translate(self, vector):
"""Translates the path by a given vector."""
seg2 = [x.translated(vector) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def rotate(self, about, angle):
"""Rotate the path by a given vector."""
seg2 = [x.rotated(about, angle) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def scale(self, by):
"""Scales the path by a given magnitude."""
seg2 = [x.scaled(by) for x in self.asSegments()]
self.activeRepresentation = SegmentRepresentation(self, seg2)
return self
def balance(self):
"""Performs Tunni balancing on the path."""
segs = self.asSegments()
for x in segs:
if isinstance(x, CubicBezier): x.balance()
self.activeRepresentation = SegmentRepresentation(self, segs)
return self
def findDiscontinuities(self):
"""Not implemented yet"""
def harmonize(self):
"""Not implemented yet"""
def roundCorners(self):
"""Not implemented yet"""
def dash(self, lineLength=50, gapLength=None):
"""Returns a list of BezierPath objects created by chopping
this path into a dashed line::
paths = path.dash(lineLength = 20, gapLength = 50)
.. figure:: dash.png
:scale: 75 %
:alt: path.dash(lineLength = 20, gapLength = 50)
"""
if not gapLength:
gapLength = lineLength
granularity = self.length
newpaths = []
points = []
for t in self.regularSampleTValue(granularity):
lenSoFar = self.lengthAtTime(t) # Super inefficient. But simple!
lenSoFar = lenSoFar % (lineLength + gapLength)
if lenSoFar >= lineLength and len(points) > 0:
# When all you have is a hammer...
bp = BezierPath.fromPoints(points, error=1, cornerTolerance=1)
points = []
if len(bp.asSegments()) > 0: newpaths.append(bp)
elif lenSoFar <= lineLength:
points.append(self.pointAtTime(t))
return newpaths
def segpairs(self):
segs = self.asSegments()
for i in range(0, len(segs) - 1):
yield (segs[i], segs[i + 1])
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 flatten(self, degree=8):
segs = []
for s in self.asSegments():
segs.extend(s.flatten(degree))
return BezierPath.fromSegments(segs)
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 pointIsInside(self, pt):
"""Returns true if the given point lies on the "inside" of the path,
assuming an 'even-odd' winding rule where self-intersections are considered
outside."""
li = self.windingNumberOfPoint(pt)
return li % 2 == 1
@property
def signed_area(self):
"""Approximates the area under a closed path by flattening and treating as a polygon.
Returns the signed area; positive means the path is counter-clockwise,
negative means it is clockwise."""
flat = self.flatten()
area = 0
for s in flat.asSegments():
area = area + (s.start.x * s.end.y) - (s.start.y * s.end.x)
area = area / 2.0
return area
@property
def area(self):
"""Approximates the area under a closed path by flattening and treating as a
polygon. Returns the unsigned area. Use :py:meth:`signed_area` if you want
the signed area."""
return abs(self.signed_area)
@property
def direction(self):
"""Returns the direction of the path: -1 for clockwise and 1 for counterclockwise."""
return math.copysign(1, self.signed_area)
@property
def centroid(self):
if not self.closed: return None
return self.bounds().centroid # Really?
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 quadraticsToCubics(self):
"""Converts all quadratic segments in the path to cubic Beziers."""
segs = self.asSegments()
for i, s in enumerate(segs):
if len(s) == 3:
segs[i] = s.toCubicBezier()
return self
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
# midpoint = (i1.point + i2.point) / 2
# # Find closest path to midpoint
# # Find the tangent at that time
# inorm2 = i2.seg1.normalAtTime(i2.t1)
def distanceToPath(self, other, samples=10):
"""Finds the distance to the other curve at its closest point,
along with the t values for the closest point at each segment
and the relevant segments.
Returns: ``distance, t1, t2, seg1, seg2``."""
from beziers.utils.curvedistance import curveDistance
segs1 = self.asSegments()
segs2 = other.asSegments()
minDistance = None
# Find closest segment pair.
for s1 in segs1:
samples1 = s1.sample(samples)
for s2 in segs2:
samples2 = s2.sample(samples)
d = min([
p1.squareDistanceFrom(p2) for p1 in samples1
for p2 in samples2
])
if not minDistance or d < minDistance:
minDistance = d
closestPair = (s1, s2)
c = curveDistance(closestPair[0], closestPair[1])
return (c[0], c[1], c[2], closestPair[0], closestPair[1])
def tidy(self, **kwargs):
"""Tidies a curve by adding extremes, and then running
``removeIrrelevantSegments`` and ``smooth``. ``relLength``,
``absLength``, ``maxCollectionSize``, ``lengthLimit`` and
``cornerTolerance`` parameters are passed to the relevant routine."""
self.addExtremes()
self.removeIrrelevantSegments(**{
k: v
for k, v in kwargs.items() if k in ["relLength", "absLength"]
})
self.smooth(
**{
k: v
for k, v in kwargs.items() if k in
["maxCollectionSize", "lengthLimit", "cornerTolerance"]
})
def removeIrrelevantSegments(self, relLength=1 / 50000, absLength=0):
"""Removes small and collinear line segments. Collinear line
segments are adjacent line segments which are heading in the same
direction, and hence can be collapsed into a single segment.
Small segments (those less than ``absLength`` units, or less than
``relLength`` as a fraction of the path's total length) are
removed entirely."""
segs = self.asSegments()
newsegs = [segs[0]]
smallLength = self.length * relLength
for i in range(1, len(segs)):
prev = newsegs[-1]
this = segs[i]
if this.length < smallLength or this.length < absLength:
this[0] = prev[0]
newsegs[-1] = this
continue
if len(prev) == 2 and len(this) == 2:
if math.isclose(
prev.tangentAtTime(0).angle,
this.tangentAtTime(0).angle):
this[0] = prev[0]
newsegs[-1] = this
continue
newsegs.append(this)
self.activeRepresentation = SegmentRepresentation(self, newsegs)
return self
def smooth(self, maxCollectionSize=30, lengthLimit=20, cornerTolerance=10):
"""Smooths a curve, by collating lists of small (at most ``lengthLimit``
units long) segments at most ``maxCollectionSize`` segments at a time,
and running them through a curve fitting algorithm. The list collation
also stops when one segment turns more than ``cornerTolerance`` degrees
away from the previous one, so that corners are not smoothed."""
smallLineLength = lengthLimit
segs = self.asSegments()
i = 0
collection = []
while i < len(segs):
s = segs[i]
if s.length < smallLineLength and len(
collection) <= maxCollectionSize:
collection.append(s)
else:
corner = False
if len(collection) > 1:
last = collection[-1]
if abs(
last.tangentAtTime(1).angle -
s.tangentAtTime(0).angle) > math.radians(
cornerTolerance):
corner = True
if len(collection
) > maxCollectionSize or corner or i == len(segs) - 2:
points = [x.start for x in collection]
bp = BezierPath.fromPoints(points)
if len(bp.asSegments()) > 0:
segs[i - len(collection):i] = bp.asSegments()
i -= len(collection)
collection = []
i += 1
if len(collection) > 0:
points = [x.start for x in collection]
bp = BezierPath.fromPoints(points)
if len(bp.asSegments()) > 0:
segs[i - (1 + len(collection)):i - 1] = bp.asSegments()
self.activeRepresentation = SegmentRepresentation(self, segs)
return self