def _pointWithinThreshold(x, y, curve, eps):
"""
See whether *(x, y)* is within *eps* of *curve*.
"""
path = QPainterPath()
path.addEllipse(x - eps, y - eps, 2 * eps, 2 * eps)
curvePath = QPainterPath()
if curve[-1].segmentType == "curve":
p1, p2, p3, p4 = curve
curvePath.moveTo(p1.x, p1.y)
curvePath.cubicTo(p2.x, p2.y, p3.x, p3.y, p4.x, p4.y)
curvePath.cubicTo(p3.x, p3.y, p2.x, p2.y, p1.x, p1.y)
else:
first = curve[0]
curvePath.moveTo(first.x, first.y)
# PACK for fontTools
pts = []
for pt in curve:
pts.append((pt.x, pt.y))
# draw
for pt1, pt2 in decomposeQuadraticSegment(pts[1:]):
curvePath.quadTo(*pt1 + pt2)
for pt1, pt2 in decomposeQuadraticSegment(list(reversed(pts[:-1]))):
curvePath.quadTo(*pt1 + pt2)
return path.intersects(curvePath)
def _pointWithinThreshold(x, y, curve, eps):
"""
See whether *(x, y)* is within *eps* of *curve*.
"""
path = QPainterPath()
path.addEllipse(x - eps, y - eps, 2 * eps, 2 * eps)
curvePath = QPainterPath()
if curve[-1].segmentType == "curve":
p1, p2, p3, p4 = curve
curvePath.moveTo(p1.x, p1.y)
curvePath.cubicTo(p2.x, p2.y, p3.x, p3.y, p4.x, p4.y)
curvePath.cubicTo(p3.x, p3.y, p2.x, p2.y, p1.x, p1.y)
else:
first = curve[0]
curvePath.moveTo(first.x, first.y)
# PACK for fontTools
pts = []
for pt in curve:
pts.append((pt.x, pt.y))
# draw
for pt1, pt2 in decomposeQuadraticSegment(pts[1:]):
curvePath.quadTo(*pt1+pt2)
for pt1, pt2 in decomposeQuadraticSegment(list(reversed(pts[:-1]))):
curvePath.quadTo(*pt1+pt2)
return path.intersects(curvePath)
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 = 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 qCurveTo(self, *points):
decomp = decomposeQuadraticSegment(points)
for pair in decomp:
if pair[1] is None:
pair = (pair[0],decomp[0][0])
shifted = self.shiftList(pair)
print(self.indent+"path.quadTo(%gf,%gf,%gf,%gf);" % tuple(shifted[0]+shifted[1]))
def qCurveTo(self, *points):
if points and points[-1] is None:
print("// this shouldn't happen but it does")
print(self.indent +
"path.moveTo(%gf,%gf);" % self.shift(points[0]))
points = points[:-1]
decomp = decomposeQuadraticSegment(points)
for pair in decomp:
shifted = self.shiftList(pair)
if shifted[0] and shifted[1]:
print(self.indent + "path.quadTo(%gf,%gf,%gf,%gf);" %
tuple(shifted[0] + shifted[1]))
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]
# 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
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)
self.flat = _scalePoints(self.flat, scale=clipperScale)
self.used = False
def qcurveIntersections(x1, y1, x2, y2, *pts):
"""
Computes intersection between a cubic spline and a line segment.
Adapted from: https://www.particleincell.com/2013/cubic-line-intersection/
Takes four defcon points describing curve and four scalars describing line
parameters.
"""
sol = []
# PACK for fontTools
points = []
for pt in pts:
points.append((pt.x, pt.y))
p1 = (pts[0].x, pts[0].y)
for p2, p3 in decomposeQuadraticSegment(points[1:]):
bx, by = (y1 - y2), (x2 - x1)
m = x1 * y2 - x2 * y1
a, b, c = bezierTools.calcQuadraticParameters(p1, p2, p3)
# prepare for next turn
p1 = p3
pc0 = bx * a[0] - by * a[1]
pc1 = (bx * b[0] + by * b[1]) / pc0
pc2 = (bx * c[0] + by * c[1] + m) / pc0
r = bezierTools.solveQuadratic(pc0, pc1, pc2)
for t in r:
if t < 0 or t > 1:
continue
s0 = a[0] * (1 - t) ** 2 + b[0] * 2 * t * (1 - t) + c[0] * t ** 2
s1 = a[1] * (1 - t) ** 2 + b[1] * 2 * t * (1 - t) + c[1] * t ** 2
if (x2 - x1) != 0:
s = (s0 - x1) / (x2 - x1)
else:
s = (s1 - y1) / (y2 - y1)
if s < 0 or s > 1:
continue
sol.append((s0, s1, t))
return sol
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 qCurveTo(self, *points):
decomp = decomposeQuadraticSegment(points)
for pair in decomp:
self.update(pair[1])
def qCurveTo(self, *points):
_qCurveToOne = self._qCurveToOne
for pt1, pt2 in decomposeQuadraticSegment(points):
_qCurveToOne(pt1, pt2)
self.__currentPoint = pt2