"""fontTools.pens.pointInsidePen -- Pen implementing "point inside" testing
for shapes.
"""
from fontTools.pens.basePen import BasePen
from fontTools.misc.bezierTools import solveQuadratic,solveCubic
__all__ = ["PointInsidePen"]
# working around floating point errors
EPSILON = 1e-10
ONE_PLUS_EPSILON = 1 + EPSILON
ZERO_MINUS_EPSILON = 0 - EPSILON
class PointInsidePen(BasePen):
"""This pen implements "point inside" testing: to test whether
a given point lies inside the shape (black) or outside (white).
Instances of this class can be recycled, as long as the
setTestPoint() method is used to set the new point to test.
Typical usage:
pen = PointInsidePen(glyphSet, (100, 200))
outline.draw(pen)
isInside = pen.getResult()
Both the even-odd algorithm and the non-zero-winding-rule
algorithm are implemented. The latter is the default, specify
True for the evenOdd argument of __init__ or setTestPoint
to use the even-odd algorithm.
"""
# This class implements the classical "shoot a ray from the test point
# to infinity and count how many times it intersects the outline" (as well
# as the non-zero variant, where the counter is incremented if the outline
# intersects the ray in one direction and decremented if it intersects in
# the other direction).
# I found an amazingly clear explanation of the subtleties involved in
# implementing this correctly for polygons here:
# http://graphics.cs.ucdavis.edu/~okreylos/TAship/Spring2000/PointInPolygon.html
# I extended the principles outlined on that page to curves.
def __init__(self, glyphSet, testPoint, evenOdd=0):
BasePen.__init__(self, glyphSet)
self.setTestPoint(testPoint, evenOdd)
def setTestPoint(self, testPoint, evenOdd=0):
"""Set the point to test. Call this _before_ the outline gets drawn."""
self.testPoint = testPoint
self.evenOdd = evenOdd
self.firstPoint = None
self.intersectionCount = 0
def getResult(self):
"""After the shape has been drawn, getResult() returns True if the test
point lies within the (black) shape, and False if it doesn't.
"""
if self.firstPoint is not None:
# always make sure the sub paths are closed; the algorithm only works
# for closed paths.
self.closePath()
if self.evenOdd:
result = self.intersectionCount % 2
else:
result = self.intersectionCount
return not not result
def _addIntersection(self, goingUp):
if self.evenOdd or goingUp:
self.intersectionCount += 1
else:
self.intersectionCount -= 1
def _moveTo(self, point):
if self.firstPoint is not None:
# always make sure the sub paths are closed; the algorithm only works
# for closed paths.
self.closePath()
self.firstPoint = point
def _lineTo(self, point):
x, y = self.testPoint
x1, y1 = self._getCurrentPoint()
x2, y2 = point
if x1 < x and x2 < x:
return
if y1 < y and y2 < y:
return
if y1 >= y and y2 >= y:
return
dx = x2 - x1
dy = y2 - y1
t = float(y - y1) / dy
ix = dx * t + x1
if ix < x:
return
self._addIntersection(y2 > y1)
def _curveToOne(self, bcp1, bcp2, point):
x, y = self.testPoint
x1, y1 = self._getCurrentPoint()
x2, y2 = bcp1
x3, y3 = bcp2
x4, y4 = point
if x1 < x and x2 < x and x3 < x and x4 < x:
return
if y1 < y and y2 < y and y3 < y and y4 < y:
return
if y1 >= y and y2 >= y and y3 >= y and y4 >= y:
return
dy = y1
cy = (y2 - dy) * 3.0
by = (y3 - y2) * 3.0 - cy
ay = y4 - dy - cy - by
solutions = solveCubic(ay, by, cy, dy - y)
solutions.sort()
solutions = [t for t in solutions if ZERO_MINUS_EPSILON <= t <= ONE_PLUS_EPSILON]
if not solutions:
return
dx = x1
cx = (x2 - dx) * 3.0
bx = (x3 - x2) * 3.0 - cx
ax = x4 - dx - cx - bx
above = y1 >= y
lastT = None
for t in solutions:
if t == lastT:
continue
lastT = t
t2 = t * t
t3 = t2 * t
direction = 3*ay*t2 + 2*by*t + cy
if direction == 0.0:
direction = 6*ay*t + 2*by
if direction == 0.0:
direction = ay
goingUp = direction > 0.0
xt = ax*t3 + bx*t2 + cx*t + dx
if xt < x:
above = goingUp
continue
if t == 0.0:
if not goingUp:
self._addIntersection(goingUp)
elif t == 1.0:
if not above:
self._addIntersection(goingUp)
else:
if above != goingUp:
self._addIntersection(goingUp)
#else:
# we're not really intersecting, merely touching the 'top'
above = goingUp
def _qCurveToOne_unfinished(self, bcp, point):
# XXX need to finish this, for now doing it through a cubic
# (BasePen implements _qCurveTo in terms of a cubic) will
# have to do.
x, y = self.testPoint
x1, y1 = self._getCurrentPoint()
x2, y2 = bcp
x3, y3 = point
c = y1
b = (y2 - c) * 2.0
a = y3 - c - b
solutions = solveQuadratic(a, b, c - y)
solutions.sort()
solutions = [t for t in solutions if ZERO_MINUS_EPSILON <= t <= ONE_PLUS_EPSILON]
if not solutions:
return
XXX
def _closePath(self):
if self._getCurrentPoint() != self.firstPoint:
self.lineTo(self.firstPoint)
self.firstPoint = None
_endPath = _closePath
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