Source code for fontTools.pens.pointInsidePen

"""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"]


[docs] 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=False): BasePen.__init__(self, glyphSet) self.setTestPoint(testPoint, evenOdd)
[docs] def setTestPoint(self, testPoint, evenOdd=False): """Set the point to test. Call this _before_ the outline gets drawn.""" self.testPoint = testPoint self.evenOdd = evenOdd self.firstPoint = None self.intersectionCount = 0
[docs] def getWinding(self): if self.firstPoint is not None: # always make sure the sub paths are closed; the algorithm only works # for closed paths. self.closePath() return self.intersectionCount
[docs] 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. """ winding = self.getWinding() if self.evenOdd: result = winding % 2 else: # non-zero result = self.intersectionCount != 0 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 = (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 = sorted(solveCubic(ay, by, cy, dy - y)) solutions = [t for t in solutions if -0.0 <= t <= 1.0] 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 incomingGoingUp = outgoingGoingUp = direction > 0.0 if direction == 0.0: direction = 6 * ay * t + 2 * by outgoingGoingUp = direction > 0.0 incomingGoingUp = not outgoingGoingUp if direction == 0.0: direction = ay incomingGoingUp = outgoingGoingUp = direction > 0.0 xt = ax * t3 + bx * t2 + cx * t + dx if xt < x: continue if t in (0.0, -0.0): if not outgoingGoingUp: self._addIntersection(outgoingGoingUp) elif t == 1.0: if incomingGoingUp: self._addIntersection(incomingGoingUp) else: if incomingGoingUp == outgoingGoingUp: self._addIntersection(outgoingGoingUp) # else: # we're not really intersecting, merely touching 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 = sorted(solveQuadratic(a, b, c - y)) 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 def _endPath(self): """Insideness is not defined for open contours.""" raise NotImplementedError