Lib/fontTools/pens/pointInsidePen.py

"""fontTools.pens.pointInsidePen -- Pen implementing "point inside" testing
for shapes.
"""

from __future__ import print_function, division, absolute_import
from fontTools.misc.py23 import *
from fontTools.pens.basePen import BasePen
from fontTools.misc.bezierTools import solveQuadratic, solveCubic


__all__ = ["PointInsidePen"]


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)

	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

	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

	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. <= t <= 1.]
		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