fontTools/pens/basePen.py

"""fontTools.pens.basePen.py -- Tools and base classes to build pen objects.

The Pen Protocol

A Pen is a kind of object that standardizes the way how to "draw" outlines:
it is a middle man between an outline and a drawing. In other words:
it is an abstraction for drawing outlines, making sure that outline objects
don't need to know the details about how and where they're being drawn, and
that drawings don't need to know the details of how outlines are stored.

The most basic pattern is this:

    outline.draw(pen)  # 'outline' draws itself onto 'pen'

Pens can be used to render outlines to the screen, but also to construct
new outlines. Eg. an outline object can be both a drawable object (it has a
draw() method) as well as a pen itself: you *build* an outline using pen
methods.

The AbstractPen class defines the Pen protocol. It implements almost
nothing (only no-op closePath() and endPath() methods), but is useful
for documentation purposes. Subclassing it basically tells the reader:
"this class implements the Pen protocol.". An examples of an AbstractPen
subclass is fontTools.pens.transformPen.TransformPen.

The BasePen class is a base implementation useful for pens that actually
draw (for example a pen renders outlines using a native graphics engine).
BasePen contains a lot of base functionality, making it very easy to build
a pen that fully conforms to the pen protocol. Note that if you subclass
BasePen, you _don't_ override moveTo(), lineTo(), etc., but _moveTo(),
_lineTo(), etc. See the BasePen doc string for details. Examples of
BasePen subclasses are fontTools.pens.boundsPen.BoundsPen and
fontTools.pens.cocoaPen.CocoaPen.

Coordinates are usually expressed as (x, y) tuples, but generally any
sequence of length 2 will do.
"""


__all__ = ["AbstractPen", "BasePen"]


class AbstractPen:

	def moveTo(self, pt):
		"""Begin a new sub path, set the current point to 'pt'. You must
		end each sub path with a call to pen.closePath() or pen.endPath().
		"""
		raise NotImplementedError

	def lineTo(self, pt):
		"""Draw a straight line from the current point to 'pt'."""
		raise NotImplementedError

	def curveTo(self, *points):
		"""Draw a cubic bezier with an arbitrary number of control points.

		The last point specified is on-curve, all others are off-curve
		(control) points. If the number of control points is > 2, the
		segment is split into multiple bezier segments. This works
		like this:

		Let n be the number of control points (which is the number of
		arguments to this call minus 1). If n==2, a plain vanilla cubic
		bezier is drawn. If n==1, we fall back to a quadratic segment and
		if n==0 we draw a straight line. It gets interesting when n>2:
		n-1 PostScript-style cubic segments will be drawn as if it were
		one curve.

		The conversion algorithm used for n>2 is inspired by NURB
		splines, and is conceptually equivalent to the TrueType "implied
		points" principle. See also qCurveTo().
		"""
		raise NotImplementedError

	def qCurveTo(self, *points):
		"""Draw a whole string of quadratic curve segments.

		The last point specified is on-curve, all others are off-curve
		points.

		This method implements TrueType-style curves, breaking up curves
		using 'implied points': between each two consequtive off-curve points,
		there is one implied point exactly in the middle between them.

		The last argument (normally the on-curve point) may be None.
		This is to support contours that have NO on-curve points (a rarely
		seen feature of TrueType outlines).
		"""
		raise NotImplementedError

	def closePath(self):
		"""Close the current sub path. You must call either pen.closePath()
		or pen.endPath() after each sub path.
		"""
		pass

	def endPath(self):
		"""End the current sub path, but don't close it. You must call
		either pen.closePath() or pen.endPath() after each sub path.
		"""
		pass

	def addComponent(self, glyphName, transformation):
		"""Add a sub glyph. The 'transformation' argument must be a 6-tuple
		containing an affine transformation, or a Transform object from the
		fontTools.misc.transform module. More precisely: it should be a
		sequence containing 6 numbers.
		"""
		raise NotImplementedError


class BasePen(AbstractPen):

	"""Base class for drawing pens. You must override _moveTo, _lineTo and
	_curveToOne. You may additionally override _closePath, _endPath,
	addComponent and/or _qCurveToOne. You should not override any other
	methods.
	"""

	def __init__(self, glyphSet):
		self.glyphSet = glyphSet
		self.__currentPoint = None

	# must override

	def _moveTo(self, pt):
		raise NotImplementedError

	def _lineTo(self, pt):
		raise NotImplementedError

	def _curveToOne(self, pt1, pt2, pt3):
		raise NotImplementedError

	# may override

	def _closePath(self):
		pass

	def _endPath(self):
		pass

	def _qCurveToOne(self, pt1, pt2):
		"""This method implements the basic quadratic curve type. The
		default implementation delegates the work to the cubic curve
		function. Optionally override with a native implementation.
		"""
		pt0x, pt0y = self.__currentPoint
		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)
		self._curveToOne((mid1x, mid1y), (mid2x, mid2y), pt2)

	def addComponent(self, glyphName, transformation):
		"""This default implementation simply transforms the points
		of the base glyph and draws it onto self.
		"""
		from fontTools.pens.transformPen import TransformPen
		tPen = TransformPen(self, transformation)
		self.glyphSet[glyphName].draw(tPen)

	# don't override

	def _getCurrentPoint(self):
		"""Return the current point. This is not part of the public
		interface, yet is useful for subclasses.
		"""
		return self.__currentPoint

	def closePath(self):
		self._closePath()
		self.__currentPoint = None

	def endPath(self):
		self._endPath()
		self.__currentPoint = None

	def moveTo(self, pt):
		self._moveTo(pt)
		self.__currentPoint = pt

	def lineTo(self, pt):
		self._lineTo(pt)
		self.__currentPoint = pt

	def curveTo(self, *points):
		n = len(points) - 1  # 'n' is the number of control points
		assert n >= 0
		if n == 2:
			# The common case, we have exactly two BCP's, so this is a standard
			# cubic bezier.
			self._curveToOne(*points)
			self.__currentPoint = points[-1]
		elif n > 2:
			# n is the number of control points; split curve into n-1 cubic
			# bezier segments. The algorithm used here is inspired by NURB
			# splines and the TrueType "implied point" principle, and ensures
			# the smoothest possible connection between two curve segments,
			# with no disruption in the curvature. It is practical since it
			# allows one to construct multiple bezier segments with a much
			# smaller amount of points.
			pt1, pt2, pt3 = points[0], None, None
			for i in range(2, n+1):
				# calculate points in between control points.
				nDivisions = min(i, 3, n-i+2)
				d = float(nDivisions)
				for j in range(1, nDivisions):
					factor = j / d
					temp1 = points[i-1]
					temp2 = points[i-2]
					temp = (temp2[0] + factor * (temp1[0] - temp2[0]),
					        temp2[1] + factor * (temp1[1] - temp2[1]))
					if pt2 is None:
						pt2 = temp
					else:
						pt3 = (0.5 * (pt2[0] + temp[0]),
						       0.5 * (pt2[1] + temp[1]))
						self._curveToOne(pt1, pt2, pt3)
						self.__currentPoint = pt3
						pt1, pt2, pt3 = temp, None, None
			self._curveToOne(pt1, points[-2], points[-1])
			self.__currentPoint = points[-1]
		elif n == 1:
			self.qCurveTo(*points)
		elif n == 0:
			self.lineTo(points[0])
		else:
			raise AssertionError, "can't get there from here"

	def qCurveTo(self, *points):
		n = len(points) - 1  # 'n' is the number of control points
		assert n >= 0
		if points[-1] is None:
			# Special case for TrueType quadratics: it is possible to
			# define a contour with NO on-curve points. BasePen supports
			# this by allowing the final argument (the expected on-curve
			# point) to be None. We simulate the feature by making the implied
			# on-curve point between the last and the first off-curve points
			# explicit.
			x, y = points[-2]  # last off-curve point
			nx, ny = points[0] # first off-curve point
			impliedStartPoint = (0.5 * (x + nx), 0.5 * (y + ny))
			self.__currentPoint = impliedStartPoint
			self._moveTo(impliedStartPoint)
			points = points[:-1] + (impliedStartPoint,)
		if n > 0:
			# Split the string of points into discrete quadratic curve
			# segments. Between any two consecutive off-curve points
			# there's an implied on-curve point exactly in the middle.
			# This is where the segment splits.
			_qCurveToOne = self._qCurveToOne
			for i in range(n - 1):
				x, y = points[i]
				nx, ny = points[i+1]
				impliedPt = (0.5 * (x + nx), 0.5 * (y + ny))
				_qCurveToOne(points[i], impliedPt)
				self.__currentPoint = impliedPt
			_qCurveToOne(points[-2], points[-1])
			self.__currentPoint = points[-1]
		else:
			self.lineTo(points[0])


class _TestPen(BasePen):
	"""Test class that prints PostScript to stdout."""
	def _moveTo(self, pt):
		print "%s %s moveto" % (pt[0], pt[1])
	def _lineTo(self, pt):
		print "%s %s lineto" % (pt[0], pt[1])
	def _curveToOne(self, bcp1, bcp2, pt):
		print "%s %s %s %s %s %s curveto" % (bcp1[0], bcp1[1],
				bcp2[0], bcp2[1], pt[0], pt[1])
	def _closePath(self):
		print "closepath"


if __name__ == "__main__":
	pen = _TestPen(None)
	pen.moveTo((0, 0))
	pen.lineTo((0, 100))
	pen.qCurveTo((50, 75), (60, 50), (50, 25), (0, 0))
	pen.closePath()

	pen = _TestPen(None)
	# testing the "no on-curve point" scenario
	pen.qCurveTo((0, 0), (0, 100), (100, 100), (100, 0), None)
	pen.closePath()