path: root/Lib/fontTools/ttLib/tables/_g_l_y_f.py

"""_g_l_y_f.py -- Converter classes for the 'glyf' table."""

from collections import namedtuple
from fontTools.misc import sstruct
from fontTools import ttLib
from fontTools import version
from fontTools.misc.textTools import tostr, safeEval, pad
from fontTools.misc.arrayTools import calcIntBounds, pointInRect
from fontTools.misc.bezierTools import calcQuadraticBounds
from fontTools.misc.fixedTools import (
	fixedToFloat as fi2fl,
	floatToFixed as fl2fi,
	floatToFixedToStr as fl2str,
	strToFixedToFloat as str2fl,
	otRound,
)
from numbers import Number
from . import DefaultTable
from . import ttProgram
import sys
import struct
import array
import logging
import os
from fontTools.misc import xmlWriter
from fontTools.misc.filenames import userNameToFileName
from fontTools.misc.loggingTools import deprecateFunction

log = logging.getLogger(__name__)

# We compute the version the same as is computed in ttlib/__init__
# so that we can write 'ttLibVersion' attribute of the glyf TTX files
# when glyf is written to separate files.
version = ".".join(version.split('.')[:2])

#
# The Apple and MS rasterizers behave differently for
# scaled composite components: one does scale first and then translate
# and the other does it vice versa. MS defined some flags to indicate
# the difference, but it seems nobody actually _sets_ those flags.
#
# Funny thing: Apple seems to _only_ do their thing in the
# WE_HAVE_A_SCALE (eg. Chicago) case, and not when it's WE_HAVE_AN_X_AND_Y_SCALE
# (eg. Charcoal)...
#
SCALE_COMPONENT_OFFSET_DEFAULT = 0   # 0 == MS, 1 == Apple


class table__g_l_y_f(DefaultTable.DefaultTable):
	"""Glyph Data Table

	This class represents the `glyf <https://docs.microsoft.com/en-us/typography/opentype/spec/glyf>`_
 	table, which contains outlines for glyphs in TrueType format. In many cases,
 	it is easier to access and manipulate glyph outlines through the ``GlyphSet``
 	object returned from :py:meth:`fontTools.ttLib.ttFont.getGlyphSet`::

 			>> from fontTools.pens.boundsPen import BoundsPen
 			>> glyphset = font.getGlyphSet()
			>> bp = BoundsPen(glyphset)
			>> glyphset["A"].draw(bp)
			>> bp.bounds
			(19, 0, 633, 716)

	However, this class can be used for low-level access to the ``glyf`` table data.
	Objects of this class support dictionary-like access, mapping glyph names to
	:py:class:`Glyph` objects::

			>> glyf = font["glyf"]
			>> len(glyf["Aacute"].components)
			2

	Note that when adding glyphs to the font via low-level access to the ``glyf``
	table, the new glyphs must also be added to the ``hmtx``/``vmtx`` table::

			>> font["glyf"]["divisionslash"] = Glyph()
			>> font["hmtx"]["divisionslash"] = (640, 0)

	"""

	# this attribute controls the amount of padding applied to glyph data upon compile.
	# Glyph lenghts are aligned to multiples of the specified value. 
	# Allowed values are (0, 1, 2, 4). '0' means no padding; '1' (default) also means
	# no padding, except for when padding would allow to use short loca offsets.
	padding = 1

	def decompile(self, data, ttFont):
		loca = ttFont['loca']
		pos = int(loca[0])
		nextPos = 0
		noname = 0
		self.glyphs = {}
		self.glyphOrder = glyphOrder = ttFont.getGlyphOrder()
		for i in range(0, len(loca)-1):
			try:
				glyphName = glyphOrder[i]
			except IndexError:
				noname = noname + 1
				glyphName = 'ttxautoglyph%s' % i
			nextPos = int(loca[i+1])
			glyphdata = data[pos:nextPos]
			if len(glyphdata) != (nextPos - pos):
				raise ttLib.TTLibError("not enough 'glyf' table data")
			glyph = Glyph(glyphdata)
			self.glyphs[glyphName] = glyph
			pos = nextPos
		if len(data) - nextPos >= 4:
			log.warning(
				"too much 'glyf' table data: expected %d, received %d bytes",
				nextPos, len(data))
		if noname:
			log.warning('%s glyphs have no name', noname)
		if ttFont.lazy is False: # Be lazy for None and True
			self.ensureDecompiled()

	def ensureDecompiled(self, recurse=False):
		# The recurse argument is unused, but part of the signature of
		# ensureDecompiled across the library.
		for glyph in self.glyphs.values():
			glyph.expand(self)

	def compile(self, ttFont):
		if not hasattr(self, "glyphOrder"):
			self.glyphOrder = ttFont.getGlyphOrder()
		padding = self.padding
		assert padding in (0, 1, 2, 4)
		locations = []
		currentLocation = 0
		dataList = []
		recalcBBoxes = ttFont.recalcBBoxes
		for glyphName in self.glyphOrder:
			glyph = self.glyphs[glyphName]
			glyphData = glyph.compile(self, recalcBBoxes)
			if padding > 1:
				glyphData = pad(glyphData, size=padding)
			locations.append(currentLocation)
			currentLocation = currentLocation + len(glyphData)
			dataList.append(glyphData)
		locations.append(currentLocation)

		if padding == 1 and currentLocation < 0x20000:
			# See if we can pad any odd-lengthed glyphs to allow loca
			# table to use the short offsets.
			indices = [i for i,glyphData in enumerate(dataList) if len(glyphData) % 2 == 1]
			if indices and currentLocation + len(indices) < 0x20000:
				# It fits.  Do it.
				for i in indices:
					dataList[i] += b'\0'
				currentLocation = 0
				for i,glyphData in enumerate(dataList):
					locations[i] = currentLocation
					currentLocation += len(glyphData)
				locations[len(dataList)] = currentLocation

		data = b''.join(dataList)
		if 'loca' in ttFont:
			ttFont['loca'].set(locations)
		if 'maxp' in ttFont:
			ttFont['maxp'].numGlyphs = len(self.glyphs)
		if not data:
		# As a special case when all glyph in the font are empty, add a zero byte
		# to the table, so that OTS doesn’t reject it, and to make the table work
		# on Windows as well.
		# See https://github.com/khaledhosny/ots/issues/52
			data = b"\0"
		return data

	def toXML(self, writer, ttFont, splitGlyphs=False):
		notice = (
			"The xMin, yMin, xMax and yMax values\n"
			"will be recalculated by the compiler.")
		glyphNames = ttFont.getGlyphNames()
		if not splitGlyphs:
			writer.newline()
			writer.comment(notice)
			writer.newline()
			writer.newline()
		numGlyphs = len(glyphNames)
		if splitGlyphs:
			path, ext = os.path.splitext(writer.file.name)
			existingGlyphFiles = set()
		for glyphName in glyphNames:
			glyph = self.get(glyphName)
			if glyph is None:
				log.warning("glyph '%s' does not exist in glyf table", glyphName)
				continue
			if glyph.numberOfContours:
				if splitGlyphs:
					glyphPath = userNameToFileName(
						tostr(glyphName, 'utf-8'),
						existingGlyphFiles,
						prefix=path + ".",
						suffix=ext)
					existingGlyphFiles.add(glyphPath.lower())
					glyphWriter = xmlWriter.XMLWriter(
						glyphPath, idlefunc=writer.idlefunc,
						newlinestr=writer.newlinestr)
					glyphWriter.begintag("ttFont", ttLibVersion=version)
					glyphWriter.newline()
					glyphWriter.begintag("glyf")
					glyphWriter.newline()
					glyphWriter.comment(notice)
					glyphWriter.newline()
					writer.simpletag("TTGlyph", src=os.path.basename(glyphPath))
				else:
					glyphWriter = writer
				glyphWriter.begintag('TTGlyph', [
							("name", glyphName),
							("xMin", glyph.xMin),
							("yMin", glyph.yMin),
							("xMax", glyph.xMax),
							("yMax", glyph.yMax),
							])
				glyphWriter.newline()
				glyph.toXML(glyphWriter, ttFont)
				glyphWriter.endtag('TTGlyph')
				glyphWriter.newline()
				if splitGlyphs:
					glyphWriter.endtag("glyf")
					glyphWriter.newline()
					glyphWriter.endtag("ttFont")
					glyphWriter.newline()
					glyphWriter.close()
			else:
				writer.simpletag('TTGlyph', name=glyphName)
				writer.comment("contains no outline data")
				if not splitGlyphs:
					writer.newline()
			writer.newline()

	def fromXML(self, name, attrs, content, ttFont):
		if name != "TTGlyph":
			return
		if not hasattr(self, "glyphs"):
			self.glyphs = {}
		if not hasattr(self, "glyphOrder"):
			self.glyphOrder = ttFont.getGlyphOrder()
		glyphName = attrs["name"]
		log.debug("unpacking glyph '%s'", glyphName)
		glyph = Glyph()
		for attr in ['xMin', 'yMin', 'xMax', 'yMax']:
			setattr(glyph, attr, safeEval(attrs.get(attr, '0')))
		self.glyphs[glyphName] = glyph
		for element in content:
			if not isinstance(element, tuple):
				continue
			name, attrs, content = element
			glyph.fromXML(name, attrs, content, ttFont)
		if not ttFont.recalcBBoxes:
			glyph.compact(self, 0)

	def setGlyphOrder(self, glyphOrder):
		"""Sets the glyph order

		Args:
			glyphOrder ([str]): List of glyph names in order.
		"""
		self.glyphOrder = glyphOrder

	def getGlyphName(self, glyphID):
		"""Returns the name for the glyph with the given ID.

		Raises a ``KeyError`` if the glyph name is not found in the font.
		"""
		return self.glyphOrder[glyphID]

	def getGlyphID(self, glyphName):
		"""Returns the ID of the glyph with the given name.

		Raises a ``ValueError`` if the glyph is not found in the font.
		"""
		# XXX optimize with reverse dict!!!
		return self.glyphOrder.index(glyphName)

	def removeHinting(self):
		"""Removes TrueType hints from all glyphs in the glyphset.

		See :py:meth:`Glyph.removeHinting`.
		"""
		for glyph in self.glyphs.values():
			glyph.removeHinting()

	def keys(self):
		return self.glyphs.keys()

	def has_key(self, glyphName):
		return glyphName in self.glyphs

	__contains__ = has_key

	def get(self, glyphName, default=None):
		glyph = self.glyphs.get(glyphName, default)
		if glyph is not None:
			glyph.expand(self)
		return glyph

	def __getitem__(self, glyphName):
		glyph = self.glyphs[glyphName]
		glyph.expand(self)
		return glyph

	def __setitem__(self, glyphName, glyph):
		self.glyphs[glyphName] = glyph
		if glyphName not in self.glyphOrder:
			self.glyphOrder.append(glyphName)

	def __delitem__(self, glyphName):
		del self.glyphs[glyphName]
		self.glyphOrder.remove(glyphName)

	def __len__(self):
		assert len(self.glyphOrder) == len(self.glyphs)
		return len(self.glyphs)

	def _getPhantomPoints(self, glyphName, hMetrics, vMetrics=None):
		"""Compute the four "phantom points" for the given glyph from its bounding box
		and the horizontal and vertical advance widths and sidebearings stored in the
		ttFont's "hmtx" and "vmtx" tables.

		'hMetrics' should be ttFont['hmtx'].metrics.

		'vMetrics' should be ttFont['vmtx'].metrics if there is "vmtx" or None otherwise.
		If there is no vMetrics passed in, vertical phantom points are set to the zero coordinate.

		https://docs.microsoft.com/en-us/typography/opentype/spec/tt_instructing_glyphs#phantoms
		"""
		glyph = self[glyphName]
		if not hasattr(glyph, 'xMin'):
			glyph.recalcBounds(self)

		horizontalAdvanceWidth, leftSideBearing = hMetrics[glyphName]
		leftSideX = glyph.xMin - leftSideBearing
		rightSideX = leftSideX + horizontalAdvanceWidth

		if vMetrics:
			verticalAdvanceWidth, topSideBearing = vMetrics[glyphName]
			topSideY = topSideBearing + glyph.yMax
			bottomSideY = topSideY - verticalAdvanceWidth
		else:
			bottomSideY = topSideY = 0

		return [
			(leftSideX, 0),
			(rightSideX, 0),
			(0, topSideY),
			(0, bottomSideY),
		]

	def _getCoordinatesAndControls(self, glyphName, hMetrics, vMetrics=None):
		"""Return glyph coordinates and controls as expected by "gvar" table.

		The coordinates includes four "phantom points" for the glyph metrics,
		as mandated by the "gvar" spec.

		The glyph controls is a namedtuple with the following attributes:
			- numberOfContours: -1 for composite glyphs.
			- endPts: list of indices of end points for each contour in simple
			glyphs, or component indices in composite glyphs (used for IUP
			optimization).
			- flags: array of contour point flags for simple glyphs (None for
			composite glyphs).
			- components: list of base glyph names (str) for each component in
			composite glyphs (None for simple glyphs).

		The "hMetrics" and vMetrics are used to compute the "phantom points" (see
		the "_getPhantomPoints" method).

		Return None if the requested glyphName is not present.
		"""
		glyph = self.get(glyphName)
		if glyph is None:
			return None
		if glyph.isComposite():
			coords = GlyphCoordinates(
				[(getattr(c, 'x', 0), getattr(c, 'y', 0)) for c in glyph.components]
			)
			controls = _GlyphControls(
				numberOfContours=glyph.numberOfContours,
				endPts=list(range(len(glyph.components))),
				flags=None,
				components=[c.glyphName for c in glyph.components],
			)
		else:
			coords, endPts, flags = glyph.getCoordinates(self)
			coords = coords.copy()
			controls = _GlyphControls(
				numberOfContours=glyph.numberOfContours,
				endPts=endPts,
				flags=flags,
				components=None,
			)
		# Add phantom points for (left, right, top, bottom) positions.
		phantomPoints = self._getPhantomPoints(glyphName, hMetrics, vMetrics)
		coords.extend(phantomPoints)
		return coords, controls

	def _setCoordinates(self, glyphName, coord, hMetrics, vMetrics=None):
		"""Set coordinates and metrics for the given glyph.

		"coord" is an array of GlyphCoordinates which must include the "phantom
		points" as the last four coordinates.

		Both the horizontal/vertical advances and left/top sidebearings in "hmtx"
		and "vmtx" tables (if any) are updated from four phantom points and
		the glyph's bounding boxes.

		The "hMetrics" and vMetrics are used to propagate "phantom points"
		into "hmtx" and "vmtx" tables if desired.  (see the "_getPhantomPoints"
		method).
		"""
		glyph = self[glyphName]

		# Handle phantom points for (left, right, top, bottom) positions.
		assert len(coord) >= 4
		leftSideX = coord[-4][0]
		rightSideX = coord[-3][0]
		topSideY = coord[-2][1]
		bottomSideY = coord[-1][1]

		coord = coord[:-4]

		if glyph.isComposite():
			assert len(coord) == len(glyph.components)
			for p, comp in zip(coord, glyph.components):
				if hasattr(comp, 'x'):
					comp.x, comp.y = p
		elif glyph.numberOfContours == 0:
			assert len(coord) == 0
		else:
			assert len(coord) == len(glyph.coordinates)
			glyph.coordinates = GlyphCoordinates(coord)

		glyph.recalcBounds(self)

		horizontalAdvanceWidth = otRound(rightSideX - leftSideX)
		if horizontalAdvanceWidth < 0:
			# unlikely, but it can happen, see:
			# https://github.com/fonttools/fonttools/pull/1198
			horizontalAdvanceWidth = 0
		leftSideBearing = otRound(glyph.xMin - leftSideX)
		hMetrics[glyphName] = horizontalAdvanceWidth, leftSideBearing

		if vMetrics is not None:
			verticalAdvanceWidth = otRound(topSideY - bottomSideY)
			if verticalAdvanceWidth < 0:  # unlikely but do the same as horizontal
				verticalAdvanceWidth = 0
			topSideBearing = otRound(topSideY - glyph.yMax)
			vMetrics[glyphName] = verticalAdvanceWidth, topSideBearing


	# Deprecated

	def _synthesizeVMetrics(self, glyphName, ttFont, defaultVerticalOrigin):
		"""This method is wrong and deprecated.
		For rationale see:
		https://github.com/fonttools/fonttools/pull/2266/files#r613569473
		"""
		vMetrics = getattr(ttFont.get('vmtx'), 'metrics', None)
		if vMetrics is None:
			verticalAdvanceWidth = ttFont["head"].unitsPerEm
			topSideY = getattr(ttFont.get('hhea'), 'ascent', None)
			if topSideY is None:
				if defaultVerticalOrigin is not None:
					topSideY = defaultVerticalOrigin
				else:
					topSideY = verticalAdvanceWidth
			glyph = self[glyphName]
			glyph.recalcBounds(self)
			topSideBearing = otRound(topSideY - glyph.yMax)
			vMetrics = {glyphName: (verticalAdvanceWidth, topSideBearing)}
		return vMetrics

	@deprecateFunction("use '_getPhantomPoints' instead", category=DeprecationWarning)
	def getPhantomPoints(self, glyphName, ttFont, defaultVerticalOrigin=None):
		"""Old public name for self._getPhantomPoints().
		See: https://github.com/fonttools/fonttools/pull/2266"""
		hMetrics = ttFont['hmtx'].metrics
		vMetrics = self._synthesizeVMetrics(glyphName, ttFont, defaultVerticalOrigin)
		return self._getPhantomPoints(glyphName, hMetrics, vMetrics)

	@deprecateFunction("use '_getCoordinatesAndControls' instead", category=DeprecationWarning)
	def getCoordinatesAndControls(self, glyphName, ttFont, defaultVerticalOrigin=None):
		"""Old public name for self._getCoordinatesAndControls().
		See: https://github.com/fonttools/fonttools/pull/2266"""
		hMetrics = ttFont['hmtx'].metrics
		vMetrics = self._synthesizeVMetrics(glyphName, ttFont, defaultVerticalOrigin)
		return self._getCoordinatesAndControls(glyphName, hMetrics, vMetrics)

	@deprecateFunction("use '_setCoordinates' instead", category=DeprecationWarning)
	def setCoordinates(self, glyphName, ttFont):
		"""Old public name for self._setCoordinates().
		See: https://github.com/fonttools/fonttools/pull/2266"""
		hMetrics = ttFont['hmtx'].metrics
		vMetrics = getattr(ttFont.get('vmtx'), 'metrics', None)
		self._setCoordinates(glyphName, hMetrics, vMetrics)


_GlyphControls = namedtuple(
	"_GlyphControls", "numberOfContours endPts flags components"
)


glyphHeaderFormat = """
		>	# big endian
		numberOfContours:	h
		xMin:				h
		yMin:				h
		xMax:				h
		yMax:				h
"""

# flags
flagOnCurve = 0x01
flagXShort = 0x02
flagYShort = 0x04
flagRepeat = 0x08
flagXsame =  0x10
flagYsame = 0x20
flagOverlapSimple = 0x40
flagReserved = 0x80

# These flags are kept for XML output after decompiling the coordinates
keepFlags = flagOnCurve + flagOverlapSimple

_flagSignBytes = {
	0: 2,
	flagXsame: 0,
	flagXShort|flagXsame: +1,
	flagXShort: -1,
	flagYsame: 0,
	flagYShort|flagYsame: +1,
	flagYShort: -1,
}

def flagBest(x, y, onCurve):
	"""For a given x,y delta pair, returns the flag that packs this pair
	most efficiently, as well as the number of byte cost of such flag."""

	flag = flagOnCurve if onCurve else 0
	cost = 0
	# do x
	if x == 0:
		flag = flag | flagXsame
	elif -255 <= x <= 255:
		flag = flag | flagXShort
		if x > 0:
			flag = flag | flagXsame
		cost += 1
	else:
		cost += 2
	# do y
	if y == 0:
		flag = flag | flagYsame
	elif -255 <= y <= 255:
		flag = flag | flagYShort
		if y > 0:
			flag = flag | flagYsame
		cost += 1
	else:
		cost += 2
	return flag, cost

def flagFits(newFlag, oldFlag, mask):
	newBytes = _flagSignBytes[newFlag & mask]
	oldBytes = _flagSignBytes[oldFlag & mask]
	return newBytes == oldBytes or abs(newBytes) > abs(oldBytes)

def flagSupports(newFlag, oldFlag):
	return ((oldFlag & flagOnCurve) == (newFlag & flagOnCurve) and
		flagFits(newFlag, oldFlag, flagXsame|flagXShort) and
		flagFits(newFlag, oldFlag, flagYsame|flagYShort))

def flagEncodeCoord(flag, mask, coord, coordBytes):
	byteCount = _flagSignBytes[flag & mask]
	if byteCount == 1:
		coordBytes.append(coord)
	elif byteCount == -1:
		coordBytes.append(-coord)
	elif byteCount == 2:
		coordBytes.extend(struct.pack('>h', coord))

def flagEncodeCoords(flag, x, y, xBytes, yBytes):
	flagEncodeCoord(flag, flagXsame|flagXShort, x, xBytes)
	flagEncodeCoord(flag, flagYsame|flagYShort, y, yBytes)


ARG_1_AND_2_ARE_WORDS		= 0x0001  # if set args are words otherwise they are bytes
ARGS_ARE_XY_VALUES		= 0x0002  # if set args are xy values, otherwise they are points
ROUND_XY_TO_GRID		= 0x0004  # for the xy values if above is true
WE_HAVE_A_SCALE			= 0x0008  # Sx = Sy, otherwise scale == 1.0
NON_OVERLAPPING			= 0x0010  # set to same value for all components (obsolete!)
MORE_COMPONENTS			= 0x0020  # indicates at least one more glyph after this one
WE_HAVE_AN_X_AND_Y_SCALE	= 0x0040  # Sx, Sy
WE_HAVE_A_TWO_BY_TWO		= 0x0080  # t00, t01, t10, t11
WE_HAVE_INSTRUCTIONS		= 0x0100  # instructions follow
USE_MY_METRICS			= 0x0200  # apply these metrics to parent glyph
OVERLAP_COMPOUND		= 0x0400  # used by Apple in GX fonts
SCALED_COMPONENT_OFFSET		= 0x0800  # composite designed to have the component offset scaled (designed for Apple)
UNSCALED_COMPONENT_OFFSET	= 0x1000  # composite designed not to have the component offset scaled (designed for MS)


CompositeMaxpValues = namedtuple('CompositeMaxpValues', ['nPoints', 'nContours', 'maxComponentDepth'])


class Glyph(object):
	"""This class represents an individual TrueType glyph.

	TrueType glyph objects come in two flavours: simple and composite. Simple
	glyph objects contain contours, represented via the ``.coordinates``,
	``.flags``, ``.numberOfContours``, and ``.endPtsOfContours`` attributes;
	composite glyphs contain components, available through the ``.components``
	attributes.

	Because the ``.coordinates`` attribute (and other simple glyph attributes mentioned
	above) is only set on simple glyphs and the ``.components`` attribute is only
	set on composite glyphs, it is necessary to use the :py:meth:`isComposite`
	method to test whether a glyph is simple or composite before attempting to
	access its data.

	For a composite glyph, the components can also be accessed via array-like access::

		>> assert(font["glyf"]["Aacute"].isComposite())
		>> font["glyf"]["Aacute"][0]
		<fontTools.ttLib.tables._g_l_y_f.GlyphComponent at 0x1027b2ee0>

	"""

	def __init__(self, data=b""):
		if not data:
			# empty char
			self.numberOfContours = 0
			return
		self.data = data

	def compact(self, glyfTable, recalcBBoxes=True):
		data = self.compile(glyfTable, recalcBBoxes)
		self.__dict__.clear()
		self.data = data

	def expand(self, glyfTable):
		if not hasattr(self, "data"):
			# already unpacked
			return
		if not self.data:
			# empty char
			del self.data
			self.numberOfContours = 0
			return
		dummy, data = sstruct.unpack2(glyphHeaderFormat, self.data, self)
		del self.data
		# Some fonts (eg. Neirizi.ttf) have a 0 for numberOfContours in
		# some glyphs; decompileCoordinates assumes that there's at least
		# one, so short-circuit here.
		if self.numberOfContours == 0:
			return
		if self.isComposite():
			self.decompileComponents(data, glyfTable)
		else:
			self.decompileCoordinates(data)

	def compile(self, glyfTable, recalcBBoxes=True):
		if hasattr(self, "data"):
			if recalcBBoxes:
				# must unpack glyph in order to recalculate bounding box
				self.expand(glyfTable)
			else:
				return self.data
		if self.numberOfContours == 0:
			return b''
		if recalcBBoxes:
			self.recalcBounds(glyfTable)
		data = sstruct.pack(glyphHeaderFormat, self)
		if self.isComposite():
			data = data + self.compileComponents(glyfTable)
		else:
			data = data + self.compileCoordinates()
		return data

	def toXML(self, writer, ttFont):
		if self.isComposite():
			for compo in self.components:
				compo.toXML(writer, ttFont)
			haveInstructions = hasattr(self, "program")
		else:
			last = 0
			for i in range(self.numberOfContours):
				writer.begintag("contour")
				writer.newline()
				for j in range(last, self.endPtsOfContours[i] + 1):
					attrs = [
							("x", self.coordinates[j][0]),
							("y", self.coordinates[j][1]),
							("on", self.flags[j] & flagOnCurve),
						]
					if self.flags[j] & flagOverlapSimple:
						# Apple's rasterizer uses flagOverlapSimple in the first contour/first pt to flag glyphs that contain overlapping contours
						attrs.append(("overlap", 1))
					writer.simpletag("pt", attrs)
					writer.newline()
				last = self.endPtsOfContours[i] + 1
				writer.endtag("contour")
				writer.newline()
			haveInstructions = self.numberOfContours > 0
		if haveInstructions:
			if self.program:
				writer.begintag("instructions")
				writer.newline()
				self.program.toXML(writer, ttFont)
				writer.endtag("instructions")
			else:
				writer.simpletag("instructions")
			writer.newline()

	def fromXML(self, name, attrs, content, ttFont):
		if name == "contour":
			if self.numberOfContours < 0:
				raise ttLib.TTLibError("can't mix composites and contours in glyph")
			self.numberOfContours = self.numberOfContours + 1
			coordinates = GlyphCoordinates()
			flags = bytearray()
			for element in content:
				if not isinstance(element, tuple):
					continue
				name, attrs, content = element
				if name != "pt":
					continue  # ignore anything but "pt"
				coordinates.append((safeEval(attrs["x"]), safeEval(attrs["y"])))
				flag = bool(safeEval(attrs["on"]))
				if "overlap" in attrs and bool(safeEval(attrs["overlap"])):
					flag |= flagOverlapSimple
				flags.append(flag)
			if not hasattr(self, "coordinates"):
				self.coordinates = coordinates
				self.flags = flags
				self.endPtsOfContours = [len(coordinates)-1]
			else:
				self.coordinates.extend (coordinates)
				self.flags.extend(flags)
				self.endPtsOfContours.append(len(self.coordinates)-1)
		elif name == "component":
			if self.numberOfContours > 0:
				raise ttLib.TTLibError("can't mix composites and contours in glyph")
			self.numberOfContours = -1
			if not hasattr(self, "components"):
				self.components = []
			component = GlyphComponent()
			self.components.append(component)
			component.fromXML(name, attrs, content, ttFont)
		elif name == "instructions":
			self.program = ttProgram.Program()
			for element in content:
				if not isinstance(element, tuple):
					continue
				name, attrs, content = element
				self.program.fromXML(name, attrs, content, ttFont)

	def getCompositeMaxpValues(self, glyfTable, maxComponentDepth=1):
		assert self.isComposite()
		nContours = 0
		nPoints = 0
		initialMaxComponentDepth = maxComponentDepth
		for compo in self.components:
			baseGlyph = glyfTable[compo.glyphName]
			if baseGlyph.numberOfContours == 0:
				continue
			elif baseGlyph.numberOfContours > 0:
				nP, nC = baseGlyph.getMaxpValues()
			else:
				nP, nC, componentDepth = baseGlyph.getCompositeMaxpValues(
						glyfTable, initialMaxComponentDepth + 1)
				maxComponentDepth = max(maxComponentDepth, componentDepth)
			nPoints = nPoints + nP
			nContours = nContours + nC
		return CompositeMaxpValues(nPoints, nContours, maxComponentDepth)

	def getMaxpValues(self):
		assert self.numberOfContours > 0
		return len(self.coordinates), len(self.endPtsOfContours)

	def decompileComponents(self, data, glyfTable):
		self.components = []
		more = 1
		haveInstructions = 0
		while more:
			component = GlyphComponent()
			more, haveInstr, data = component.decompile(data, glyfTable)
			haveInstructions = haveInstructions | haveInstr
			self.components.append(component)
		if haveInstructions:
			numInstructions, = struct.unpack(">h", data[:2])
			data = data[2:]
			self.program = ttProgram.Program()
			self.program.fromBytecode(data[:numInstructions])
			data = data[numInstructions:]
			if len(data) >= 4:
				log.warning(
					"too much glyph data at the end of composite glyph: %d excess bytes",
					len(data))

	def decompileCoordinates(self, data):
		endPtsOfContours = array.array("h")
		endPtsOfContours.frombytes(data[:2*self.numberOfContours])
		if sys.byteorder != "big": endPtsOfContours.byteswap()
		self.endPtsOfContours = endPtsOfContours.tolist()

		pos = 2*self.numberOfContours
		instructionLength, = struct.unpack(">h", data[pos:pos+2])
		self.program = ttProgram.Program()
		self.program.fromBytecode(data[pos+2:pos+2+instructionLength])
		pos += 2 + instructionLength
		nCoordinates = self.endPtsOfContours[-1] + 1
		flags, xCoordinates, yCoordinates = \
				self.decompileCoordinatesRaw(nCoordinates, data, pos)

		# fill in repetitions and apply signs
		self.coordinates = coordinates = GlyphCoordinates.zeros(nCoordinates)
		xIndex = 0
		yIndex = 0
		for i in range(nCoordinates):
			flag = flags[i]
			# x coordinate
			if flag & flagXShort:
				if flag & flagXsame:
					x = xCoordinates[xIndex]
				else:
					x = -xCoordinates[xIndex]
				xIndex = xIndex + 1
			elif flag & flagXsame:
				x = 0
			else:
				x = xCoordinates[xIndex]
				xIndex = xIndex + 1
			# y coordinate
			if flag & flagYShort:
				if flag & flagYsame:
					y = yCoordinates[yIndex]
				else:
					y = -yCoordinates[yIndex]
				yIndex = yIndex + 1
			elif flag & flagYsame:
				y = 0
			else:
				y = yCoordinates[yIndex]
				yIndex = yIndex + 1
			coordinates[i] = (x, y)
		assert xIndex == len(xCoordinates)
		assert yIndex == len(yCoordinates)
		coordinates.relativeToAbsolute()
		# discard all flags except "keepFlags"
		for i in range(len(flags)):
			flags[i] &= keepFlags
		self.flags = flags

	def decompileCoordinatesRaw(self, nCoordinates, data, pos=0):
		# unpack flags and prepare unpacking of coordinates
		flags = bytearray(nCoordinates)
		# Warning: deep Python trickery going on. We use the struct module to unpack
		# the coordinates. We build a format string based on the flags, so we can
		# unpack the coordinates in one struct.unpack() call.
		xFormat = ">" # big endian
		yFormat = ">" # big endian
		j = 0
		while True:
			flag = data[pos]
			pos += 1
			repeat = 1
			if flag & flagRepeat:
				repeat = data[pos] + 1
				pos += 1
			for k in range(repeat):
				if flag & flagXShort:
					xFormat = xFormat + 'B'
				elif not (flag & flagXsame):
					xFormat = xFormat + 'h'
				if flag & flagYShort:
					yFormat = yFormat + 'B'
				elif not (flag & flagYsame):
					yFormat = yFormat + 'h'
				flags[j] = flag
				j = j + 1
			if j >= nCoordinates:
				break
		assert j == nCoordinates, "bad glyph flags"
		# unpack raw coordinates, krrrrrr-tching!
		xDataLen = struct.calcsize(xFormat)
		yDataLen = struct.calcsize(yFormat)
		if len(data) - pos - (xDataLen + yDataLen) >= 4:
			log.warning(
				"too much glyph data: %d excess bytes", len(data) - pos - (xDataLen + yDataLen))
		xCoordinates = struct.unpack(xFormat, data[pos:pos+xDataLen])
		yCoordinates = struct.unpack(yFormat, data[pos+xDataLen:pos+xDataLen+yDataLen])
		return flags, xCoordinates, yCoordinates

	def compileComponents(self, glyfTable):
		data = b""
		lastcomponent = len(self.components) - 1
		more = 1
		haveInstructions = 0
		for i in range(len(self.components)):
			if i == lastcomponent:
				haveInstructions = hasattr(self, "program")
				more = 0
			compo = self.components[i]
			data = data + compo.compile(more, haveInstructions, glyfTable)
		if haveInstructions:
			instructions = self.program.getBytecode()
			data = data + struct.pack(">h", len(instructions)) + instructions
		return data

	def compileCoordinates(self):
		assert len(self.coordinates) == len(self.flags)
		data = []
		endPtsOfContours = array.array("h", self.endPtsOfContours)
		if sys.byteorder != "big": endPtsOfContours.byteswap()
		data.append(endPtsOfContours.tobytes())
		instructions = self.program.getBytecode()
		data.append(struct.pack(">h", len(instructions)))
		data.append(instructions)

		deltas = self.coordinates.copy()
		deltas.toInt()
		deltas.absoluteToRelative()

		# TODO(behdad): Add a configuration option for this?
		deltas = self.compileDeltasGreedy(self.flags, deltas)
		#deltas = self.compileDeltasOptimal(self.flags, deltas)

		data.extend(deltas)
		return b''.join(data)

	def compileDeltasGreedy(self, flags, deltas):
		# Implements greedy algorithm for packing coordinate deltas:
		# uses shortest representation one coordinate at a time.
		compressedFlags = bytearray()
		compressedXs = bytearray()
		compressedYs = bytearray()
		lastflag = None
		repeat = 0
		for flag,(x,y) in zip(flags, deltas):
			# Oh, the horrors of TrueType
			# do x
			if x == 0:
				flag = flag | flagXsame
			elif -255 <= x <= 255:
				flag = flag | flagXShort
				if x > 0:
					flag = flag | flagXsame
				else:
					x = -x
				compressedXs.append(x)
			else:
				compressedXs.extend(struct.pack('>h', x))
			# do y
			if y == 0:
				flag = flag | flagYsame
			elif -255 <= y <= 255:
				flag = flag | flagYShort
				if y > 0:
					flag = flag | flagYsame
				else:
					y = -y
				compressedYs.append(y)
			else:
				compressedYs.extend(struct.pack('>h', y))
			# handle repeating flags
			if flag == lastflag and repeat != 255:
				repeat = repeat + 1
				if repeat == 1:
					compressedFlags.append(flag)
				else:
					compressedFlags[-2] = flag | flagRepeat
					compressedFlags[-1] = repeat
			else:
				repeat = 0
				compressedFlags.append(flag)
			lastflag = flag
		return (compressedFlags, compressedXs, compressedYs)

	def compileDeltasOptimal(self, flags, deltas):
		# Implements optimal, dynaic-programming, algorithm for packing coordinate
		# deltas.  The savings are negligible :(.
		candidates = []
		bestTuple = None
		bestCost = 0
		repeat = 0
		for flag,(x,y) in zip(flags, deltas):
			# Oh, the horrors of TrueType
			flag, coordBytes = flagBest(x, y, flag)
			bestCost += 1 + coordBytes
			newCandidates = [(bestCost, bestTuple, flag, coordBytes),
							(bestCost+1, bestTuple, (flag|flagRepeat), coordBytes)]
			for lastCost,lastTuple,lastFlag,coordBytes in candidates:
				if lastCost + coordBytes <= bestCost + 1 and (lastFlag & flagRepeat) and (lastFlag < 0xff00) and flagSupports(lastFlag, flag):
					if (lastFlag & 0xFF) == (flag|flagRepeat) and lastCost == bestCost + 1:
						continue
					newCandidates.append((lastCost + coordBytes, lastTuple, lastFlag+256, coordBytes))
			candidates = newCandidates
			bestTuple = min(candidates, key=lambda t:t[0])
			bestCost = bestTuple[0]

		flags = []
		while bestTuple:
			cost, bestTuple, flag, coordBytes = bestTuple
			flags.append(flag)
		flags.reverse()

		compressedFlags = bytearray()
		compressedXs = bytearray()
		compressedYs = bytearray()
		coords = iter(deltas)
		ff = []
		for flag in flags:
			repeatCount, flag = flag >> 8, flag & 0xFF
			compressedFlags.append(flag)
			if flag & flagRepeat:
				assert(repeatCount > 0)
				compressedFlags.append(repeatCount)
			else:
				assert(repeatCount == 0)
			for i in range(1 + repeatCount):
				x,y = next(coords)
				flagEncodeCoords(flag, x, y, compressedXs, compressedYs)
				ff.append(flag)
		try:
			next(coords)
			raise Exception("internal error")
		except StopIteration:
			pass

		return (compressedFlags, compressedXs, compressedYs)

	def recalcBounds(self, glyfTable):
		"""Recalculates the bounds of the glyph.

		Each glyph object stores its bounding box in the
		``xMin``/``yMin``/``xMax``/``yMax`` attributes. These bounds must be
		recomputed when the ``coordinates`` change. The ``table__g_l_y_f`` bounds
		must be provided to resolve component bounds.
		"""
		coords, endPts, flags = self.getCoordinates(glyfTable)
		self.xMin, self.yMin, self.xMax, self.yMax = calcIntBounds(coords)

	def isComposite(self):
		"""Test whether a glyph has components"""
		if hasattr(self, "data") and self.data:
			return struct.unpack(">h", self.data[:2])[0] == -1
		else:
			return self.numberOfContours == -1

	def __getitem__(self, componentIndex):
		if not self.isComposite():
			raise ttLib.TTLibError("can't use glyph as sequence")
		return self.components[componentIndex]

	def getCoordinates(self, glyfTable):
		"""Return the coordinates, end points and flags

		This method returns three values: A :py:class:`GlyphCoordinates` object,
		a list of the indexes of the final points of each contour (allowing you
		to split up the coordinates list into contours) and a list of flags.

		On simple glyphs, this method returns information from the glyph's own
		contours; on composite glyphs, it "flattens" all components recursively
		to return a list of coordinates representing all the components involved
		in the glyph.

		To interpret the flags for each point, see the "Simple Glyph Flags"
		section of the `glyf table specification <https://docs.microsoft.com/en-us/typography/opentype/spec/glyf#simple-glyph-description>`.
		"""

		if self.numberOfContours > 0:
			return self.coordinates, self.endPtsOfContours, self.flags
		elif self.isComposite():
			# it's a composite
			allCoords = GlyphCoordinates()
			allFlags = bytearray()
			allEndPts = []
			for compo in self.components:
				g = glyfTable[compo.glyphName]
				try:
					coordinates, endPts, flags = g.getCoordinates(glyfTable)
				except RecursionError:
					raise ttLib.TTLibError("glyph '%s' contains a recursive component reference" % compo.glyphName)
				coordinates = GlyphCoordinates(coordinates)
				if hasattr(compo, "firstPt"):
					# component uses two reference points: we apply the transform _before_
					# computing the offset between the points
					if hasattr(compo, "transform"):
						coordinates.transform(compo.transform)
					x1,y1 = allCoords[compo.firstPt]
					x2,y2 = coordinates[compo.secondPt]
					move = x1-x2, y1-y2
					coordinates.translate(move)
				else:
					# component uses XY offsets
					move = compo.x, compo.y
					if not hasattr(compo, "transform"):
						coordinates.translate(move)
					else:
						apple_way = compo.flags & SCALED_COMPONENT_OFFSET
						ms_way = compo.flags & UNSCALED_COMPONENT_OFFSET
						assert not (apple_way and ms_way)
						if not (apple_way or ms_way):
							scale_component_offset = SCALE_COMPONENT_OFFSET_DEFAULT  # see top of this file
						else:
							scale_component_offset = apple_way
						if scale_component_offset:
							# the Apple way: first move, then scale (ie. scale the component offset)
							coordinates.translate(move)
							coordinates.transform(compo.transform)
						else:
							# the MS way: first scale, then move
							coordinates.transform(compo.transform)
							coordinates.translate(move)
				offset = len(allCoords)
				allEndPts.extend(e + offset for e in endPts)
				allCoords.extend(coordinates)
				allFlags.extend(flags)
			return allCoords, allEndPts, allFlags
		else:
			return GlyphCoordinates(), [], bytearray()

	def getComponentNames(self, glyfTable):
		"""Returns a list of names of component glyphs used in this glyph

		This method can be used on simple glyphs (in which case it returns an
		empty list) or composite glyphs.
		"""
		if not hasattr(self, "data"):
			if self.isComposite():
				return [c.glyphName for c in self.components]
			else:
				return []

		# Extract components without expanding glyph

		if not self.data or struct.unpack(">h", self.data[:2])[0] >= 0:
			return []  # Not composite

		data = self.data
		i = 10
		components = []
		more = 1
		while more:
			flags, glyphID = struct.unpack(">HH", data[i:i+4])
			i += 4
			flags = int(flags)
			components.append(glyfTable.getGlyphName(int(glyphID)))

			if flags & ARG_1_AND_2_ARE_WORDS: i += 4
			else: i += 2
			if flags & WE_HAVE_A_SCALE: i += 2
			elif flags & WE_HAVE_AN_X_AND_Y_SCALE: i += 4
			elif flags & WE_HAVE_A_TWO_BY_TWO: i += 8
			more = flags & MORE_COMPONENTS

		return components

	def trim(self, remove_hinting=False):
		""" Remove padding and, if requested, hinting, from a glyph.
			This works on both expanded and compacted glyphs, without
			expanding it."""
		if not hasattr(self, "data"):
			if remove_hinting:
				if self.isComposite():
					if hasattr(self, "program"):
						del self.program
				else:
					self.program = ttProgram.Program()
					self.program.fromBytecode([])
			# No padding to trim.
			return
		if not self.data:
			return
		numContours = struct.unpack(">h", self.data[:2])[0]
		data = bytearray(self.data)
		i = 10
		if numContours >= 0:
			i += 2 * numContours # endPtsOfContours
			nCoordinates = ((data[i-2] << 8) | data[i-1]) + 1
			instructionLen = (data[i] << 8) | data[i+1]
			if remove_hinting:
				# Zero instruction length
				data[i] = data [i+1] = 0
				i += 2
				if instructionLen:
					# Splice it out
					data = data[:i] + data[i+instructionLen:]
				instructionLen = 0
			else:
				i += 2 + instructionLen

			coordBytes = 0
			j = 0
			while True:
				flag = data[i]
				i = i + 1
				repeat = 1
				if flag & flagRepeat:
					repeat = data[i] + 1
					i = i + 1
				xBytes = yBytes = 0
				if flag & flagXShort:
					xBytes = 1
				elif not (flag & flagXsame):
					xBytes = 2
				if flag & flagYShort:
					yBytes = 1
				elif not (flag & flagYsame):
					yBytes = 2
				coordBytes += (xBytes + yBytes) * repeat
				j += repeat
				if j >= nCoordinates:
					break
			assert j == nCoordinates, "bad glyph flags"
			i += coordBytes
			# Remove padding
			data = data[:i]
		else:
			more = 1
			we_have_instructions = False
			while more:
				flags =(data[i] << 8) | data[i+1]
				if remove_hinting:
					flags &= ~WE_HAVE_INSTRUCTIONS
				if flags & WE_HAVE_INSTRUCTIONS:
					we_have_instructions = True
				data[i+0] = flags >> 8
				data[i+1] = flags & 0xFF
				i += 4
				flags = int(flags)

				if flags & ARG_1_AND_2_ARE_WORDS: i += 4
				else: i += 2
				if flags & WE_HAVE_A_SCALE: i += 2
				elif flags & WE_HAVE_AN_X_AND_Y_SCALE: i += 4
				elif flags & WE_HAVE_A_TWO_BY_TWO: i += 8
				more = flags & MORE_COMPONENTS
			if we_have_instructions:
				instructionLen = (data[i] << 8) | data[i+1]
				i += 2 + instructionLen
			# Remove padding
			data = data[:i]

		self.data = data

	def removeHinting(self):
		"""Removes TrueType hinting instructions from the glyph."""
		self.trim (remove_hinting=True)

	def draw(self, pen, glyfTable, offset=0):
		"""Draws the glyph using the supplied pen object.

		Arguments:
			pen: An object conforming to the pen protocol.
			glyfTable: A :py:class:`table__g_l_y_f` object, to resolve components.
			offset (int): A horizontal offset. If provided, all coordinates are
				translated by this offset.
		"""

		if self.isComposite():
			for component in self.components:
				glyphName, transform = component.getComponentInfo()
				pen.addComponent(glyphName, transform)
			return

		coordinates, endPts, flags = self.getCoordinates(glyfTable)
		if offset:
			coordinates = coordinates.copy()
			coordinates.translate((offset, 0))
		start = 0
		for end in endPts:
			end = end + 1
			contour = coordinates[start:end]
			cFlags = [flagOnCurve & f for f in flags[start:end]]
			start = end
			if 1 not in cFlags:
				# There is not a single on-curve point on the curve,
				# use pen.qCurveTo's special case by specifying None
				# as the on-curve point.
				contour.append(None)
				pen.qCurveTo(*contour)
			else:
				# Shuffle the points so that contour the is guaranteed
				# to *end* in an on-curve point, which we'll use for
				# the moveTo.
				firstOnCurve = cFlags.index(1) + 1
				contour = contour[firstOnCurve:] + contour[:firstOnCurve]
				cFlags = cFlags[firstOnCurve:] + cFlags[:firstOnCurve]
				pen.moveTo(contour[-1])
				while contour:
					nextOnCurve = cFlags.index(1) + 1
					if nextOnCurve == 1:
						# Skip a final lineTo(), as it is implied by
						# pen.closePath()
						if len(contour) > 1:
							pen.lineTo(contour[0])
					else:
						pen.qCurveTo(*contour[:nextOnCurve])
					contour = contour[nextOnCurve:]
					cFlags = cFlags[nextOnCurve:]
			pen.closePath()

	def drawPoints(self, pen, glyfTable, offset=0):
		"""Draw the glyph using the supplied pointPen. As opposed to Glyph.draw(),
		this will not change the point indices.
		"""

		if self.isComposite():
			for component in self.components:
				glyphName, transform = component.getComponentInfo()
				pen.addComponent(glyphName, transform)
			return

		coordinates, endPts, flags = self.getCoordinates(glyfTable)
		if offset:
			coordinates = coordinates.copy()
			coordinates.translate((offset, 0))
		start = 0
		for end in endPts:
			end = end + 1
			contour = coordinates[start:end]
			cFlags = flags[start:end]
			start = end
			pen.beginPath()
			# Start with the appropriate segment type based on the final segment
			segmentType = "line" if cFlags[-1] == 1 else "qcurve"
			for i, pt in enumerate(contour):
				if cFlags[i] & flagOnCurve == 1:
					pen.addPoint(pt, segmentType=segmentType)
					segmentType = "line"
				else:
					pen.addPoint(pt)
					segmentType = "qcurve"
			pen.endPath()

	def __eq__(self, other):
		if type(self) != type(other):
			return NotImplemented
		return self.__dict__ == other.__dict__

	def __ne__(self, other):
		result = self.__eq__(other)
		return result if result is NotImplemented else not result

class GlyphComponent(object):
	"""Represents a component within a composite glyph.

	The component is represented internally with four attributes: ``glyphName``,
	``x``, ``y`` and ``transform``. If there is no "two-by-two" matrix (i.e
	no scaling, reflection, or rotation; only translation), the ``transform``
	attribute is not present.
	"""
	# The above documentation is not *completely* true, but is *true enough* because
	# the rare firstPt/lastPt attributes are not totally supported and nobody seems to
	# mind - see below.

	def __init__(self):
		pass

	def getComponentInfo(self):
		"""Return information about the component

		This method returns a tuple of two values: the glyph name of the component's
		base glyph, and a transformation matrix. As opposed to accessing the attributes
		directly, ``getComponentInfo`` always returns a six-element tuple of the
		component's transformation matrix, even when the two-by-two ``.transform``
		matrix is not present.
		"""
		# XXX Ignoring self.firstPt & self.lastpt for now: I need to implement
		# something equivalent in fontTools.objects.glyph (I'd rather not
		# convert it to an absolute offset, since it is valuable information).
		# This method will now raise "AttributeError: x" on glyphs that use
		# this TT feature.
		if hasattr(self, "transform"):
			[[xx, xy], [yx, yy]] = self.transform
			trans = (xx, xy, yx, yy, self.x, self.y)
		else:
			trans = (1, 0, 0, 1, self.x, self.y)
		return self.glyphName, trans

	def decompile(self, data, glyfTable):
		flags, glyphID = struct.unpack(">HH", data[:4])
		self.flags = int(flags)
		glyphID = int(glyphID)
		self.glyphName = glyfTable.getGlyphName(int(glyphID))
		data = data[4:]

		if self.flags & ARG_1_AND_2_ARE_WORDS:
			if self.flags & ARGS_ARE_XY_VALUES:
				self.x, self.y = struct.unpack(">hh", data[:4])
			else:
				x, y = struct.unpack(">HH", data[:4])
				self.firstPt, self.secondPt = int(x), int(y)
			data = data[4:]
		else:
			if self.flags & ARGS_ARE_XY_VALUES:
				self.x, self.y = struct.unpack(">bb", data[:2])
			else:
				x, y = struct.unpack(">BB", data[:2])
				self.firstPt, self.secondPt = int(x), int(y)
			data = data[2:]

		if self.flags & WE_HAVE_A_SCALE:
			scale, = struct.unpack(">h", data[:2])
			self.transform = [[fi2fl(scale,14), 0], [0, fi2fl(scale,14)]]  # fixed 2.14
			data = data[2:]
		elif self.flags & WE_HAVE_AN_X_AND_Y_SCALE:
			xscale, yscale = struct.unpack(">hh", data[:4])
			self.transform = [[fi2fl(xscale,14), 0], [0, fi2fl(yscale,14)]]  # fixed 2.14
			data = data[4:]
		elif self.flags & WE_HAVE_A_TWO_BY_TWO:
			(xscale, scale01,
					scale10, yscale) = struct.unpack(">hhhh", data[:8])
			self.transform = [[fi2fl(xscale,14), fi2fl(scale01,14)],
							[fi2fl(scale10,14), fi2fl(yscale,14)]] # fixed 2.14
			data = data[8:]
		more = self.flags & MORE_COMPONENTS
		haveInstructions = self.flags & WE_HAVE_INSTRUCTIONS
		self.flags = self.flags & (ROUND_XY_TO_GRID | USE_MY_METRICS |
				SCALED_COMPONENT_OFFSET | UNSCALED_COMPONENT_OFFSET |
				NON_OVERLAPPING | OVERLAP_COMPOUND)
		return more, haveInstructions, data

	def compile(self, more, haveInstructions, glyfTable):
		data = b""

		# reset all flags we will calculate ourselves
		flags = self.flags & (ROUND_XY_TO_GRID | USE_MY_METRICS |
				SCALED_COMPONENT_OFFSET | UNSCALED_COMPONENT_OFFSET |
				NON_OVERLAPPING | OVERLAP_COMPOUND)
		if more:
			flags = flags | MORE_COMPONENTS
		if haveInstructions:
			flags = flags | WE_HAVE_INSTRUCTIONS

		if hasattr(self, "firstPt"):
			if (0 <= self.firstPt <= 255) and (0 <= self.secondPt <= 255):
				data = data + struct.pack(">BB", self.firstPt, self.secondPt)
			else:
				data = data + struct.pack(">HH", self.firstPt, self.secondPt)
				flags = flags | ARG_1_AND_2_ARE_WORDS
		else:
			x = otRound(self.x)
			y = otRound(self.y)
			flags = flags | ARGS_ARE_XY_VALUES
			if (-128 <= x <= 127) and (-128 <= y <= 127):
				data = data + struct.pack(">bb", x, y)
			else:
				data = data + struct.pack(">hh", x, y)
				flags = flags | ARG_1_AND_2_ARE_WORDS

		if hasattr(self, "transform"):
			transform = [[fl2fi(x,14) for x in row] for row in self.transform]
			if transform[0][1] or transform[1][0]:
				flags = flags | WE_HAVE_A_TWO_BY_TWO
				data = data + struct.pack(">hhhh",
						transform[0][0], transform[0][1],
						transform[1][0], transform[1][1])
			elif transform[0][0] != transform[1][1]:
				flags = flags | WE_HAVE_AN_X_AND_Y_SCALE
				data = data + struct.pack(">hh",
						transform[0][0], transform[1][1])
			else:
				flags = flags | WE_HAVE_A_SCALE
				data = data + struct.pack(">h",
						transform[0][0])

		glyphID = glyfTable.getGlyphID(self.glyphName)
		return struct.pack(">HH", flags, glyphID) + data

	def toXML(self, writer, ttFont):
		attrs = [("glyphName", self.glyphName)]
		if not hasattr(self, "firstPt"):
			attrs = attrs + [("x", self.x), ("y", self.y)]
		else:
			attrs = attrs + [("firstPt", self.firstPt), ("secondPt", self.secondPt)]

		if hasattr(self, "transform"):
			transform = self.transform
			if transform[0][1] or transform[1][0]:
				attrs = attrs + [
					("scalex", fl2str(transform[0][0], 14)),
					("scale01", fl2str(transform[0][1], 14)),
					("scale10", fl2str(transform[1][0], 14)),
					("scaley", fl2str(transform[1][1], 14)),
				]
			elif transform[0][0] != transform[1][1]:
				attrs = attrs + [
					("scalex", fl2str(transform[0][0], 14)),
					("scaley", fl2str(transform[1][1], 14)),
				]
			else:
				attrs = attrs + [("scale", fl2str(transform[0][0], 14))]
		attrs = attrs + [("flags", hex(self.flags))]
		writer.simpletag("component", attrs)
		writer.newline()

	def fromXML(self, name, attrs, content, ttFont):
		self.glyphName = attrs["glyphName"]
		if "firstPt" in attrs:
			self.firstPt = safeEval(attrs["firstPt"])
			self.secondPt = safeEval(attrs["secondPt"])
		else:
			self.x = safeEval(attrs["x"])
			self.y = safeEval(attrs["y"])
		if "scale01" in attrs:
			scalex = str2fl(attrs["scalex"], 14)
			scale01 = str2fl(attrs["scale01"], 14)
			scale10 = str2fl(attrs["scale10"], 14)
			scaley = str2fl(attrs["scaley"], 14)
			self.transform = [[scalex, scale01], [scale10, scaley]]
		elif "scalex" in attrs:
			scalex = str2fl(attrs["scalex"], 14)
			scaley = str2fl(attrs["scaley"], 14)
			self.transform = [[scalex, 0], [0, scaley]]
		elif "scale" in attrs:
			scale = str2fl(attrs["scale"], 14)
			self.transform = [[scale, 0], [0, scale]]
		self.flags = safeEval(attrs["flags"])

	def __eq__(self, other):
		if type(self) != type(other):
			return NotImplemented
		return self.__dict__ == other.__dict__

	def __ne__(self, other):
		result = self.__eq__(other)
		return result if result is NotImplemented else not result

class GlyphCoordinates(object):
	"""A list of glyph coordinates.

	Unlike an ordinary list, this is a numpy-like matrix object which supports
	matrix addition, scalar multiplication and other operations described below.
	"""
	def __init__(self, iterable=[]):
		self._a = array.array('d')
		self.extend(iterable)

	@property
	def array(self):
		"""Returns the underlying array of coordinates"""
		return self._a

	@staticmethod
	def zeros(count):
		"""Creates a new ``GlyphCoordinates`` object with all coordinates set to (0,0)"""
		g = GlyphCoordinates()
		g._a.frombytes(bytes(count * 2 * g._a.itemsize))
		return g

	def copy(self):
		"""Creates a new ``GlyphCoordinates`` object which is a copy of the current one."""
		c = GlyphCoordinates()
		c._a.extend(self._a)
		return c

	def __len__(self):
		"""Returns the number of coordinates in the array."""
		return len(self._a) // 2

	def __getitem__(self, k):
		"""Returns a two element tuple (x,y)"""
		if isinstance(k, slice):
			indices = range(*k.indices(len(self)))
			return [self[i] for i in indices]
		a = self._a
		x = a[2*k]
		y = a[2*k+1]
		return (int(x) if x.is_integer() else x,
			int(y) if y.is_integer() else y)

	def __setitem__(self, k, v):
		"""Sets a point's coordinates to a two element tuple (x,y)"""
		if isinstance(k, slice):
			indices = range(*k.indices(len(self)))
			# XXX This only works if len(v) == len(indices)
			for j,i in enumerate(indices):
				self[i] = v[j]
			return
		self._a[2*k],self._a[2*k+1] = v

	def __delitem__(self, i):
		"""Removes a point from the list"""
		i = (2*i) % len(self._a)
		del self._a[i]
		del self._a[i]

	def __repr__(self):
		return 'GlyphCoordinates(['+','.join(str(c) for c in self)+'])'

	def append(self, p):
		self._a.extend(tuple(p))

	def extend(self, iterable):
		for p in iterable:
			self._a.extend(p)

	def toInt(self, *, round=otRound):
		a = self._a
		for i in range(len(a)):
			a[i] = round(a[i])

	def relativeToAbsolute(self):
		a = self._a
		x,y = 0,0
		for i in range(0, len(a), 2):
			a[i  ] = x = a[i  ] + x
			a[i+1] = y = a[i+1] + y

	def absoluteToRelative(self):
		a = self._a
		x,y = 0,0
		for i in range(0, len(a), 2):
			nx = a[i  ]
			ny = a[i+1]
			a[i]   = nx - x
			a[i+1] = ny - y
			x = nx
			y = ny

	def translate(self, p):
		"""
		>>> GlyphCoordinates([(1,2)]).translate((.5,0))
		"""
		x,y = p
		if x == 0 and y == 0:
			return
		a = self._a
		for i in range(0, len(a), 2):
			a[i]   += x
			a[i+1] += y

	def scale(self, p):
		"""
		>>> GlyphCoordinates([(1,2)]).scale((.5,0))
		"""
		x,y = p
		if x == 1 and y == 1:
			return
		a = self._a
		for i in range(0, len(a), 2):
			a[i]   *= x
			a[i+1] *= y

	def transform(self, t):
		"""
		>>> GlyphCoordinates([(1,2)]).transform(((.5,0),(.2,.5)))
		"""
		a = self._a
		for i in range(0, len(a), 2):
			x = a[i  ]
			y = a[i+1]
			px = x * t[0][0] + y * t[1][0]
			py = x * t[0][1] + y * t[1][1]
			a[i]   = px
			a[i+1] = py

	def __eq__(self, other):
		"""
		>>> g = GlyphCoordinates([(1,2)])
		>>> g2 = GlyphCoordinates([(1.0,2)])
		>>> g3 = GlyphCoordinates([(1.5,2)])
		>>> g == g2
		True
		>>> g == g3
		False
		>>> g2 == g3
		False
		"""
		if type(self) != type(other):
			return NotImplemented
		return self._a == other._a

	def __ne__(self, other):
		"""
		>>> g = GlyphCoordinates([(1,2)])
		>>> g2 = GlyphCoordinates([(1.0,2)])
		>>> g3 = GlyphCoordinates([(1.5,2)])
		>>> g != g2
		False
		>>> g != g3
		True
		>>> g2 != g3
		True
		"""
		result = self.__eq__(other)
		return result if result is NotImplemented else not result

	# Math operations

	def __pos__(self):
		"""
		>>> g = GlyphCoordinates([(1,2)])
		>>> g
		GlyphCoordinates([(1, 2)])
		>>> g2 = +g
		>>> g2
		GlyphCoordinates([(1, 2)])
		>>> g2.translate((1,0))
		>>> g2
		GlyphCoordinates([(2, 2)])
		>>> g
		GlyphCoordinates([(1, 2)])
		"""
		return self.copy()
	def __neg__(self):
		"""
		>>> g = GlyphCoordinates([(1,2)])
		>>> g
		GlyphCoordinates([(1, 2)])
		>>> g2 = -g
		>>> g2
		GlyphCoordinates([(-1, -2)])
		>>> g
		GlyphCoordinates([(1, 2)])
		"""
		r = self.copy()
		a = r._a
		for i in range(len(a)):
			a[i] = -a[i]
		return r
	def __round__(self, *, round=otRound):
		r = self.copy()
		r.toInt(round=round)
		return r

	def __add__(self, other): return self.copy().__iadd__(other)
	def __sub__(self, other): return self.copy().__isub__(other)
	def __mul__(self, other): return self.copy().__imul__(other)
	def __truediv__(self, other): return self.copy().__itruediv__(other)

	__radd__ = __add__
	__rmul__ = __mul__
	def __rsub__(self, other): return other + (-self)

	def __iadd__(self, other):
		"""
		>>> g = GlyphCoordinates([(1,2)])
		>>> g += (.5,0)
		>>> g
		GlyphCoordinates([(1.5, 2)])
		>>> g2 = GlyphCoordinates([(3,4)])
		>>> g += g2
		>>> g
		GlyphCoordinates([(4.5, 6)])
		"""
		if isinstance(other, tuple):
			assert len(other) ==  2
			self.translate(other)
			return self
		if isinstance(other, GlyphCoordinates):
			other = other._a
			a = self._a
			assert len(a) == len(other)
			for i in range(len(a)):
				a[i] += other[i]
			return self
		return NotImplemented

	def __isub__(self, other):
		"""
		>>> g = GlyphCoordinates([(1,2)])
		>>> g -= (.5,0)
		>>> g
		GlyphCoordinates([(0.5, 2)])
		>>> g2 = GlyphCoordinates([(3,4)])
		>>> g -= g2
		>>> g
		GlyphCoordinates([(-2.5, -2)])
		"""
		if isinstance(other, tuple):
			assert len(other) ==  2
			self.translate((-other[0],-other[1]))
			return self
		if isinstance(other, GlyphCoordinates):
			other = other._a
			a = self._a
			assert len(a) == len(other)
			for i in range(len(a)):
				a[i] -= other[i]
			return self
		return NotImplemented

	def __imul__(self, other):
		"""
		>>> g = GlyphCoordinates([(1,2)])
		>>> g *= (2,.5)
		>>> g *= 2
		>>> g
		GlyphCoordinates([(4, 2)])
		>>> g = GlyphCoordinates([(1,2)])
		>>> g *= 2
		>>> g
		GlyphCoordinates([(2, 4)])
		"""
		if isinstance(other, tuple):
			assert len(other) ==  2
			self.scale(other)
			return self
		if isinstance(other, Number):
			if other == 1:
				return self
			a = self._a
			for i in range(len(a)):
				a[i] *= other
			return self
		return NotImplemented

	def __itruediv__(self, other):
		"""
		>>> g = GlyphCoordinates([(1,3)])
		>>> g /= (.5,1.5)
		>>> g /= 2
		>>> g
		GlyphCoordinates([(1, 1)])
		"""
		if isinstance(other, Number):
			other = (other, other)
		if isinstance(other, tuple):
			if other == (1,1):
				return self
			assert len(other) ==  2
			self.scale((1./other[0],1./other[1]))
			return self
		return NotImplemented

	def __bool__(self):
		"""
		>>> g = GlyphCoordinates([])
		>>> bool(g)
		False
		>>> g = GlyphCoordinates([(0,0), (0.,0)])
		>>> bool(g)
		True
		>>> g = GlyphCoordinates([(0,0), (1,0)])
		>>> bool(g)
		True
		>>> g = GlyphCoordinates([(0,.5), (0,0)])
		>>> bool(g)
		True
		"""
		return bool(self._a)

	__nonzero__ = __bool__


if __name__ == "__main__":
	import doctest, sys
	sys.exit(doctest.testmod().failed)