"""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",
"decomposeSuperBezierSegment", "decomposeQuadraticSegment"]
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. See decomposeSuperBezierSegment().
The conversion algorithm used for n>2 is inspired by NURB
splines, and is conceptually equivalent to the TrueType "implied
points" principle. See also decomposeQuadraticSegment().
"""
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. See
also decomposeQuadraticSegment().
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
try:
glyph = self.glyphSet[glyphName]
except KeyError:
pass
else:
tPen = TransformPen(self, transformation)
glyph.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. Even though decomposeSuperBezierSegment() handles
# this case just fine, we special-case it anyway since it's so
# common.
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.
_curveToOne = self._curveToOne
for pt1, pt2, pt3 in decomposeSuperBezierSegment(points):
_curveToOne(pt1, pt2, pt3)
self.__currentPoint = pt3
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 pt1, pt2 in decomposeQuadraticSegment(points):
_qCurveToOne(pt1, pt2)
self.__currentPoint = pt2
else:
self.lineTo(points[0])
def decomposeSuperBezierSegment(points):
"""Split the SuperBezier described by 'points' into a list of regular
bezier segments. The 'points' argument must be a sequence with length
3 or greater, containing (x, y) coordinates. The last point is the
destination on-curve point, the rest of the points are off-curve points.
The start point should not be supplied.
This function returns a list of (pt1, pt2, pt3) tuples, which each
specify a regular curveto-style bezier segment.
"""
n = len(points) - 1
assert n > 1
bezierSegments = []
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]))
bezierSegments.append((pt1, pt2, pt3))
pt1, pt2, pt3 = temp, None, None
bezierSegments.append((pt1, points[-2], points[-1]))
return bezierSegments
def decomposeQuadraticSegment(points):
"""Split the quadratic curve segment described by 'points' into a list
of "atomic" quadratic segments. The 'points' argument must be a sequence
with length 2 or greater, containing (x, y) coordinates. The last point
is the destination on-curve point, the rest of the points are off-curve
points. The start point should not be supplied.
This function returns a list of (pt1, pt2) tuples, which each specify a
plain quadratic bezier segment.
"""
n = len(points) - 1
assert n > 0
quadSegments = []
for i in range(n - 1):
x, y = points[i]
nx, ny = points[i+1]
impliedPt = (0.5 * (x + nx), 0.5 * (y + ny))
quadSegments.append((points[i], impliedPt))
quadSegments.append((points[-2], points[-1]))
return quadSegments
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.curveTo((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()
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