# Source code for fontTools.pens.basePen

    """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 :py:class:`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.
    """

    from typing import Tuple, Dict

    from fontTools.misc.loggingTools import LogMixin
    from fontTools.misc.transform import DecomposedTransform, Identity

    __all__ = [
        "AbstractPen",
        "NullPen",
        "BasePen",
        "PenError",
        "decomposeSuperBezierSegment",
        "decomposeQuadraticSegment",
    ]

    class PenError(Exception):
        """Represents an error during penning."""

    class OpenContourError(PenError):
        pass

    class AbstractPen:

        def moveTo(self, pt: Tuple[float, float]) -> None:
            """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: Tuple[float, float]) -> None:
            """Draw a straight line from the current point to 'pt'."""
            raise NotImplementedError

        def curveTo(self, *points: Tuple[float, float]) -> None:
            """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: Tuple[float, float]) -> None:
            """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) -> None:
            """Close the current sub path. You must call either pen.closePath()
            or pen.endPath() after each sub path.
            """
            pass

        def endPath(self) -> None:
            """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: str,
            transformation: Tuple[float, float, float, float, float, float],
        ) -> None:
            """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

        def addVarComponent(
            self,
            glyphName: str,
            transformation: DecomposedTransform,
            location: Dict[str, float],
        ) -> None:
            """Add a VarComponent sub glyph. The 'transformation' argument
            must be a DecomposedTransform from the fontTools.misc.transform module,
            and the 'location' argument must be a dictionary mapping axis tags
            to their locations.
            """
            # GlyphSet decomposes for us
            raise AttributeError

    class NullPen(AbstractPen):
        """A pen that does nothing."""

        def moveTo(self, pt):
            pass

        def lineTo(self, pt):
            pass

        def curveTo(self, *points):
            pass

        def qCurveTo(self, *points):
            pass

        def closePath(self):
            pass

        def endPath(self):
            pass

        def addComponent(self, glyphName, transformation):
            pass

        def addVarComponent(self, glyphName, transformation, location):
            pass

    class LoggingPen(LogMixin, AbstractPen):
        """A pen with a ``log`` property (see fontTools.misc.loggingTools.LogMixin)"""

        pass

    class MissingComponentError(KeyError):
        """Indicates a component pointing to a non-existent glyph in the glyphset."""

    class DecomposingPen(LoggingPen):
        """Implements a 'addComponent' method that decomposes components
        (i.e. draws them onto self as simple contours).
        It can also be used as a mixin class (e.g. see ContourRecordingPen).

        You must override moveTo, lineTo, curveTo and qCurveTo. You may
        additionally override closePath, endPath and addComponent.

        By default a warning message is logged when a base glyph is missing;
        set the class variable ``skipMissingComponents`` to False if you want
        all instances of a sub-class to raise a :class:`MissingComponentError`
        exception by default.
        """

        skipMissingComponents = True
        # alias error for convenience
        MissingComponentError = MissingComponentError

        def __init__(
            self,
            glyphSet,
            *args,
            skipMissingComponents=None,
            reverseFlipped=False,
            **kwargs,
        ):
            """Takes a 'glyphSet' argument (dict), in which the glyphs that are referenced
            as components are looked up by their name.

            If the optional 'reverseFlipped' argument is True, components whose transformation
            matrix has a negative determinant will be decomposed with a reversed path direction
            to compensate for the flip.

            The optional 'skipMissingComponents' argument can be set to True/False to
            override the homonymous class attribute for a given pen instance.
            """
            super(DecomposingPen, self).__init__(*args, **kwargs)
            self.glyphSet = glyphSet
            self.skipMissingComponents = (
                self.__class__.skipMissingComponents
                if skipMissingComponents is None
                else skipMissingComponents
            )
            self.reverseFlipped = reverseFlipped

        def addComponent(self, glyphName, transformation):
            """Transform the points of the base glyph and draw it onto self."""
            from fontTools.pens.transformPen import TransformPen

            try:
                glyph = self.glyphSet[glyphName]
            except KeyError:
                if not self.skipMissingComponents:
                    raise MissingComponentError(glyphName)
                self.log.warning("glyph '%s' is missing from glyphSet; skipped" % glyphName)
            else:
                pen = self
                if transformation != Identity:
                    pen = TransformPen(pen, transformation)
                if self.reverseFlipped:
                    # if the transformation has a negative determinant, it will
                    # reverse the contour direction of the component
                    a, b, c, d = transformation[:4]
                    det = a * d - b * c
                    if det < 0:
                        from fontTools.pens.reverseContourPen import ReverseContourPen

                        pen = ReverseContourPen(pen)
                glyph.draw(pen)

        def addVarComponent(self, glyphName, transformation, location):
            # GlyphSet decomposes for us
            raise AttributeError

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

        def __init__(self, glyphSet=None):
            super(BasePen, self).__init__(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)

        # 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)
            for j in range(1, nDivisions):
                factor = j / nDivisions
                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()