KIKIMR-19287: add task_stats_drawing script

1 files changed, 495 insertions, 0 deletions

diff --git a/contrib/python/fonttools/fontTools/misc/transform.py b/contrib/python/fonttools/fontTools/misc/transform.py
new file mode 100644
index 00000000000..f85b54b7312
--- /dev/null
+++ b/contrib/python/fonttools/fontTools/misc/transform.py
@@ -0,0 +1,495 @@
+"""Affine 2D transformation matrix class.
+
+The Transform class implements various transformation matrix operations,
+both on the matrix itself, as well as on 2D coordinates.
+
+Transform instances are effectively immutable: all methods that operate on the
+transformation itself always return a new instance. This has as the
+interesting side effect that Transform instances are hashable, ie. they can be
+used as dictionary keys.
+
+This module exports the following symbols:
+
+Transform
+	this is the main class
+Identity
+	Transform instance set to the identity transformation
+Offset
+	Convenience function that returns a translating transformation
+Scale
+	Convenience function that returns a scaling transformation
+
+The DecomposedTransform class implements a transformation with separate
+translate, rotation, scale, skew, and transformation-center components.
+
+:Example:
+
+	>>> t = Transform(2, 0, 0, 3, 0, 0)
+	>>> t.transformPoint((100, 100))
+	(200, 300)
+	>>> t = Scale(2, 3)
+	>>> t.transformPoint((100, 100))
+	(200, 300)
+	>>> t.transformPoint((0, 0))
+	(0, 0)
+	>>> t = Offset(2, 3)
+	>>> t.transformPoint((100, 100))
+	(102, 103)
+	>>> t.transformPoint((0, 0))
+	(2, 3)
+	>>> t2 = t.scale(0.5)
+	>>> t2.transformPoint((100, 100))
+	(52.0, 53.0)
+	>>> import math
+	>>> t3 = t2.rotate(math.pi / 2)
+	>>> t3.transformPoint((0, 0))
+	(2.0, 3.0)
+	>>> t3.transformPoint((100, 100))
+	(-48.0, 53.0)
+	>>> t = Identity.scale(0.5).translate(100, 200).skew(0.1, 0.2)
+	>>> t.transformPoints([(0, 0), (1, 1), (100, 100)])
+	[(50.0, 100.0), (50.550167336042726, 100.60135501775433), (105.01673360427253, 160.13550177543362)]
+	>>>
+"""
+
+import math
+from typing import NamedTuple
+from dataclasses import dataclass
+
+
+__all__ = ["Transform", "Identity", "Offset", "Scale", "DecomposedTransform"]
+
+
+_EPSILON = 1e-15
+_ONE_EPSILON = 1 - _EPSILON
+_MINUS_ONE_EPSILON = -1 + _EPSILON
+
+
+def _normSinCos(v):
+    if abs(v) < _EPSILON:
+        v = 0
+    elif v > _ONE_EPSILON:
+        v = 1
+    elif v < _MINUS_ONE_EPSILON:
+        v = -1
+    return v
+
+
+class Transform(NamedTuple):
+
+    """2x2 transformation matrix plus offset, a.k.a. Affine transform.
+    Transform instances are immutable: all transforming methods, eg.
+    rotate(), return a new Transform instance.
+
+    :Example:
+
+            >>> t = Transform()
+            >>> t
+            <Transform [1 0 0 1 0 0]>
+            >>> t.scale(2)
+            <Transform [2 0 0 2 0 0]>
+            >>> t.scale(2.5, 5.5)
+            <Transform [2.5 0 0 5.5 0 0]>
+            >>>
+            >>> t.scale(2, 3).transformPoint((100, 100))
+            (200, 300)
+
+    Transform's constructor takes six arguments, all of which are
+    optional, and can be used as keyword arguments::
+
+            >>> Transform(12)
+            <Transform [12 0 0 1 0 0]>
+            >>> Transform(dx=12)
+            <Transform [1 0 0 1 12 0]>
+            >>> Transform(yx=12)
+            <Transform [1 0 12 1 0 0]>
+
+    Transform instances also behave like sequences of length 6::
+
+            >>> len(Identity)
+            6
+            >>> list(Identity)
+            [1, 0, 0, 1, 0, 0]
+            >>> tuple(Identity)
+            (1, 0, 0, 1, 0, 0)
+
+    Transform instances are comparable::
+
+            >>> t1 = Identity.scale(2, 3).translate(4, 6)
+            >>> t2 = Identity.translate(8, 18).scale(2, 3)
+            >>> t1 == t2
+            1
+
+    But beware of floating point rounding errors::
+
+            >>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6)
+            >>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3)
+            >>> t1
+            <Transform [0.2 0 0 0.3 0.08 0.18]>
+            >>> t2
+            <Transform [0.2 0 0 0.3 0.08 0.18]>
+            >>> t1 == t2
+            0
+
+    Transform instances are hashable, meaning you can use them as
+    keys in dictionaries::
+
+            >>> d = {Scale(12, 13): None}
+            >>> d
+            {<Transform [12 0 0 13 0 0]>: None}
+
+    But again, beware of floating point rounding errors::
+
+            >>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6)
+            >>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3)
+            >>> t1
+            <Transform [0.2 0 0 0.3 0.08 0.18]>
+            >>> t2
+            <Transform [0.2 0 0 0.3 0.08 0.18]>
+            >>> d = {t1: None}
+            >>> d
+            {<Transform [0.2 0 0 0.3 0.08 0.18]>: None}
+            >>> d[t2]
+            Traceback (most recent call last):
+              File "<stdin>", line 1, in ?
+            KeyError: <Transform [0.2 0 0 0.3 0.08 0.18]>
+    """
+
+    xx: float = 1
+    xy: float = 0
+    yx: float = 0
+    yy: float = 1
+    dx: float = 0
+    dy: float = 0
+
+    def transformPoint(self, p):
+        """Transform a point.
+
+        :Example:
+
+                >>> t = Transform()
+                >>> t = t.scale(2.5, 5.5)
+                >>> t.transformPoint((100, 100))
+                (250.0, 550.0)
+        """
+        (x, y) = p
+        xx, xy, yx, yy, dx, dy = self
+        return (xx * x + yx * y + dx, xy * x + yy * y + dy)
+
+    def transformPoints(self, points):
+        """Transform a list of points.
+
+        :Example:
+
+                >>> t = Scale(2, 3)
+                >>> t.transformPoints([(0, 0), (0, 100), (100, 100), (100, 0)])
+                [(0, 0), (0, 300), (200, 300), (200, 0)]
+                >>>
+        """
+        xx, xy, yx, yy, dx, dy = self
+        return [(xx * x + yx * y + dx, xy * x + yy * y + dy) for x, y in points]
+
+    def transformVector(self, v):
+        """Transform an (dx, dy) vector, treating translation as zero.
+
+        :Example:
+
+                >>> t = Transform(2, 0, 0, 2, 10, 20)
+                >>> t.transformVector((3, -4))
+                (6, -8)
+                >>>
+        """
+        (dx, dy) = v
+        xx, xy, yx, yy = self[:4]
+        return (xx * dx + yx * dy, xy * dx + yy * dy)
+
+    def transformVectors(self, vectors):
+        """Transform a list of (dx, dy) vector, treating translation as zero.
+
+        :Example:
+                >>> t = Transform(2, 0, 0, 2, 10, 20)
+                >>> t.transformVectors([(3, -4), (5, -6)])
+                [(6, -8), (10, -12)]
+                >>>
+        """
+        xx, xy, yx, yy = self[:4]
+        return [(xx * dx + yx * dy, xy * dx + yy * dy) for dx, dy in vectors]
+
+    def translate(self, x=0, y=0):
+        """Return a new transformation, translated (offset) by x, y.
+
+        :Example:
+                >>> t = Transform()
+                >>> t.translate(20, 30)
+                <Transform [1 0 0 1 20 30]>
+                >>>
+        """
+        return self.transform((1, 0, 0, 1, x, y))
+
+    def scale(self, x=1, y=None):
+        """Return a new transformation, scaled by x, y. The 'y' argument
+        may be None, which implies to use the x value for y as well.
+
+        :Example:
+                >>> t = Transform()
+                >>> t.scale(5)
+                <Transform [5 0 0 5 0 0]>
+                >>> t.scale(5, 6)
+                <Transform [5 0 0 6 0 0]>
+                >>>
+        """
+        if y is None:
+            y = x
+        return self.transform((x, 0, 0, y, 0, 0))
+
+    def rotate(self, angle):
+        """Return a new transformation, rotated by 'angle' (radians).
+
+        :Example:
+                >>> import math
+                >>> t = Transform()
+                >>> t.rotate(math.pi / 2)
+                <Transform [0 1 -1 0 0 0]>
+                >>>
+        """
+        import math
+
+        c = _normSinCos(math.cos(angle))
+        s = _normSinCos(math.sin(angle))
+        return self.transform((c, s, -s, c, 0, 0))
+
+    def skew(self, x=0, y=0):
+        """Return a new transformation, skewed by x and y.
+
+        :Example:
+                >>> import math
+                >>> t = Transform()
+                >>> t.skew(math.pi / 4)
+                <Transform [1 0 1 1 0 0]>
+                >>>
+        """
+        import math
+
+        return self.transform((1, math.tan(y), math.tan(x), 1, 0, 0))
+
+    def transform(self, other):
+        """Return a new transformation, transformed by another
+        transformation.
+
+        :Example:
+                >>> t = Transform(2, 0, 0, 3, 1, 6)
+                >>> t.transform((4, 3, 2, 1, 5, 6))
+                <Transform [8 9 4 3 11 24]>
+                >>>
+        """
+        xx1, xy1, yx1, yy1, dx1, dy1 = other
+        xx2, xy2, yx2, yy2, dx2, dy2 = self
+        return self.__class__(
+            xx1 * xx2 + xy1 * yx2,
+            xx1 * xy2 + xy1 * yy2,
+            yx1 * xx2 + yy1 * yx2,
+            yx1 * xy2 + yy1 * yy2,
+            xx2 * dx1 + yx2 * dy1 + dx2,
+            xy2 * dx1 + yy2 * dy1 + dy2,
+        )
+
+    def reverseTransform(self, other):
+        """Return a new transformation, which is the other transformation
+        transformed by self. self.reverseTransform(other) is equivalent to
+        other.transform(self).
+
+        :Example:
+                >>> t = Transform(2, 0, 0, 3, 1, 6)
+                >>> t.reverseTransform((4, 3, 2, 1, 5, 6))
+                <Transform [8 6 6 3 21 15]>
+                >>> Transform(4, 3, 2, 1, 5, 6).transform((2, 0, 0, 3, 1, 6))
+                <Transform [8 6 6 3 21 15]>
+                >>>
+        """
+        xx1, xy1, yx1, yy1, dx1, dy1 = self
+        xx2, xy2, yx2, yy2, dx2, dy2 = other
+        return self.__class__(
+            xx1 * xx2 + xy1 * yx2,
+            xx1 * xy2 + xy1 * yy2,
+            yx1 * xx2 + yy1 * yx2,
+            yx1 * xy2 + yy1 * yy2,
+            xx2 * dx1 + yx2 * dy1 + dx2,
+            xy2 * dx1 + yy2 * dy1 + dy2,
+        )
+
+    def inverse(self):
+        """Return the inverse transformation.
+
+        :Example:
+                >>> t = Identity.translate(2, 3).scale(4, 5)
+                >>> t.transformPoint((10, 20))
+                (42, 103)
+                >>> it = t.inverse()
+                >>> it.transformPoint((42, 103))
+                (10.0, 20.0)
+                >>>
+        """
+        if self == Identity:
+            return self
+        xx, xy, yx, yy, dx, dy = self
+        det = xx * yy - yx * xy
+        xx, xy, yx, yy = yy / det, -xy / det, -yx / det, xx / det
+        dx, dy = -xx * dx - yx * dy, -xy * dx - yy * dy
+        return self.__class__(xx, xy, yx, yy, dx, dy)
+
+    def toPS(self):
+        """Return a PostScript representation
+
+        :Example:
+
+                >>> t = Identity.scale(2, 3).translate(4, 5)
+                >>> t.toPS()
+                '[2 0 0 3 8 15]'
+                >>>
+        """
+        return "[%s %s %s %s %s %s]" % self
+
+    def toDecomposed(self) -> "DecomposedTransform":
+        """Decompose into a DecomposedTransform."""
+        return DecomposedTransform.fromTransform(self)
+
+    def __bool__(self):
+        """Returns True if transform is not identity, False otherwise.
+
+        :Example:
+
+                >>> bool(Identity)
+                False
+                >>> bool(Transform())
+                False
+                >>> bool(Scale(1.))
+                False
+                >>> bool(Scale(2))
+                True
+                >>> bool(Offset())
+                False
+                >>> bool(Offset(0))
+                False
+                >>> bool(Offset(2))
+                True
+        """
+        return self != Identity
+
+    def __repr__(self):
+        return "<%s [%g %g %g %g %g %g]>" % ((self.__class__.__name__,) + self)
+
+
+Identity = Transform()
+
+
+def Offset(x=0, y=0):
+    """Return the identity transformation offset by x, y.
+
+    :Example:
+            >>> Offset(2, 3)
+            <Transform [1 0 0 1 2 3]>
+            >>>
+    """
+    return Transform(1, 0, 0, 1, x, y)
+
+
+def Scale(x, y=None):
+    """Return the identity transformation scaled by x, y. The 'y' argument
+    may be None, which implies to use the x value for y as well.
+
+    :Example:
+            >>> Scale(2, 3)
+            <Transform [2 0 0 3 0 0]>
+            >>>
+    """
+    if y is None:
+        y = x
+    return Transform(x, 0, 0, y, 0, 0)
+
+
+@dataclass
+class DecomposedTransform:
+    """The DecomposedTransform class implements a transformation with separate
+    translate, rotation, scale, skew, and transformation-center components.
+    """
+
+    translateX: float = 0
+    translateY: float = 0
+    rotation: float = 0  # in degrees, counter-clockwise
+    scaleX: float = 1
+    scaleY: float = 1
+    skewX: float = 0  # in degrees, clockwise
+    skewY: float = 0  # in degrees, counter-clockwise
+    tCenterX: float = 0
+    tCenterY: float = 0
+
+    @classmethod
+    def fromTransform(self, transform):
+        # Adapted from an answer on
+        # https://math.stackexchange.com/questions/13150/extracting-rotation-scale-values-from-2d-transformation-matrix
+        a, b, c, d, x, y = transform
+
+        sx = math.copysign(1, a)
+        if sx < 0:
+            a *= sx
+            b *= sx
+
+        delta = a * d - b * c
+
+        rotation = 0
+        scaleX = scaleY = 0
+        skewX = skewY = 0
+
+        # Apply the QR-like decomposition.
+        if a != 0 or b != 0:
+            r = math.sqrt(a * a + b * b)
+            rotation = math.acos(a / r) if b >= 0 else -math.acos(a / r)
+            scaleX, scaleY = (r, delta / r)
+            skewX, skewY = (math.atan((a * c + b * d) / (r * r)), 0)
+        elif c != 0 or d != 0:
+            s = math.sqrt(c * c + d * d)
+            rotation = math.pi / 2 - (
+                math.acos(-c / s) if d >= 0 else -math.acos(c / s)
+            )
+            scaleX, scaleY = (delta / s, s)
+            skewX, skewY = (0, math.atan((a * c + b * d) / (s * s)))
+        else:
+            # a = b = c = d = 0
+            pass
+
+        return DecomposedTransform(
+            x,
+            y,
+            math.degrees(rotation),
+            scaleX * sx,
+            scaleY,
+            math.degrees(skewX) * sx,
+            math.degrees(skewY),
+            0,
+            0,
+        )
+
+    def toTransform(self):
+        """Return the Transform() equivalent of this transformation.
+
+        :Example:
+                >>> DecomposedTransform(scaleX=2, scaleY=2).toTransform()
+                <Transform [2 0 0 2 0 0]>
+                >>>
+        """
+        t = Transform()
+        t = t.translate(
+            self.translateX + self.tCenterX, self.translateY + self.tCenterY
+        )
+        t = t.rotate(math.radians(self.rotation))
+        t = t.scale(self.scaleX, self.scaleY)
+        t = t.skew(math.radians(self.skewX), math.radians(self.skewY))
+        t = t.translate(-self.tCenterX, -self.tCenterY)
+        return t
+
+
+if __name__ == "__main__":
+    import sys
+    import doctest
+
+    sys.exit(doctest.testmod().failed)