xref: /aosp_15_r20/external/fonttools/Lib/fontTools/misc/transform.py (revision e1fe3e4ad2793916b15cccdc4a7da52a7e1dd0e9)

"""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)