Adding upstream version 1.0.2.upstream/1.0.2upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1084 insertions, 0 deletions

diff --git a/share/extensions/inkex/transforms.py b/share/extensions/inkex/transforms.py
new file mode 100644
index 0000000..89c8563
--- /dev/null
+++ b/share/extensions/inkex/transforms.py
@@ -0,0 +1,1084 @@
+# coding=utf-8
+#
+# Copyright (C) 2006 Jean-Francois Barraud, barraud@math.univ-lille1.fr
+# Copyright (C) 2010 Alvin Penner, penner@vaxxine.com
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+# barraud@math.univ-lille1.fr
+#
+# This code defines several functions to make handling of transform
+# attribute easier.
+#
+"""
+Provide transformation parsing to extensions
+"""
+
+import re
+import sys
+from decimal import Decimal
+from math import cos, radians, sin, sqrt, tan, fabs, atan2, hypot, pi
+
+try:
+    from math import isfinite
+except ImportError:
+    isfinite = lambda n: isinstance(n, (int, float)) and n not in (float('+inf'), float('-inf'))
+
+from .tween import interpcoord
+from .utils import strargs, KeyDict, PY3
+
+try:
+    from typing import overload, cast, List, Any, Callable, Generator, Iterator, Tuple, Union, Optional, Sequence  # pylint: disable=unused-import
+
+    VectorLike = Union["ImmutableVector2d", Tuple[float, float]]  # pylint: disable=invalid-name
+    MatrixLike = Union[str, Tuple[Tuple[float,float,float], Tuple[float,float,float]], Tuple[float,float,float,float,float,float], "Transform"] 
+    BoundingIntervalArgs = Union['BoundingInterval', Tuple[float, float], float]  # pylint: disable=invalid-name
+except ImportError:
+    overload = lambda x: x
+    cast = lambda x, y: y
+
+# All the names that get added to the inkex API itself.
+__all__ = (
+    'BoundingBox',
+    'DirectedLineSegment',
+    'ImmutableVector2d',
+    'Transform',
+    'Vector2d',
+)
+
+if PY3:
+    unicode = str  # pylint: disable=redefined-builtin,invalid-name
+
+# Old settings, supported because users click 'ok' without looking.
+XAN = KeyDict({'l': 'left', 'r': 'right', 'm': 'center_x'})
+YAN = KeyDict({'t': 'top', 'b': 'bottom', 'm': 'center_y'})
+# Anchoring objects with given directions (see inx options)
+CUSTOM_DIRECTION = {270: 'tb', 90: 'bt', 0: 'lr', 360: 'lr', 180: 'rl'}
+DIRECTION = ['tb', 'bt', 'lr', 'rl', 'ro', 'ri']
+
+
+class ImmutableVector2d(object):
+    _x = 0.0
+    _y = 0.0
+
+    x = property(lambda self: self._x) # type: property
+    y = property(lambda self: self._y) # type: property 
+
+    @overload
+    def __init__(self):
+        # type: () -> None 
+        pass
+
+    @overload
+    def __init__(self, v):
+        # type: (Union[VectorLike, str]) -> None
+        pass
+
+    @overload
+    def __init__(self, x, y):
+        # type: (float, float) -> None
+        pass
+
+    def __init__(self, *args):
+        if len(args) == 0:
+            x, y = 0.0, 0.0
+        elif len(args) == 1:
+            x, y = self._parse(args[0])
+        elif len(args) == 2:
+            x, y = map(float, args)
+        else:
+            raise ValueError("too many arguments")
+        self._x, self._y = float(x), float(y)
+
+    @staticmethod
+    def _parse(point):
+        # type: (Union[VectorLike, str]) -> Tuple[float, float]
+        if isinstance(point, ImmutableVector2d):
+            x, y = point.x, point.y
+        elif isinstance(point, (tuple, list)) and len(point) == 2:
+            x, y = map(float, point)
+        elif isinstance(point, str) and point.count(',') == 1:
+            x, y = map(float, point.split(','))
+        else:
+            raise ValueError("Can't parse {}".format(repr(point)))
+        return x, y
+
+    def __add__(self, other):
+        # type: (VectorLike) -> Vector2d
+        other = Vector2d(other)
+        return Vector2d(self.x + other.x, self.y + other.y)
+
+    def __radd__(self, other):
+        # type: (VectorLike) -> Vector2d
+        other = Vector2d(other)
+        return Vector2d(self.x + other.x, self.y + other.y)
+
+    def __sub__(self, other):
+        # type: (VectorLike) -> Vector2d
+        other = Vector2d(other)
+        return Vector2d(self.x - other.x, self.y - other.y)
+
+    def __rsub__(self, other):
+        # type: (VectorLike) -> Vector2d
+        other = Vector2d(other)
+        return Vector2d(-self.x + other.x, -self.y + other.y)
+
+    def __neg__(self):
+        # type: () -> Vector2d
+        return Vector2d(-self.x, -self.y)
+
+    def __pos__(self):
+        # type: () -> Vector2d
+        return Vector2d(self.x, self.y)
+
+    def __floordiv__(self, factor): 
+        # type: (float) -> Vector2d
+        return Vector2d(self.x / float(factor), self.y / float(factor))
+
+    def __truediv__(self, factor):
+        # type: (float) -> Vector2d
+        return Vector2d(self.x / float(factor), self.y / float(factor))
+
+    def __div__(self, factor):
+        # type: (float) -> Vector2d
+        return Vector2d(self.x / float(factor), self.y / float(factor))
+
+    def __mul__(self, factor):
+        # type: (float) -> Vector2d
+        return Vector2d(self.x * factor, self.y * factor)
+
+    def __abs__(self):
+        # type: () -> float
+        return self.length
+
+    def __rmul__(self, factor):
+        # type: (float) -> VectorLike
+        return Vector2d(self.x * factor, self.y * factor)
+
+    def __repr__(self):
+        # type: () -> str
+        return "Vector2d({:.6g}, {:.6g})".format(self.x, self.y)
+
+    def __str__(self):
+        # type: () -> str
+        return "{:.6g}, {:.6g}".format(self.x, self.y)
+
+    def __iter__(self):
+        # type: () -> Generator[float, None, None]
+        yield self.x
+        yield self.y
+
+    def __len__(self):
+        # type: () -> int
+        return 2
+
+    def __getitem__(self, item):
+        # type: (int) -> float
+        return (self.x, self.y)[item]
+
+    def to_tuple(self):
+        # type : () -> Tuple[float, float]
+        return self.x, self.y
+
+    def dot(self, other):
+        # type: (VectorLike) -> float
+        other = Vector2d(other)
+        return self.x * other.x + self.y * other.y
+
+    def is_close(self, other, rtol=1e-5, atol=1e-8):
+        # type: (Union[VectorLike, str, Tuple[float,float]], float, float) -> float
+        other = Vector2d(other)
+        delta = (self - other).length
+        return delta < (atol + rtol * other.length)
+
+    @property
+    def length(self):
+        # type: () -> float
+        return sqrt(fabs(self.dot(self)))
+
+
+class Vector2d(ImmutableVector2d):
+    """
+    Represents an element of 2-dimensional Euclidean space
+    """
+
+    @ImmutableVector2d.x.setter
+    def x(self, value):
+        # type: (Union[float, int, str]) -> None
+        self._x = float(value)
+
+    @ImmutableVector2d.y.setter
+    def y(self, value):
+        # type: (Union[float, int, str]) -> None
+        self._y = float(value)
+
+    def __iadd__(self, other):
+        # type: (VectorLike) -> Vector2d
+        other = Vector2d(other)
+        self.x += other.x
+        self.y += other.y
+        return self
+
+    def __isub__(self, other):
+        # type: (VectorLike) -> Vector2d 
+        other = Vector2d(other)
+        self.x -= other.x
+        self.y -= other.y
+        return self
+
+    def __imul__(self, factor):
+        # type: (float) -> Vector2d
+        self.x *= factor
+        self.y *= factor
+        return self
+
+    def __idiv__(self, factor):
+        # type: (float) -> Vector2d
+        self.x /= factor
+        self.y /= factor
+        return self
+
+    def __itruediv__(self, factor):
+        # type: (float) -> Vector2d
+        self.x /= factor
+        self.y /= factor
+        return self
+
+    def __ifloordiv__(self, factor):
+        # type: (float) -> Vector2d
+        self.x /= factor
+        self.y /= factor
+        return self
+
+    @overload
+    def assign(self, x, y):
+        # type: (float, float) -> None
+        pass
+
+    @overload
+    def assign(self, other):
+        # type: (VectorLike, str) -> None
+        pass
+
+    def assign(self, *args):
+        self.x, self.y = Vector2d(*args)
+
+
+
+class Transform(object):
+    """A transformation object which will always reduce to a matrix and can
+    then be used in combination with other transformations for reducing
+    finding a point and printing svg ready output.
+
+    Use with svg transform attribute input:
+
+      tr = Transform("scale(45, 32)")
+
+    Use with triad matrix input (internal representation):
+
+      tr = Transform(((1.0, 0.0, 0.0), (0.0, 1.0, 0.0)))
+
+    Use with hexad matrix input (i.e. svg matrix(...)):
+
+      tr = Transform((1.0, 0.0, 0.0, 1.0, 0.0, 0.0))
+
+    Once you have a transformation you can operate tr * tr to compose,
+    any of the above inputs are also valid operators for composing.
+    """
+    TRM = re.compile(r'(translate|scale|rotate|skewX|skewY|matrix)\s*\(([^)]*)\)\s*,?')
+    absolute_tolerance = 1e-5 # type: float
+
+
+    def __init__(
+            self,
+            matrix=None, # type: Optional[MatrixLike]
+            callback=None, # type: Optional[Callable[[Transform], Transform]]
+            **extra):
+        # type: (...) -> None
+        self.callback = None
+        self.matrix = ((1.0, 0.0, 0.0), (0.0, 1.0, 0.0))
+        if matrix is not None:
+            self._set_matrix(matrix)
+
+        self.add_kwargs(**extra)
+        # Set callback last, so it doesn't kick off just setting up the internal value
+        self.callback = callback
+
+    def _set_matrix(self, matrix):
+        # type: (MatrixLike) -> None 
+        """Parse a given string as an svg transformation instruction."""
+        if isinstance(matrix, (str, unicode)):
+            for func, values in self.TRM.findall(matrix.strip()):
+                getattr(self, 'add_' + func.lower())(*strargs(values))
+        elif isinstance(matrix, Transform):
+            self.matrix = matrix.matrix
+        elif isinstance(matrix, (tuple, list)) and len(matrix) == 2:
+            row1 = matrix[0]
+            row2 = matrix[1]
+            if isinstance(row1, (tuple, list)) and isinstance(row2, (tuple, list)):
+                if len(row1) == 3 and len(row2) == 3:
+                    row1 = cast("Tuple[float, float, float]", tuple(map(float, row1)))
+                    row2 = cast("Tuple[float, float, float]", tuple(map(float, row2)))
+                    self.matrix = row1, row2
+                else:
+                    raise ValueError("Matrix '{}' is not a valid transformation matrix".format(matrix))
+            else:
+                raise ValueError("Matrix '{}' is not a valid transformation matrix".format(matrix))
+        elif isinstance(matrix, (list, tuple)) and len(matrix) == 6:
+            tmatrix = cast("Union[List[float], Tuple[float,float,float,float,float,float]]", matrix)
+            row1 = (float(tmatrix[0]), float(tmatrix[2]), float(tmatrix[4]))
+            row2 = (float(tmatrix[1]), float(tmatrix[3]), float(tmatrix[5]))
+            self.matrix = row1, row2
+        elif not isinstance(matrix, (list, tuple)):
+            raise ValueError("Invalid transform type: {}".format(type(matrix).__name__))
+        else:
+            raise ValueError("Matrix '{}' is not a valid transformation matrix".format(matrix))
+
+
+    # These provide quick access to the svg matrix:
+    #
+    # [ a, c, e ]
+    # [ b, d, f ]
+    #
+    a = property(lambda self: self.matrix[0][0])  # pylint: disable=invalid-name
+    b = property(lambda self: self.matrix[1][0])  # pylint: disable=invalid-name
+    c = property(lambda self: self.matrix[0][1])  # pylint: disable=invalid-name
+    d = property(lambda self: self.matrix[1][1])  # pylint: disable=invalid-name
+    e = property(lambda self: self.matrix[0][2])  # pylint: disable=invalid-name
+    f = property(lambda self: self.matrix[1][2])  # pylint: disable=invalid-name
+
+    def __bool__(self):
+        # type: () -> bool
+        return not self.__eq__(Transform())
+
+    __nonzero__ = __bool__
+
+    @overload
+    def add_matrix(self, a):
+        # type: (MatrixLike) -> None 
+        pass
+
+    @overload
+    def add_matrix(self, a, b, c, d, e, f):
+        # type: (float, float, float, float, float, float) -> None 
+        pass
+
+    @overload
+    def add_matrix(self, a, b):
+        # type: (Tuple[float, float, float], Tuple[float, float, float]) -> None 
+        pass
+
+    def add_matrix(self, *args):
+        """Add matrix in order they appear in the svg hexad"""
+        if len(args) == 1:
+            self.__imul__(Transform(args[0]))
+        elif len(args) == 2 or len(args) == 6:
+            self.__imul__(Transform(args))
+        else:
+            raise ValueError("Invalid number of arguments {}".format(args))
+
+    def add_kwargs(self, **kwargs):
+        """Add translations, scales, rotations etc using key word arguments"""
+        for key, value in reversed(list(kwargs.items())):
+            func = getattr(self, 'add_' + key)
+            if isinstance(value, tuple):
+                func(*value)
+            elif value is not None:
+                func(value)
+
+    @overload
+    def add_translate(self, dr):
+        # type: (VectorLike) -> None
+        pass
+
+    @overload
+    def add_translate(self, tr_x, tr_y=0.0):
+        # type: (float, Optional[float]) -> None
+        pass
+
+    def add_translate(self, *args):
+        if len(args) == 1 and isinstance(args[0], (int, float)):
+            tr_x, tr_y = args[0], 0.0
+        else:
+            tr_x, tr_y = Vector2d(*args)
+        self.__imul__(((1.0, 0.0, tr_x), (0.0, 1.0, tr_y)))
+
+    def add_scale(self, sc_x, sc_y=None):
+        """Add scale to this transformation"""
+        sc_y = sc_x if sc_y is None else sc_y
+        self.__imul__(((sc_x, 0.0, 0.0), (0.0, sc_y, 0.0)))
+
+    @overload
+    def add_rotate(self, deg, center):
+        # type: (float, VectorLike) -> None
+        pass
+
+    @overload
+    def add_rotate(self, deg, center_x, center_y):
+        # type: (float, float, float) -> None
+        pass
+
+    @overload
+    def add_rotate(self, deg):
+        # type: (float) -> None
+        pass
+
+    @overload
+    def add_rotate(self, deg, a):
+        # type: (float, Union[VectorLike, str]) -> None
+        pass
+
+    @overload
+    def add_rotate(self, deg, a, b):
+        # type: (float, float, float) -> None
+        pass
+
+    def add_rotate(self, deg, *args):
+        """Add rotation to this transformation"""
+        center_x, center_y = Vector2d(*args)
+        _cos, _sin = cos(radians(deg)), sin(radians(deg))
+        self.__imul__(((_cos, -_sin, center_x), (_sin, _cos, center_y)))
+        self.__imul__(((1.0, 0.0, -center_x), (0.0, 1.0, -center_y)))
+
+    def add_skewx(self, deg):
+        # type: (float) -> None
+        """Add skew x to this transformation"""
+        self.__imul__(((1.0, tan(radians(deg)), 0.0), (0.0, 1.0, 0.0)))
+
+    def add_skewy(self, deg):
+        # type: (float) -> None
+        """Add skew y to this transformation"""
+        self.__imul__(((1.0, 0.0, 0.0), (tan(radians(deg)), 1.0, 0.0)))
+
+    def to_hexad(self):
+        # type: () -> Iterator[float]
+        """Returns the transform as a hexad matrix (used in svg)"""
+        return (val for lst in zip(*self.matrix) for val in lst)
+
+    def is_translate(self, exactly=False):
+        # type: (bool) -> bool
+        """Returns True if this transformation is ONLY translate"""
+        tol = self.absolute_tolerance if not exactly else 0.0
+        return fabs(self.a - 1) <= tol and abs(self.d - 1) <= tol and fabs(self.b) <= tol and fabs(self.c) <= tol
+
+    def is_scale(self, exactly=False):
+        # type: (bool) -> bool
+        """Returns True if this transformation is ONLY scale"""
+        tol = self.absolute_tolerance if not exactly else 0.0
+        return (fabs(self.e) <= tol and fabs(self.f) <= tol and
+                fabs(self.b) <= tol and fabs(self.c) <= tol)
+
+    def is_rotate(self, exactly=False):
+        # type: (bool) -> bool
+        """Returns True if this transformation is ONLY rotate"""
+        tol = self.absolute_tolerance if not exactly else 0.0
+        return self._is_URT(exactly=exactly) and \
+               fabs(self.e) <= tol and fabs(self.f) <= tol and fabs(self.a ** 2 + self.b ** 2 - 1) <= tol
+
+    def rotation_degrees(self):
+        # type: () -> float
+        """Return the amount of rotation in this transform"""
+        if not self._is_URT(exactly=False):
+            raise ValueError("Rotation angle is undefined for non-uniformly scaled or skewed matrices")
+        return atan2(self.b, self.a) * 180 / pi
+
+    def __str__(self):
+        # type: () -> str
+        """Format the given matrix into a string representation for svg"""
+        hexad = tuple(self.to_hexad())
+        if self.is_translate():
+            if not self:
+                return ""
+            return "translate({:.6g}, {:.6g})".format(self.e, self.f)
+        elif self.is_scale():
+            return "scale({:.6g}, {:.6g})".format(self.a, self.d)
+        elif self.is_rotate():
+            return "rotate({:.6g})".format(self.rotation_degrees())
+        return "matrix({})".format(" ".join(format(var, '.6g') for var in hexad))
+
+    def __repr__(self):
+        # type: () -> str
+        """String representation of this object"""
+        return "{}((({}), ({})))".format(
+            type(self).__name__,
+            ', '.join(format(var, '.6g') for var in self.matrix[0]),
+            ', '.join(format(var, '.6g') for var in self.matrix[1]))
+
+    def __eq__(self, matrix):
+        # typing this requires writing a proof for mypy that matrix is really
+        # MatrixLike
+        """Test if this transformation is equal to the given matrix"""
+        if isinstance(matrix, (str, tuple, list, Transform)):
+            val = all(fabs(l - r) <= self.absolute_tolerance
+                      for l, r in zip(self.to_hexad(), Transform(matrix).to_hexad()))
+        else:
+            val = False
+        return val
+
+    def __mul__(self, matrix):
+        # type: (MatrixLike) -> Transform
+        """Combine this transform's internal matrix with the given matrix"""
+        # Conform the input to a known quantity (and convert if needed)
+        other = Transform(matrix)
+        # Return a transformation as the combined result
+        return Transform((
+            self.a * other.a + self.c * other.b,
+            self.b * other.a + self.d * other.b,
+            self.a * other.c + self.c * other.d,
+            self.b * other.c + self.d * other.d,
+            self.a * other.e + self.c * other.f + self.e,
+            self.b * other.e + self.d * other.f + self.f))
+
+    def __imul__(self, matrix):
+        # type: (MatrixLike) -> Transform
+        """In place multiplication of transform matrices"""
+        self.matrix = (self * matrix).matrix
+        if self.callback is not None:
+            self.callback(self)
+        return self
+
+    def __neg__(self):
+        # type: () -> Transform
+        """Returns an inverted transformation"""
+        det = (self.a * self.d) - (self.c * self.b)
+        # invert the rotation/scaling part
+        new_a = self.d / det
+        new_d = self.a / det
+        new_c = -self.c / det
+        new_b = -self.b / det
+        # invert the translational part
+        new_e = -(new_a * self.e + new_c * self.f)
+        new_f = -(new_b * self.e + new_d * self.f)
+        return Transform((new_a, new_b, new_c, new_d, new_e, new_f))
+
+    def apply_to_point(self, point):
+        # type: (VectorLike) -> Vector2d
+        """Transform a tuple (X, Y)"""
+        if isinstance(point, str):
+            raise ValueError("Will not transform string '{}'".format(point))
+        point = Vector2d(point)
+        return Vector2d(self.a * point.x + self.c * point.y + self.e,
+                        self.b * point.x + self.d * point.y + self.f)
+
+    def _is_URT(self, exactly=False):
+        # type: (bool) -> bool
+        """
+        Checks that transformation can be decomposed into product of
+        Uniform scale (U), Rotation around origin (R) and translation (T)
+
+        :return: decomposition as U*R*T is possible
+        """
+        tol = self.absolute_tolerance if not exactly else 0.0
+        return (fabs(self.a - self.d) <= tol) and (fabs(self.b + self.c) <= tol)
+
+    def interpolate(self, other, fraction):
+        # type: (Transform, float) -> Transform
+        """Interpolate with another Transform."""
+        return Transform((
+            interpcoord(self.a, other.a, fraction),
+            interpcoord(self.b, other.b, fraction),
+            interpcoord(self.c, other.c, fraction),
+            interpcoord(self.d, other.d, fraction),
+            interpcoord(self.e, other.e, fraction),
+            interpcoord(self.f, other.f, fraction)))
+
+
+class BoundingInterval(object):  # pylint: disable=too-few-public-methods
+    """A pair of numbers that represent the minimum and maximum values."""
+
+    @overload
+    def __init__(self, other=None):
+        # type: (Optional[BoundingInterval]) -> None
+        pass
+
+    @overload
+    def __init__(self, pair):
+        # type: (Tuple[float, float]) -> None
+        pass
+
+    @overload
+    def __init__(self, value):
+        # type: (float) -> None
+        pass
+
+    @overload
+    def __init__(self, x, y):
+        # type: (float, float) -> None
+        pass
+
+    def __init__(self, x=None, y=None):
+        if y is not None:
+            if isinstance(x, (int, float, Decimal)) and isinstance(y, (int, float, Decimal)):
+                self.minimum = x
+                self.maximum = y
+            else:
+                raise ValueError("Not a number for scaling: {} ({},{})"
+                                 .format(str((x, y)), type(x).__name__, type(y).__name__))
+
+        else:
+            value = x
+            if value is None:
+                # identity for addition, zero for intersection
+                self.minimum, self.maximum = float('+inf'), float('-inf')
+            elif isinstance(value, BoundingInterval):
+                self.minimum = value.minimum
+                self.maximum = value.maximum
+            elif isinstance(value, (tuple, list)) and len(value) == 2:
+                self.minimum, self.maximum = min(value), max(value)
+            elif isinstance(value, (int, float, Decimal)):
+                self.minimum = self.maximum = value
+            else:
+                raise ValueError("Not a number for scaling: {} ({})"
+                                 .format(str(value), type(value).__name__))
+
+    def __bool__(self):
+        # type: () -> bool
+        return (isfinite(self.minimum) and isfinite(self.maximum))
+
+    __nonzero__ = __bool__
+
+    def __neg__(self):
+        # type: () -> BoundingInterval
+        return BoundingInterval((-self.maximum, -self.minimum))
+
+    def __add__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        """Calculate the bounding interval that covers both given bounding intervals"""
+        new = BoundingInterval(self)
+        if other is not None:
+            new += other
+        return new
+
+    def __iadd__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        other = BoundingInterval(other)
+        self.minimum = min((self.minimum, other.minimum))
+        self.maximum = max((self.maximum, other.maximum))
+        return self
+
+    def __radd__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        if other is None:
+            return BoundingInterval(self)
+        return self + other
+
+    def __and__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        """Calculate the bounding interval where both given bounding intervals overlap"""
+        new = BoundingInterval(self)
+        if other is not None:
+            new &= other
+        return new
+
+    def __iand__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        other = BoundingInterval(other)
+        self.minimum = max((self.minimum, other.minimum))
+        self.maximum = min((self.maximum, other.maximum))
+        if self.minimum > self.maximum:
+            self.minimum, self.maximum = float('+inf'), float('-inf')
+        return self
+
+    def __rand__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        if other is None:
+            return BoundingInterval(self)
+        return self & other
+
+    def __mul__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        new = BoundingInterval(self)
+        if other is not None:
+            new *= other
+        return new
+
+    def __imul__(self, other):
+        # type: (BoundingInterval) -> BoundingInterval
+        self.minimum *= other
+        self.maximum *= other
+        return self
+
+    def __iter__(self):
+        # type: () -> Generator[BoundingInterval, None, None]
+        yield self.minimum
+        yield self.maximum
+
+    def __eq__(self, other):
+        # type (object) -> bool
+        return tuple(self) == tuple(BoundingInterval(other))
+
+    def __contains__(self, value):
+        # type: (float) -> bool
+        return self.minimum <= value <= self.maximum
+
+    def __repr__(self):
+        # type: () -> str
+        return "BoundingInterval({}, {})".format(self.minimum, self.maximum)
+
+    @property
+    def center(self):
+        # type: () -> float
+        """Pick the middle of the line"""
+        return self.minimum + ((self.maximum - self.minimum) / 2)
+
+    @property
+    def size(self):
+        # type: () -> float
+        """Return the size difference minimum and maximum"""
+        return self.maximum - self.minimum
+
+
+class BoundingBox(object):  # pylint: disable=too-few-public-methods
+    """
+    Some functions to compute a rough bbox of a given list of objects.
+
+    BoundingBox(other)
+    BoundingBox(x, y)
+    BoundingBox((x1, x2), (y1, y2))
+    """
+
+    width = property(lambda self: self.x.size)
+    height = property(lambda self: self.y.size)
+    top = property(lambda self: self.y.minimum)
+    left = property(lambda self: self.x.minimum)
+    bottom = property(lambda self: self.y.maximum)
+    right = property(lambda self: self.x.maximum)
+    center_x = property(lambda self: self.x.center)
+    center_y = property(lambda self: self.y.center)
+
+    @overload
+    def __init__(self, other=None):
+        # type: (Optional[BoundingBox]) -> None
+        pass
+
+    @overload
+    def __init__(self, x, y):
+        # type: (BoundingIntervalArgs, BoundingIntervalArgs) -> None
+        pass
+
+    def __init__(self, x=None, y=None):
+        if y is None:
+            if x is None:
+                # identity for addition, zero for intersection
+                pass
+            elif isinstance(x, BoundingBox):
+                x, y = x.x, x.y
+            else:
+                raise ValueError("Not a number for scaling: {} ({})"
+                                 .format(str(x), type(x).__name__))
+        self.x = BoundingInterval(x)
+        self.y = BoundingInterval(y)
+
+    def __bool__(self):
+        # type: () -> bool
+        return bool(self.x) and bool(self.y)
+
+    __nonzero__ = __bool__
+
+    def __neg__(self):
+        # type: () -> BoundingBox
+        return BoundingBox(-self.x, -self.y)
+
+    def __add__(self, other):
+        # type: (Optional[BoundingBox]) -> BoundingBox
+        """Calculate the bounding box that covers both given bounding boxes"""
+        new = BoundingBox(self)
+        new += BoundingBox(other)
+        return new
+
+    def __iadd__(self, other):
+        # type: (Optional[BoundingBox]) -> BoundingBox
+        other = BoundingBox(other)
+        self.x += other.x
+        self.y += other.y
+        return self
+
+    def __radd__(self, other):
+        # type: (Optional[BoundingBox]) -> BoundingBox
+        return self + other
+
+    def __and__(self, other):
+        # type: (Optional[BoundingBox]) -> BoundingBox
+        """Calculate the bounding box where both given bounding boxes overlap"""
+        new = BoundingBox(self)
+        new &= BoundingBox(other)
+        return new
+
+    def __iand__(self, other):
+        # type: (Optional[BoundingBox]) -> BoundingBox
+        new = BoundingBox(self)
+        other = BoundingBox(other)
+        self.x = self.x & other.x
+        self.y = self.y & other.y
+        if not self.x or not self.y:
+            self.x, self.y = BoundingInterval(), BoundingInterval()
+        return self
+
+    def __rand__(self, other):
+        # type: (Optional[BoundingBox]) -> BoundingBox
+        return self & other
+
+    def __mul__(self, factor):
+        # type: (float) -> BoundingBox
+        new = BoundingBox(self)
+        new *= factor
+        return new
+
+    def __imul__(self, factor):
+        # type: (float) -> BoundingBox
+        self.x *= factor
+        self.y *= factor
+        return self
+
+    def __eq__(self, other):
+        # type (object) -> bool
+        if isinstance(other, BoundingBox):
+            return tuple(self) == tuple(other)
+        return False
+
+    def __iter__(self):
+        # type: () -> Generator[BoundingBox, None, None]
+        yield self.x
+        yield self.y
+
+    @property
+    def minimum(self):
+        # type: () -> Vector2d
+        """Return the minimum x,y coords"""
+        return Vector2d(self.x.minimum, self.y.minimum)
+
+    @property
+    def maximum(self):
+        # type: () -> Vector2d
+        """Return the maximum x,y coords"""
+        return Vector2d(self.x.maximum, self.y.maximum)
+
+    def __repr__(self):
+        # type: () -> str
+        return "BoundingBox({},{})".format(tuple(self.x), tuple(self.y))
+
+    @property
+    def center(self):
+        # type: () -> Vector2d
+        """Returns the middle of the bounding box"""
+        return Vector2d(self.x.center, self.y.center)
+
+    def get_anchor(self, xanchor, yanchor, direction=0, selbox=None):
+        # type: (str, str, Union[int, str], Optional[BoundingBox]) -> float
+        """Calls get_distance with the given anchor options"""
+        return self.anchor_distance(
+                getattr(self, XAN[xanchor]),
+                getattr(self, YAN[yanchor]),
+                direction=direction,
+                selbox=selbox)
+
+    @staticmethod
+    def anchor_distance(x, y, direction=0, selbox=None):
+        # type: (float, float, Union[int, str], Optional[BoundingBox]) -> float 
+        """Using the x,y returns a single sortable value based on direction and angle
+
+        direction - int (custom angle), tb/bt (top/bottom), lr/rl (left/right), ri/ro (radial)
+        selbox - The bounding box of the whole selection for radial anchors
+        """
+        rot = 0.0
+        if isinstance(direction, int):  # Angle
+            if direction not in CUSTOM_DIRECTION:
+                return hypot(x, y) * (cos(radians(-direction) - atan2(y, x)))
+            direction = CUSTOM_DIRECTION[direction]
+
+        if direction in ('ro', 'ri'):
+            if selbox is None:
+                raise ValueError("Radial distance not available without selection bounding box")
+            rot = hypot(selbox.x.center - x, selbox.y.center - y)
+
+        return [y, -y, x, -x, rot, -rot][DIRECTION.index(direction)]
+
+
+class DirectedLineSegment(object):
+    """
+    A directed line segment
+
+    DirectedLineSegment(((x0, y0), (x1, y1)))
+    """
+
+    start = Vector2d()  # start point of segment
+    end = Vector2d()  # end point of segment
+
+    x0 = property(lambda self: self.start.x)  # pylint: disable=invalid-name
+    y0 = property(lambda self: self.start.y)  # pylint: disable=invalid-name
+    x1 = property(lambda self: self.end.x)
+    y1 = property(lambda self: self.end.y)
+    dx = property(lambda self: self.x1 - self.x0)  # pylint: disable=invalid-name
+    dy = property(lambda self: self.y1 - self.y0)  # pylint: disable=invalid-name
+
+    @overload
+    def __init__(self):
+        # type: () -> None
+        pass
+
+    @overload
+    def __init__(self, other):
+        # type: (DirectedLineSegment) -> None
+        pass
+
+    @overload
+    def __init__(self, start, end):
+        # type: (VectorLike, VectorLike) -> None
+        pass
+
+    def __init__(self, *args):
+        if not args:  # overload 0
+            start, end = Vector2d(), Vector2d()
+        elif len(args) == 1:  # overload 1
+            other, = args
+            start, end = other.start, other.end
+        elif len(args) == 2:  # overload 2
+            start, end = args
+        else:
+            raise ValueError("DirectedLineSegment() can't be constructed from {}".format(args))
+
+        self.start = Vector2d(start)
+        self.end = Vector2d(end)
+
+    def __eq__(self, other):
+        # type: (object) -> bool
+        if isinstance(other, (tuple, DirectedLineSegment)):
+            return tuple(self) == tuple(other)
+        return False
+
+    def __iter__(self):
+        # type: () -> Generator[DirectedLineSegment, None, None]
+        yield self.x0
+        yield self.x1
+        yield self.y0
+        yield self.y1
+
+    @property
+    def length(self):
+        # type: () -> float
+        """Get the length from the top left to the bottom right of the line"""
+        return sqrt((self.dx ** 2) + (self.dy ** 2))
+
+    @property
+    def angle(self):
+        # type: () -> float
+        """Get the angle of the line created by this segment"""
+        return pi * (atan2(self.dy, self.dx)) / 180
+
+    def distance_to_point(self, x, y):
+        # type: (float, float) -> Union[DirectedLineSegment, Optional[float]]
+        """Get the distance to the given point (x, y)"""
+        segment2 = DirectedLineSegment(self.start, (x, y))
+        dot2 = segment2.dot(self)
+        if dot2 <= 0:
+            return DirectedLineSegment((x, y), self.start).length
+        if self.dot(self) <= dot2:
+            return DirectedLineSegment((x, y), self.end).length
+        return self.perp_distance(x, y)
+
+    def perp_distance(self, x, y):
+        # type: (float, float) -> Optional[float]
+        """Perpendicular distance to the given point"""
+        if self.length == 0:
+            return None
+        return fabs((self.dx * (self.y0 - y)) - ((self.x0 - x) * self.dy)) / self.length
+
+    def dot(self, other):
+        # type: (DirectedLineSegment) -> float
+        """Get the dot product with the segment with another"""
+        return self.dx * other.dx + self.dy * other.dy
+
+    def point_at_ratio(self, ratio):
+        # type: (float) -> Tuple[float, float]
+        """Get the point at the given ratio along the line"""
+        return self.x0 + ratio * self.dx, self.y0 + ratio * self.dy
+
+    def point_at_length(self, length):
+        # type: (float) -> Tuple[float, float] 
+        """Get the point as the length along the line"""
+        return self.point_at_ratio(length / self.length)
+
+    def parallel(self, x, y):
+        # type: (float, float) -> DirectedLineSegment
+        """Create parallel Segment"""
+        return DirectedLineSegment((x + self.dx, y + self.dy), (x, y))
+
+    def intersect(self, other):
+        # type: (DirectedLineSegment) -> Optional[Vector2d]
+        """Get the intersection between two segments"""
+        other = DirectedLineSegment(other)
+        denom = (other.dy * self.dx) - (other.dx * self.dy)
+        num = (other.dx * (self.y0 - other.y0)) - (other.dy * (self.x0 - other.x0))
+        # num2 = (self.width * (self.top - other.top)) - (self.height * (self.left - other.left))
+
+        if denom != 0:
+            return Vector2d(
+                self.x0 + ((num / denom) * self.dx),
+                self.y0 + ((num / denom) * self.dy)
+            )
+        return None
+
+    def __repr__(self):
+        # type: () -> str
+        return "DirectedLineSegment(({0.start}), ({0.end}))".format(self)
+
+
+def cubic_extrema(py0, py1, py2, py3):
+    # type: (float, float, float, float) -> Tuple[float, float]
+    """Returns the extreme value, given a set of bezier coordinates"""
+
+    atol = 1e-9
+    cmin, cmax = min(py0, py3), max(py0, py3)
+    pd1 = py1 - py0
+    pd2 = py2 - py1
+    pd3 = py3 - py2
+
+    def _is_bigger(point):
+        if (point > 0) and (point < 1):
+            pyx = py0 * (1 - point) * (1 - point) * (1 - point) + \
+                  3 * py1 * point * (1 - point) * (1 - point) + \
+                  3 * py2 * point * point * (1 - point) + \
+                  py3 * point * point * point
+            return min(cmin, pyx), max(cmax, pyx)
+        return cmin, cmax
+
+    if fabs(pd1 - 2 * pd2 + pd3) > atol:
+        if pd2 * pd2 > pd1 * pd3:
+            pds = sqrt(pd2 * pd2 - pd1 * pd3)
+            cmin, cmax = _is_bigger((pd1 - pd2 + pds) / (pd1 - 2 * pd2 + pd3))
+            cmin, cmax = _is_bigger((pd1 - pd2 - pds) / (pd1 - 2 * pd2 + pd3))
+
+    elif fabs(pd2 - pd1) > atol:
+        cmin, cmax = _is_bigger(-pd1 / (2 * (pd2 - pd1)))
+
+    return cmin, cmax
+
+
+def quadratic_extrema(py0, py1, py2):
+    # type: (float, float, float) -> Tuple[float, float]
+    atol = 1e-9
+    cmin, cmax = min(py0, py2), max(py0, py2)
+
+    def _is_bigger(point):
+        if (point > 0) and (point < 1):
+            pyx = py0 * (1 - point) * (1 - point) + \
+                  2 * py1 * point * (1 - point) + \
+                  py2 * point * point
+            return min(cmin, pyx), max(cmax, pyx)
+        return cmin, cmax
+
+    if fabs(py0 + py2 - 2 * py1) > atol:
+        cmin, cmax = _is_bigger((py0 - py1) / (py0 + py2 - 2 * py1))
+
+    return cmin, cmax