bundle: update (2026-01-16)

extensions/botbox3000/deps/inkex/paths/__init__.py

@@ -0,0 +1,122 @@
+# coding=utf-8
+#
+# Copyright (C) 2018 Martin Owens <doctormo@gmail.com>
+# Copyright (C) 2023 Jonathan Neuhauser <jonathan.neuhauser@outlook.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.
+#
+"""Paths module.
+
+Most of the functions derivative, unit_tangent, curvature, point, split, length, ilength
+for the individual path commands are ported from
+https://github.com/mathandy/svgpathtools/ (MIT licensed)
+"""
+
+from typing import Union
+
+from ..transforms import ComplexLike
+from .interfaces import (
+    PathCommand,
+    AbsolutePathCommand,
+    RelativePathCommand,
+    LengthSettings,
+    ILengthSettings,
+)
+from .lines import Line, line, Move, move, ZoneClose, zoneClose, Horz, horz, Vert, vert
+from .curves import curve, Curve, smooth, Smooth
+from .quadratic import quadratic, Quadratic, tepidQuadratic, TepidQuadratic
+from .arc import Arc, arc, arc_to_path, matprod, rotmat, applymat, norm
+from .path import CubicSuperPath, Path, InvalidPath
+
+import numpy as np
+
+np.seterr(invalid="raise")
+
+
+# definitions that can't be inside the class due to circular dependencies
+def to_curve(self, prev: ComplexLike, prev_prev: ComplexLike = 0) -> Curve:
+    """Convert command to :py:class:`Curve`
+
+    Curve().to_curve() returns a copy
+    """
+    return Curve(*self.ccurve_points(0 + 0j, complex(prev), complex(prev_prev)))
+
+
+def to_line(self, prev: ComplexLike) -> Line:
+    """Converts this segment to a line (copies if already a line)"""
+    return Line(self.cend_point(0, complex(prev)))
+
+
+PathCommand.to_curve = to_curve  # type: ignore
+PathCommand.to_line = to_line  # type: ignore
+
+PathCommand._letter_to_class = {  # pylint: disable=protected-access
+    "M": Move,
+    "L": Line,
+    "V": Vert,
+    "H": Horz,
+    "A": Arc,
+    "C": Curve,
+    "S": Smooth,
+    "Z": ZoneClose,
+    "Q": Quadratic,
+    "T": TepidQuadratic,
+    "m": move,
+    "l": line,
+    "v": vert,
+    "h": horz,
+    "a": arc,
+    "c": curve,
+    "s": smooth,
+    "z": zoneClose,
+    "q": quadratic,
+    "t": tepidQuadratic,
+}
+
+
+# All the names that get added to the inkex API itself.
+__all__ = (
+    "Path",
+    "CubicSuperPath",
+    "PathCommand",
+    "AbsolutePathCommand",
+    "RelativePathCommand",
+    # Path commands:
+    "Line",
+    "line",
+    "Move",
+    "move",
+    "ZoneClose",
+    "zoneClose",
+    "Horz",
+    "horz",
+    "Vert",
+    "vert",
+    "Curve",
+    "curve",
+    "Smooth",
+    "smooth",
+    "Quadratic",
+    "quadratic",
+    "TepidQuadratic",
+    "tepidQuadratic",
+    "Arc",
+    "arc",
+    # errors
+    "InvalidPath",
+    # structs
+    "LengthSettings",
+    "ILengthSettings",
+)

extensions/botbox3000/deps/inkex/paths/arc.py

@@ -0,0 +1,670 @@
+# coding=utf-8
+#
+# Copyright (C) 2018 Martin Owens <doctormo@gmail.com>
+# Copyright (C) 2023 Jonathan Neuhauser <jonathan.neuhauser@outlook.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.
+#
+"""Arc path commands"""
+
+from __future__ import annotations
+from math import atan2, pi, sqrt, sin, cos, tan, acos, radians, degrees
+from cmath import exp
+from typing import overload, Tuple, List, Union, TYPE_CHECKING
+
+import numpy as np
+
+from ..transforms import Transform, Vector2d, ComplexLike
+
+from .interfaces import (
+    AbsolutePathCommand,
+    RelativePathCommand,
+    LengthSettings,
+    ILengthSettings,
+    BezierArcComputationMixin,
+)
+
+if TYPE_CHECKING:
+    from .curves import Curve
+
+
+class Arc(BezierArcComputationMixin, AbsolutePathCommand):
+    """Special Arc segment"""
+
+    letter = "A"
+
+    nargs = 7
+
+    radius: complex
+    """Radius of the Arc"""
+    x_axis_rotation: float
+
+    large_arc: bool
+    sweep: bool
+
+    endpoint: complex
+    """Endpoint (absolute) of the Arc"""
+
+    @property
+    def rx(self) -> float:
+        """x radius of the Arc"""
+        return self.radius.real
+
+    @property
+    def ry(self) -> float:
+        """y radius of the Arc"""
+        return self.radius.imag
+
+    @property
+    def x(self) -> float:
+        """x coordinate of the (absolute) endpoint of the Arc"""
+        return self.endpoint.real
+
+    @property
+    def y(self) -> float:
+        """x coordinate of the (relative) endpoint of the Arc"""
+        return self.endpoint.imag
+
+    @property
+    def args(self):
+        return (
+            self.rx,
+            self.ry,
+            self.x_axis_rotation,
+            self.large_arc,
+            self.sweep,
+            self.x,
+            self.y,
+        )
+
+    @property
+    def cargs(self):
+        """Set of arguments in complex form"""
+        return (
+            self.radius,
+            self.x_axis_rotation,
+            self.large_arc,
+            self.sweep,
+            self.endpoint,
+        )
+
+    @overload
+    def __init__(
+        self,
+        radius: ComplexLike,
+        x_axis_rotation: float,
+        large_arc: bool | int,
+        sweep: bool | int,
+        endpoint: ComplexLike,
+    ) -> None: ...
+
+    @overload
+    def __init__(
+        self,
+        rx: float,
+        ry: float,
+        x_axis_rotation: float,
+        large_arc: bool | int,
+        sweep: bool | int,
+        x: float,
+        y: float,
+    ) -> None: ...  # pylint: disable=too-many-arguments
+
+    def __init__(self, *args):
+        if len(args) == 5:
+            (
+                self.radius,
+                self.x_axis_rotation,
+                self.large_arc,
+                self.sweep,
+                self.endpoint,
+            ) = args
+            self.radius = complex(self.radius)
+            self.endpoint = complex(self.endpoint)
+        elif len(args) == 7:
+            self.radius = args[0] + args[1] * 1j
+            self.x_axis_rotation, self.large_arc, self.sweep = args[2:5]
+            self.endpoint = args[5] + args[6] * 1j
+
+    def parametrize(self, prev):
+        """Return the parametrisation of the arc:
+            (radius, phi, rot_matrix, center, theta1, deltatheta)
+        See http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
+
+        .. versionadded:: 1.4"""
+        # my notation roughly follows theirs
+        phi = radians(self.x_axis_rotation)
+        rot_matrix = exp(1j * phi)
+
+        radius = self.radius
+        rx = self.radius.real
+        ry = self.radius.imag
+        rx_sqd = rx * rx
+        ry_sqd = ry * ry
+
+        # Transform z-> z' = x' + 1j*y'
+        # = self.rot_matrix**(-1)*(z - (end+start)/2)
+        # coordinates.  This translates the ellipse so that the midpoint
+        # between self.end and self.start lies on the origin and rotates
+        # the ellipse so that the its axes align with the xy-coordinate axes.
+        # Note:  This sends self.end to -self.start
+        zp1 = (1 / rot_matrix) * (prev - self.cend_point(0j, prev)) / 2
+        x1p, y1p = zp1.real, zp1.imag
+        x1p_sqd = x1p * x1p
+        y1p_sqd = y1p * y1p
+
+        # Correct out of range radii
+        radius_check = (x1p_sqd / rx_sqd) + (y1p_sqd / ry_sqd)
+        if radius_check > 1:
+            rx *= sqrt(radius_check)
+            ry *= sqrt(radius_check)
+            radius = rx + 1j * ry
+            rx_sqd = rx * rx
+            ry_sqd = ry * ry
+
+        # Compute c'=(c_x', c_y'), the center of the ellipse in (x', y') coords
+        # Noting that, in our new coord system, (x_2', y_2') = (-x_1', -x_2')
+        # and our ellipse is cut out by of the plane by the algebraic equation
+        # (x'-c_x')**2 / r_x**2 + (y'-c_y')**2 / r_y**2 = 1,
+        # we can find c' by solving the system of two quadratics given by
+        # plugging our transformed endpoints (x_1', y_1') and (x_2', y_2')
+        tmp = rx_sqd * y1p_sqd + ry_sqd * x1p_sqd
+        radicand = (rx_sqd * ry_sqd - tmp) / tmp
+        radical = 0 if np.isclose(radicand, 0) else sqrt(radicand)
+
+        if self.large_arc == self.sweep:
+            cp = -radical * (rx * y1p / ry - 1j * ry * x1p / rx)
+        else:
+            cp = radical * (rx * y1p / ry - 1j * ry * x1p / rx)
+
+        # The center in (x,y) coordinates is easy to find knowing c'
+        center = exp(1j * phi) * cp + (prev + self.cend_point(0j, prev)) / 2
+
+        # Now we do a second transformation, from (x', y') to (u_x, u_y)
+        # coordinates, which is a translation moving the center of the
+        # ellipse to the origin and a dilation stretching the ellipse to be
+        # the unit circle
+        u1 = (x1p - cp.real) / rx + 1j * (y1p - cp.imag) / ry  # transformed start
+        u2 = (-x1p - cp.real) / rx + 1j * (-y1p - cp.imag) / ry  # transformed end
+
+        # clip in case of floating point error
+        u1 = np.clip(u1.real, -1, 1) + 1j * np.clip(u1.imag, -1, 1)
+        u2 = np.clip(u2.real, -1, 1) + 1j * np.clip(u2.imag, -1, 1)
+
+        # Now compute theta and delta (we'll define them as we go)
+        # delta is the angular distance of the arc (w.r.t the circle)
+        # theta is the angle between the positive x'-axis and the start point
+        # on the circle
+        if u1.imag > 0:
+            theta1 = degrees(acos(u1.real))
+        elif u1.imag < 0:
+            theta1 = -degrees(acos(u1.real))
+        else:
+            if u1.real > 0:  # start is on pos u_x axis
+                theta1 = 0
+            else:  # start is on neg u_x axis
+                # Note: This behavior disagrees with behavior documented in
+                # http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
+                # where theta is set to 0 in this case.
+                theta1 = 180
+
+        det_uv = u1.real * u2.imag - u1.imag * u2.real
+
+        acosand = u1.real * u2.real + u1.imag * u2.imag
+        acosand = np.clip(acosand.real, -1, 1) + np.clip(acosand.imag, -1, 1)
+
+        if det_uv > 0:
+            deltatheta = degrees(acos(acosand))
+        elif det_uv < 0:
+            deltatheta = -degrees(acos(acosand))
+        else:
+            if u1.real * u2.real + u1.imag * u2.imag > 0:
+                # u1 == u2
+                deltatheta = 0
+            else:
+                # u1 == -u2
+                # Note: This behavior disagrees with behavior documented in
+                # http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
+                # where deltatheta is set to 0 in this case.
+                deltatheta = 180
+
+        if not self.sweep and deltatheta >= 0:
+            deltatheta -= 360
+        elif self.large_arc and deltatheta <= 0:
+            deltatheta += 360
+
+        return radius, phi, rot_matrix, center, theta1, deltatheta
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        prev = last_two_points[-1]
+        for seg in self.to_curves(prev=prev):
+            seg.update_bounding_box(first, [None, prev], bbox)
+            prev = seg.cend_point(first, prev)
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (self.endpoint,)
+
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return NotImplemented
+
+    def to_curves(self, prev: ComplexLike, prev_prev: ComplexLike = 0j) -> List[Curve]:
+        """Convert this arc into bezier curves"""
+        # TODO Refactor out CubicSuperPath
+        from .path import CubicSuperPath
+
+        path = CubicSuperPath(
+            [arc_to_path(Vector2d.c2t(complex(prev)), self.args)]
+        ).to_path(curves_only=True)
+        # Ignore the first move command from to_path()
+        return list(path)[1:]
+
+    def transform(self, transform: Transform) -> Arc:
+        # pylint: disable=invalid-name, too-many-locals
+        newend = transform.capply_to_point(self.endpoint)
+
+        T: Transform = transform
+        if self.x_axis_rotation != 0:
+            T = T @ Transform(rotate=self.x_axis_rotation)
+        a, c, b, d, _, _ = list(T.to_hexad())
+        # T = | a b |
+        #     | c d |
+
+        detT = a * d - b * c
+        detT2 = detT**2
+
+        rx = float(self.rx)
+        ry = float(self.ry)
+
+        def get_degen():
+            return Arc(
+                self.radius,
+                self.x_axis_rotation,
+                self.large_arc,
+                self.sweep,
+                newend,
+            )
+
+        if rx == 0.0 or ry == 0.0 or detT2 == 0.0:
+            # degenerate arc
+            # transform only last point
+            return get_degen()
+        A = (d**2 / rx**2 + c**2 / ry**2) / detT2
+        B = -(d * b / rx**2 + c * a / ry**2) / detT2
+        D = (b**2 / rx**2 + a**2 / ry**2) / detT2
+
+        theta = atan2(-2 * B, D - A) / 2
+        theta_deg = theta * 180.0 / pi
+        DA = D - A
+        l2 = 4 * B**2 + DA**2
+
+        if l2 == 0:
+            delta = 0.0
+        else:
+            delta = 0.5 * (-(DA**2) - 4 * B**2) / sqrt(l2)
+
+        half = (A + D) / 2
+
+        try:
+            rx_ = 1.0 / sqrt(half + delta)
+            ry_ = 1.0 / sqrt(half - delta)
+
+            if detT > 0:
+                sweep = self.sweep
+            else:
+                sweep = not self.sweep > 0
+            return Arc(rx_ + 1j * ry_, theta_deg, self.large_arc, sweep, newend)
+        except ZeroDivisionError:
+            return get_degen()
+
+    def to_relative(self, prev: ComplexLike) -> RelativePathCommand:
+        return arc(
+            self.radius,
+            self.x_axis_rotation,
+            self.large_arc,
+            self.sweep,
+            self.endpoint - prev,
+        )
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.endpoint
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Arc:
+        return Arc(
+            self.radius, self.x_axis_rotation, self.large_arc, not self.sweep, prev
+        )
+
+    def _cpoint(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        # TODO surely this can be expressed in a shorter way using complex geometry?
+        radius, _, rot_matrix, center, theta1, deltatheta = self.parametrize(prev)
+        angle = (theta1 + t * deltatheta) * pi / 180
+        cosphi = rot_matrix.real
+        sinphi = rot_matrix.imag
+        rx = radius.real
+        ry = radius.imag
+
+        x = rx * cosphi * cos(angle) - ry * sinphi * sin(angle) + center.real
+        y = rx * sinphi * cos(angle) + ry * cosphi * sin(angle) + center.imag
+        return x + y * 1j
+
+    def _cderivative(
+        self, first: complex, prev: complex, prev_control: complex, t: float, n: int = 1
+    ) -> complex:
+        """returns the nth derivative of the segment at t."""
+        radius, phi, _, _, theta1, deltatheta = self.parametrize(prev)
+        angle = radians(theta1 + t * deltatheta)
+        rx = radius.real
+        ry = radius.imag
+        k = (deltatheta * pi / 180) ** n  # ((d/dt)angle)**n
+
+        if n % 4 == 0 and n > 0:
+            return (
+                rx * cos(phi) * cos(angle)
+                - ry * sin(phi) * sin(angle)
+                + 1j * (rx * sin(phi) * cos(angle) + ry * cos(phi) * sin(angle))
+            )
+        elif n % 4 == 1:
+            return k * (
+                -rx * cos(phi) * sin(angle)
+                - ry * sin(phi) * cos(angle)
+                + 1j * (-rx * sin(phi) * sin(angle) + ry * cos(phi) * cos(angle))
+            )
+        elif n % 4 == 2:
+            return k * (
+                -rx * cos(phi) * cos(angle)
+                + ry * sin(phi) * sin(angle)
+                + 1j * (-rx * sin(phi) * cos(angle) - ry * cos(phi) * sin(angle))
+            )
+        elif n % 4 == 3:
+            return k * (
+                rx * cos(phi) * sin(angle)
+                + ry * sin(phi) * cos(angle)
+                + 1j * (rx * sin(phi) * sin(angle) - ry * cos(phi) * cos(angle))
+            )
+        else:
+            raise ValueError("n should be a positive integer.")
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Arc, Arc]:
+        """returns two segments, whose union is this segment and which join
+        at self.point(t)."""
+        radius, _, _, _, _, deltatheta = self.parametrize(prev)
+
+        def crop(t0, t1):
+            return Arc(
+                radius,
+                self.x_axis_rotation,
+                not abs(deltatheta * (t1 - t0)) <= 180,
+                self.sweep,
+                self.cpoint(0j, prev, 0j, t1),
+            )
+
+        return crop(0, t), crop(t, 1)
+
+    def _ilength(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        length: float,
+        settings: ILengthSettings = ILengthSettings(),
+    ):
+        # ilength calls self.parametrize very often, so we cache the result
+        param = self.parametrize
+        params = param(prev)
+
+        def cached(prev):  # pylint: disable=unused-argument
+            return params
+
+        self.parametrize = cached  # type: ignore
+        try:
+            return super()._ilength(first, prev, prev_control, length, settings)
+        finally:
+            self.parametrize = param  # type: ignore
+
+
+class arc(RelativePathCommand, Arc):  # pylint: disable=invalid-name
+    """Relative Arc line segment"""
+
+    letter = "a"
+
+    nargs = 7
+
+    endpoint: complex
+    """Endpoint (relative) of the arc"""
+
+    @property
+    def rx(self) -> float:
+        """x radius of the arc"""
+        return self.radius.real
+
+    @property
+    def ry(self) -> float:
+        """y radius of the arc"""
+        return self.radius.imag
+
+    @property
+    def dx(self) -> float:
+        """x coordinate of the (relative) endpoint of the arc"""
+        return self.endpoint.real
+
+    @property
+    def dy(self) -> float:
+        """x coordinate of the (relative) endpoint of the arc"""
+        return self.endpoint.imag
+
+    @property
+    def args(self):
+        return (
+            self.rx,
+            self.ry,
+            self.x_axis_rotation,
+            self.large_arc,
+            self.sweep,
+            self.dx,
+            self.dy,
+        )
+
+    @overload
+    def __init__(
+        self,
+        radius: ComplexLike,
+        x_axis_rotation: float,
+        large_arc: bool,
+        sweep: bool,
+        endpoint: ComplexLike,
+    ) -> None: ...
+
+    @overload
+    def __init__(
+        self,
+        rx: float,
+        ry: float,
+        x_axis_rotation: float,
+        large_arc: bool,
+        sweep: bool,
+        dx: float,
+        dy: float,
+    ) -> None: ...  # pylint: disable=too-many-arguments
+
+    def __init__(self, *args):
+        if len(args) == 5:
+            (
+                self.radius,
+                self.x_axis_rotation,
+                self.large_arc,
+                self.sweep,
+                self.endpoint,
+            ) = args
+            self.radius = complex(self.radius)
+            self.endpoint = complex(self.endpoint)
+        elif len(args) == 7:
+            self.radius = args[0] + args[1] * 1j
+            self.x_axis_rotation, self.large_arc, self.sweep = args[2:5]
+            self.endpoint = args[5] + args[6] * 1j
+
+    def to_absolute(self, prev: ComplexLike) -> Arc:
+        return Arc(
+            self.radius,
+            self.x_axis_rotation,
+            self.large_arc,
+            self.sweep,
+            self.endpoint + prev,
+        )
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.endpoint + prev
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (self.endpoint + prev,)
+
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return NotImplemented
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> arc:
+        return arc(
+            self.radius,
+            self.x_axis_rotation,
+            self.large_arc,
+            not self.sweep,
+            -self.endpoint,
+        )
+
+    def to_curves(self, prev: ComplexLike, prev_prev: ComplexLike = 0j) -> List[Curve]:
+        return self.to_absolute(prev).to_curves(prev, prev_prev)
+
+
+def arc_to_path(point, params):
+    """Approximates an arc with cubic bezier segments.
+
+    Arguments:
+        point:  Starting point (absolute coords)
+        params: Arcs parameters as per
+              https://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands
+
+    Returns a list of triplets of points :
+    [control_point_before, node, control_point_after]
+    (first and last returned triplets are [p1, p1, *] and [*, p2, p2])
+    """
+
+    # pylint: disable=invalid-name, too-many-locals
+    A = point[:]
+    rx, ry, teta, longflag, sweepflag, x2, y2 = params[:]
+    teta = teta * pi / 180.0
+    B = [x2, y2]
+    # Degenerate ellipse
+    if rx == 0 or ry == 0 or A == B:
+        return [[A[:], A[:], A[:]], [B[:], B[:], B[:]]]
+
+    # turn coordinates so that the ellipse morph into a *unit circle* (not 0-centered)
+    mat = matprod((rotmat(teta), [[1.0 / rx, 0.0], [0.0, 1.0 / ry]], rotmat(-teta)))
+    applymat(mat, A)
+    applymat(mat, B)
+
+    k = [-(B[1] - A[1]), B[0] - A[0]]
+    d = k[0] * k[0] + k[1] * k[1]
+    k[0] /= sqrt(d)
+    k[1] /= sqrt(d)
+    d = sqrt(max(0, 1 - d / 4.0))
+    # k is the unit normal to AB vector, pointing to center O
+    # d is distance from center to AB segment (distance from O to the midpoint of AB)
+    # for the last line, remember this is a unit circle, and kd vector is ortogonal to
+    # AB (Pythagorean thm)
+
+    if longflag == sweepflag:
+        # top-right ellipse in SVG example
+        # https://www.w3.org/TR/SVG/images/paths/arcs02.svg
+        d *= -1
+
+    O = [(B[0] + A[0]) / 2.0 + d * k[0], (B[1] + A[1]) / 2.0 + d * k[1]]
+    OA = [A[0] - O[0], A[1] - O[1]]
+    OB = [B[0] - O[0], B[1] - O[1]]
+    start = acos(OA[0] / norm(OA))
+    if OA[1] < 0:
+        start *= -1
+    end = acos(OB[0] / norm(OB))
+    if OB[1] < 0:
+        end *= -1
+    # start and end are the angles from center of the circle to A and to B respectively
+
+    if sweepflag and start > end:
+        end += 2 * pi
+    if (not sweepflag) and start < end:
+        end -= 2 * pi
+
+    NbSectors = int(abs(start - end) * 2 / pi) + 1
+    dTeta = (end - start) / NbSectors
+    v = 4 * tan(dTeta / 4.0) / 3.0
+    # I would use v = tan(dTeta/2)*4*(sqrt(2)-1)/3 ?
+    p = []
+    for i in range(0, NbSectors + 1, 1):
+        angle = start + i * dTeta
+        v1 = [
+            O[0] + cos(angle) - (-v) * sin(angle),
+            O[1] + sin(angle) + (-v) * cos(angle),
+        ]
+        pt = [O[0] + cos(angle), O[1] + sin(angle)]
+        v2 = [O[0] + cos(angle) - v * sin(angle), O[1] + sin(angle) + v * cos(angle)]
+        p.append([v1, pt, v2])
+    p[0][0] = p[0][1][:]
+    p[-1][2] = p[-1][1][:]
+
+    # go back to the original coordinate system
+    mat = matprod((rotmat(teta), [[rx, 0], [0, ry]], rotmat(-teta)))
+    for pts in p:
+        applymat(mat, pts[0])
+        applymat(mat, pts[1])
+        applymat(mat, pts[2])
+    return p
+
+
+def matprod(mlist):
+    """Get the product of the mat"""
+    prod = mlist[0]
+    for mat in mlist[1:]:
+        a00 = prod[0][0] * mat[0][0] + prod[0][1] * mat[1][0]
+        a01 = prod[0][0] * mat[0][1] + prod[0][1] * mat[1][1]
+        a10 = prod[1][0] * mat[0][0] + prod[1][1] * mat[1][0]
+        a11 = prod[1][0] * mat[0][1] + prod[1][1] * mat[1][1]
+        prod = [[a00, a01], [a10, a11]]
+    return prod
+
+
+def rotmat(teta):
+    """Rotate the mat"""
+    return [[cos(teta), -sin(teta)], [sin(teta), cos(teta)]]
+
+
+def applymat(mat, point):
+    """Apply the given mat"""
+    x = mat[0][0] * point[0] + mat[0][1] * point[1]
+    y = mat[1][0] * point[0] + mat[1][1] * point[1]
+    point[0] = x
+    point[1] = y
+
+
+def norm(point):
+    """Normalise"""
+    return sqrt(point[0] * point[0] + point[1] * point[1])

extensions/botbox3000/deps/inkex/paths/curves.py

@@ -0,0 +1,499 @@
+# coding=utf-8
+#
+# Copyright (C) 2018 Martin Owens <doctormo@gmail.com>
+# Copyright (C) 2023 Jonathan Neuhauser <jonathan.neuhauser@outlook.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.
+#
+"""Curve and Smooth Path Commands"""
+
+from __future__ import annotations
+
+from typing import overload, Tuple, Callable, Union, cast
+
+import numpy as np
+
+from ..transforms import cubic_extrema, Transform, Vector2d, ComplexLike
+
+from .interfaces import (
+    AbsolutePathCommand,
+    RelativePathCommand,
+    BezierArcComputationMixin,
+    BezierComputationMixin,
+)
+
+
+class CurveMixin(BezierComputationMixin, BezierArcComputationMixin):
+    """Common functionality for curves"""
+
+    ccontrol_points: Callable[[complex, complex, complex], Tuple[complex, ...]]
+
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        """Common implementation of ccurve_points for Curves"""
+        return self.ccontrol_points(first, prev, prev_prev)
+
+    def _cderivative(
+        self, first: complex, prev: complex, prev_control: complex, t: float, n: int = 1
+    ) -> complex:
+        """Returns the nth derivative of the segment at t.
+
+        .. hint:: Bezier curves can have points where their derivative vanishes.
+        If you are interested in the tangent direction, use the :func:`unit_tangent`
+        method instead."""
+
+        points = self.ccontrol_points(first, prev, prev_control)
+
+        if n == 1:
+            return (
+                3 * (points[0] - prev) * ((1 - t) ** 2)
+                + 6 * (points[1] - points[0]) * (1 - t) * t
+                + 3 * (points[2] - points[1]) * t**2
+            )
+        elif n == 2:
+            return 6 * (
+                (1 - t) * (points[1] - 2 * points[0] + prev)
+                + t * (points[2] - 2 * points[1] + points[0])
+            )
+        elif n == 3:
+            return 6 * (points[2] - 3 * (points[1] - points[0]) - prev)
+        elif n > 3:
+            return complex(0, 0)
+        else:
+            raise ValueError("n should be a positive integer.")
+
+    def poly(self, prev, prev_control, return_coeffs=False):
+        """Returns a the cubic as a complex Polynomial object.
+
+        .. versionadded:: 1.4"""
+        points = self.ccontrol_points(0j, prev, prev_control)
+        coeffs = (
+            -prev + 3 * (points[0] - points[1]) + points[2],
+            3 * (prev - 2 * points[0] + points[1]),
+            3 * (prev + points[0]),
+            prev,
+        )
+        if return_coeffs:
+            return coeffs
+        return np.poly1d(coeffs)
+
+    def _cunit_tangent(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        return self.bezier_unit_tangent(prev, prev_control, t)
+
+    def _curvature(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ):
+        return self.segment_curvature(prev, prev_control, t)
+
+    def _abssplit(
+        self, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Curve, Curve]:
+        """Split this curve and return two Curves using DeCasteljau's algorithm"""
+        p1, p2, p3 = self.ccontrol_points(0j, prev, prev_control)
+        p1_1 = (1 - t) * prev + t * p1
+        p1_2 = (1 - t) * p1 + t * p2
+        p1_3 = (1 - t) * p2 + t * p3
+        p2_1 = (1 - t) * p1_1 + t * p1_2
+        p2_2 = (1 - t) * p1_2 + t * p1_3
+        p3_1 = (1 - t) * p2_1 + t * p2_2
+
+        return Curve(p1_1, p2_1, p3_1), Curve(p2_2, p1_3, p3)
+
+    def _relsplit(self, prev: complex, prev_control: complex, t: float):
+        """Split this curve and return two curves"""
+        c1abs, c2abs = self._abssplit(prev, prev_control, t)
+        return c1abs.to_relative(prev), c2abs.to_relative(c1abs.arg3)
+
+    def _cpoint(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        control1, control2, end = self.ccontrol_points(first, prev, prev_control)
+        return (
+            (1 - t) ** 3 * prev
+            + 3 * t * (1 - t) ** 2 * control1
+            + 3 * t**2 * (1 - t) * control2
+            + t**3 * end
+        )
+
+
+class Curve(CurveMixin, AbsolutePathCommand):
+    """Absolute Curved Line segment"""
+
+    letter = "C"
+    nargs = 6
+
+    arg1: complex
+    """The (absolute) first control point"""
+
+    arg2: complex
+    """The (absolute) second control point"""
+
+    arg3: complex
+    """The (absolute) end point"""
+
+    @property
+    def x2(self) -> float:
+        """x coordinate of the (absolute) first control point"""
+        return self.arg1.real
+
+    @property
+    def y2(self) -> float:
+        """y coordinate of the (absolute) first control point"""
+        return self.arg1.imag
+
+    @property
+    def x3(self) -> float:
+        """x coordinate of the (absolute) second control point"""
+        return self.arg2.real
+
+    @property
+    def y3(self) -> float:
+        """y coordinate of the (absolute) second control point"""
+        return self.arg2.imag
+
+    @property
+    def x4(self) -> float:
+        """x coordinate of the (absolute) end point"""
+        return self.arg3.real
+
+    @property
+    def y4(self) -> float:
+        """y coordinate of the (absolute) end point"""
+        return self.arg3.imag
+
+    @property
+    def args(self):
+        return (
+            self.arg1.real,
+            self.arg1.imag,
+            self.arg2.real,
+            self.arg2.imag,
+            self.arg3.real,
+            self.arg3.imag,
+        )
+
+    @overload
+    def __init__(self, x2: ComplexLike, x3: ComplexLike, x4: ComplexLike): ...
+
+    @overload
+    def __init__(
+        self, x2: float, y2: float, x3: float, y3: float, x4: float, y4: float
+    ): ...  # pylint: disable=too-many-arguments
+
+    def __init__(self, x2, y2, x3, y3=None, x4=None, y4=None):  # pylint: disable=too-many-arguments
+        if y3 is not None:
+            self.arg1 = x2 + y2 * 1j
+            self.arg2 = x3 + y3 * 1j
+            self.arg3 = x4 + y4 * 1j
+        else:
+            self.arg1, self.arg2, self.arg3 = complex(x2), complex(y2), complex(x3)
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        x1, x2, x3, x4 = last_two_points[-1].real, self.x2, self.x3, self.x4
+        y1, y2, y3, y4 = last_two_points[-1].imag, self.y2, self.y3, self.y4
+
+        if not (x1 in bbox.x and x2 in bbox.x and x3 in bbox.x and x4 in bbox.x):
+            bbox.x += cubic_extrema(x1, x2, x3, x4)
+
+        if not (y1 in bbox.y and y2 in bbox.y and y3 in bbox.y and y4 in bbox.y):
+            bbox.y += cubic_extrema(y1, y2, y3, y4)
+
+    def transform(self, transform: Transform) -> Curve:
+        return Curve(
+            transform.capply_to_point(self.arg1),
+            transform.capply_to_point(self.arg2),
+            transform.capply_to_point(self.arg3),
+        )
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        # pylint: disable=unused-argument
+        return (self.arg1, self.arg2, self.arg3)
+
+    def to_relative(self, prev: ComplexLike) -> curve:
+        return curve(self.arg1 - prev, self.arg2 - prev, self.arg3 - prev)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg3
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Curve:
+        return Curve(self.arg2, self.arg1, prev)
+
+    def to_bez(self):
+        """Convert to [[c1x, c1y], [c2x, c2y], [end_x, end_y]]"""
+        return [Vector2d.c2t(i) for i in self.ccontrol_points(0j, 0j, 0j)]
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Curve, Curve]:
+        return self._abssplit(prev, prev_control, t)
+
+
+class curve(CurveMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative curved line segment"""
+
+    letter = "c"
+    nargs = 6
+
+    arg1: complex
+    """The (relative) first control point"""
+
+    arg2: complex
+    """The (relative) second control point"""
+
+    arg3: complex
+    """The (relative) end point"""
+
+    @property
+    def dx2(self) -> float:
+        """x coordinate of the (relative) first control point"""
+        return self.arg1.real
+
+    @property
+    def dy2(self) -> float:
+        """y coordinate of the (relative) first control point"""
+        return self.arg1.imag
+
+    @property
+    def dx3(self) -> float:
+        """x coordinate of the (relative) second control point"""
+        return self.arg2.real
+
+    @property
+    def dy3(self) -> float:
+        """y coordinate of the (relative) second control point"""
+        return self.arg2.imag
+
+    @property
+    def dx4(self) -> float:
+        """x coordinate of the (relative) end point"""
+        return self.arg3.real
+
+    @property
+    def dy4(self) -> float:
+        """y coordinate of the (relative) end point"""
+        return self.arg3.imag
+
+    @overload
+    def __init__(self, dx2: ComplexLike, dx3: ComplexLike, dx4: ComplexLike): ...
+
+    @overload
+    def __init__(
+        self, dx2: float, dy2: float, dx3: float, dy3: float, dx4: float, dy4: float
+    ): ...  # pylint: disable=too-many-arguments
+
+    def __init__(self, dx2, dy2, dx3, dy3=None, dx4=None, dy4=None):  # pylint: disable=too-many-arguments
+        if dy3 is not None:
+            self.arg1 = dx2 + dy2 * 1j
+            self.arg2 = dx3 + dy3 * 1j
+            self.arg3 = dx4 + dy4 * 1j
+        else:
+            self.arg1, self.arg2, self.arg3 = complex(dx2), complex(dy2), complex(dx3)
+
+    @property
+    def args(self):
+        return self.dx2, self.dy2, self.dx3, self.dy3, self.dx4, self.dy4
+
+    def to_absolute(self, prev: ComplexLike) -> Curve:
+        return Curve(*self.ccurve_points(0j, complex(prev), 0j))
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg3 + prev
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> curve:
+        return curve(-self.arg3 + self.arg2, -self.arg3 + self.arg1, -self.arg3)
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        # pylint: disable=unused-argument
+        return (
+            self.arg1 + prev,
+            self.arg2 + prev,
+            self.arg3 + prev,
+        )
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[curve, curve]:
+        return self._relsplit(prev, prev_control, t)
+
+
+class Smooth(CurveMixin, AbsolutePathCommand):
+    """Absolute Smoothed Curved Line segment"""
+
+    letter = "S"
+    nargs = 4
+
+    arg1: complex
+    """The (absolute) control point"""
+
+    arg2: complex
+    """The (absolute) end point"""
+
+    @property
+    def x3(self) -> float:
+        """x coordinate of the (absolute) control point"""
+        return self.arg1.real
+
+    @property
+    def y3(self) -> float:
+        """y coordinate of the (absolute) control point"""
+        return self.arg1.imag
+
+    @property
+    def x4(self) -> float:
+        """x coordinate of the (absolute) end point"""
+        return self.arg2.real
+
+    @property
+    def y4(self) -> float:
+        """y coordinate of the (absolute) end point"""
+        return self.arg2.imag
+
+    @property
+    def args(self):
+        return self.x3, self.y3, self.x4, self.y4
+
+    @overload
+    def __init__(self, x3: ComplexLike, x4: ComplexLike): ...
+
+    @overload
+    def __init__(self, x3: float, y3: float, x4: float, y4: float): ...
+
+    def __init__(self, x3, y3, x4=None, y4=None):
+        if x4 is not None:
+            self.arg1 = x3 + y3 * 1j
+            self.arg2 = x4 + y4 * 1j
+        else:
+            self.arg1, self.arg2 = complex(x3), complex(y3)
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        # pylint: disable=no-member
+        self.to_curve(last_two_points[-1], last_two_points[-2]).update_bounding_box(
+            first, last_two_points, bbox
+        )
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        # pylint: disable=unused-argument
+        return (2 * prev - prev_prev, self.arg1, self.arg2)
+
+    def to_non_shorthand(self, prev: ComplexLike, prev_control: ComplexLike) -> Curve:
+        return self.to_curve(prev, prev_control)
+
+    def to_relative(self, prev: ComplexLike) -> smooth:
+        return smooth(self.arg1 - prev, self.arg2 - prev)
+
+    def transform(self, transform: Transform) -> Smooth:
+        return Smooth(
+            transform.capply_to_point(self.arg1), transform.capply_to_point(self.arg2)
+        )
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg2
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Smooth:
+        return Smooth(self.arg1, prev)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Curve, Curve]:
+        # We can't preserve the smooth type for a split because de Casteljau's
+        # algorithm changes the handles (obviously).
+        # Only in special cases such as splitting to subsequent smooth segments at
+        # t=1/2 such a preservation would be possible
+        crv = cast(Curve, self.to_non_shorthand(prev, prev_control))
+        return crv._split(  # pylint: disable=protected-access, no-member
+            first, prev, prev_control, t
+        )
+
+
+class smooth(CurveMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative smoothed curved line segment"""
+
+    letter = "s"
+    nargs = 4
+
+    arg1: complex
+    """The (absolute) control point"""
+
+    arg2: complex
+    """The (absolute) end point"""
+
+    @property
+    def dx3(self) -> float:
+        """x coordinate of the (relative) control point"""
+        return self.arg1.real
+
+    @property
+    def dy3(self) -> float:
+        """y coordinate of the (relative) control point"""
+        return self.arg1.imag
+
+    @property
+    def dx4(self) -> float:
+        """x coordinate of the (relative) end point"""
+        return self.arg2.real
+
+    @property
+    def dy4(self) -> float:
+        """y coordinate of the (relative) end point"""
+        return self.arg2.imag
+
+    @property
+    def args(self):
+        return self.dx3, self.dy3, self.dx4, self.dy4
+
+    @overload
+    def __init__(self, dx3: ComplexLike, dx4: ComplexLike): ...
+
+    @overload
+    def __init__(self, dx3: float, dy3: float, dx4: float, dy4: float): ...
+
+    def __init__(self, dx3, dy3, dx4=None, dy4=None):
+        if dx4 is not None:
+            self.arg1 = dx3 + dy3 * 1j
+            self.arg2 = dx4 + dy4 * 1j
+        else:
+            self.arg1, self.arg2 = complex(dx3), complex(dy3)
+
+    def to_absolute(self, prev: ComplexLike) -> Smooth:
+        return Smooth(self.arg1 + prev, self.arg2 + prev)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg2 + prev
+
+    def to_non_shorthand(self, prev: ComplexLike, prev_control: ComplexLike) -> Curve:
+        return self.to_absolute(prev).to_non_shorthand(prev, prev_control)
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike):
+        return smooth(-self.arg2 + self.arg1, -self.arg2)
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        # pylint: disable=unused-argument
+        return (2 * prev - prev_prev, self.arg1 + prev, self.arg2 + prev)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[curve, curve]:
+        return self._relsplit(prev, prev_control, t)

extensions/botbox3000/deps/inkex/paths/interfaces.py

@@ -0,0 +1,731 @@
+# coding=utf-8
+#
+# Copyright (C) 2018 Martin Owens <doctormo@gmail.com>
+# Copyright (C) 2023 Jonathan Neuhauser <jonathan.neuhauser@outlook.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.
+#
+"""Interfaces for path commands"""
+
+from __future__ import annotations
+
+import abc
+import math
+from typing import (
+    List,
+    Any,
+    Tuple,
+    Dict,
+    Type,
+    Generator,
+    Union,
+    TYPE_CHECKING,
+    Optional,
+    Callable,
+)
+from dataclasses import dataclass
+
+import numpy as np
+from ..utils import classproperty, rational_limit
+from ..transforms import Vector2d, BoundingBox, Transform, ComplexLike
+
+if TYPE_CHECKING:
+    from .curves import Curve
+    from .lines import Line
+
+
+@dataclass
+class LengthSettings:
+    """Settings for :func:`PathCommand.length`
+
+    .. versionadded::  1.4"""
+
+    min_depth: int = 5
+    error: float = 1e-5
+
+
+@dataclass
+class ILengthSettings:
+    """Settings for :func:`PathCommand.ilength`
+
+    .. versionadded:: 1.4"""
+
+    min_depth: int = 5
+
+    error: float = 1e-5
+    """
+    Error tolerance for the computations of the test segment that is performed 
+    for each iteration.
+
+    The defaults from svgpathtools are ILENGTH_ERROR=ILENGTH_LENGTH_TOL=1e-12.
+    This is rather slow, particularly _length (which then subdivides the path into
+    2^12 or more segments and adds up the length). For visual editing, this is rather
+    irrelevant (and a lot more accurate than the previous methods)."""
+
+    length_tol: float = 1e-5
+    """Total (absolute) tolerance of the resulting s value."""
+
+    maxits: int = 10000
+
+
+class PathCommand(abc.ABC):
+    """
+    Base class of all path commands
+    """
+
+    letter = ""
+    # Number of arguments that follow this path commands letter
+    nargs = -1
+
+    @classproperty  # From python 3.9 on, just combine @classmethod and @property
+    def name(cls):  # pylint: disable=no-self-argument
+        """The full name of the segment (i.e. Line, Arc, etc)"""
+        return cls.__name__  # pylint: disable=no-member
+
+    @classproperty
+    def next_command(self):
+        """The implicit next command. This is for automatic chains where the next
+        command isn't given, just a bunch on numbers which we automatically parse."""
+        return self
+
+    @property
+    def is_relative(self) -> bool:
+        """Whether the command is defined in relative coordinates, i.e. relative to
+        the previous endpoint (lower case path command letter)"""
+        raise NotImplementedError
+
+    @property
+    def is_absolute(self) -> bool:
+        """Whether the command is defined in absolute coordinates (upper case path
+        command letter)"""
+        raise NotImplementedError
+
+    def to_relative(self, prev: ComplexLike) -> RelativePathCommand:
+        """Return absolute counterpart for absolute commands or copy for relative"""
+        raise NotImplementedError
+
+    def to_absolute(self, prev: ComplexLike) -> AbsolutePathCommand:
+        """Return relative counterpart for relative commands or copy for absolute"""
+        raise NotImplementedError
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> PathCommand:
+        """Reverse path command
+
+        .. versionadded:: 1.1"""
+        raise NotImplementedError
+
+    def to_non_shorthand(
+        self,
+        prev: ComplexLike,
+        prev_control: ComplexLike,  # pylint: disable=unused-argument
+    ) -> AbsolutePathCommand:
+        """Return an absolute non-shorthand command
+
+        .. versionadded:: 1.1"""
+        return self.to_absolute(prev)
+
+    # The precision of the numbers when converting to string
+    number_template = "{:.6g}"
+
+    # Maps single letter path command to corresponding class
+    # (filled at the bottom of file, when all classes already defined)
+    _letter_to_class: Dict[str, Type[Any]] = {}
+
+    @staticmethod
+    def letter_to_class(letter):
+        """Returns class for given path command letter"""
+        return PathCommand._letter_to_class[letter]
+
+    @property
+    @abc.abstractmethod
+    def args(self) -> List[float]:
+        """Returns path command arguments as tuple of floats"""
+
+    def control_points(
+        self,
+        first: ComplexLike,
+        prev: ComplexLike,
+        prev_prev: ComplexLike,
+    ) -> Generator[Vector2d, None, None]:
+        """Returns list of path command control points"""
+        first, prev, prev_prev = complex(first), complex(prev), complex(prev_prev)
+        yield from [Vector2d(i) for i in self.ccontrol_points(first, prev, prev_prev)]
+
+    @abc.abstractmethod
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        """Returns list of path command control points"""
+
+    @classmethod
+    def _argt(cls, sep):
+        return sep.join([cls.number_template] * cls.nargs)
+
+    def __str__(self):
+        return f"{self.letter} {self._argt(' ').format(*self.args)}".strip()
+
+    def __repr__(self):
+        # pylint: disable=consider-using-f-string
+        return "{{}}({})".format(self._argt(", ")).format(self.name, *self.args)
+
+    def __eq__(self, other):
+        previous = 0j
+        if type(self) == type(other):  # pylint: disable=unidiomatic-typecheck
+            return self.args == other.args
+        if isinstance(other, tuple):
+            return self.args == other
+        if not isinstance(other, PathCommand):
+            raise ValueError("Can't compare types")
+        try:
+            if self.is_relative == other.is_relative:
+                return self.to_curve(previous) == other.to_curve(previous)
+        except ValueError:
+            pass
+        return False
+
+    @abc.abstractmethod
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        """Complex version of end_point"""
+
+    def end_point(self, first: ComplexLike, prev: ComplexLike) -> Vector2d:
+        """Returns last control point of path command"""
+        return Vector2d(self.cend_point(complex(first or 0), complex(prev or 0)))
+
+    @abc.abstractmethod
+    def update_bounding_box(
+        self, first: complex, last_two_points: List[complex], bbox: BoundingBox
+    ):
+        """Enlarges given bbox to contain path element.
+
+        Args:
+            first (complex): first point of path. Required to calculate Z segment
+            last_two_points (List[complex]): list with last two control points in abs
+                coords.
+            bbox (BoundingBox): bounding box to update
+        """
+
+    def to_curve(self, prev: ComplexLike, prev_prev: ComplexLike = 0) -> Curve:
+        # pylint: disable=unused-argument
+        """Convert command to :py:class:`Curve`
+
+        Curve().to_curve() returns a copy
+        """
+        return NotImplemented
+
+    def to_curves(self, prev: ComplexLike, prev_prev: ComplexLike = 0) -> List[Curve]:
+        """Convert command to list of :py:class:`Curve` commands"""
+        return [self.to_curve(prev, prev_prev)]
+
+    def to_line(self, prev: ComplexLike) -> Line:
+        # pylint: disable=unused-argument
+        """Converts this segment to a line (copies if already a line)"""
+        return NotImplemented
+
+    @abc.abstractmethod
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        # pylint: disable=unused-argument
+        """Converts the path element into a single cubic bezier"""
+
+    # Derivation functionality
+
+    def __check_t(self, t: Optional[float], allow_none=True):
+        if not allow_none and (t is None and self.letter not in "zZmMlLhHvV"):
+            raise ValueError("t=None only supported for Line-like commands")
+        if t is not None and not 0 <= t <= 1:
+            raise ValueError("t should be between 0 and 1")
+        return t if t is not None else 0.0
+
+    def cderivative(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t: Optional[float] = None,
+        n: int = 1,
+    ) -> complex:
+        """Returns the nth derivative of the segment at t as a complex number.
+
+        .. versionadded:: 1.4
+        """
+        if n < 1:
+            raise ValueError("n should be a positive integer")
+        # pylint: disable=protected-access
+        return self._cderivative(first, prev, prev_control, self.__check_t(t), n)
+
+    def derivative(
+        self,
+        first: ComplexLike,
+        prev: ComplexLike,
+        prev_control: ComplexLike,
+        t: Optional[float] = None,
+        n: int = 1,
+    ) -> Vector2d:
+        """Returns the nth derivative of the segment at t as a :class:`Vector2D`.
+
+        .. versionadded:: 1.4
+        """
+        return Vector2d(
+            self.cderivative(
+                complex(first or 0),
+                complex(prev or 0),
+                complex(prev_control or 0),
+                t,
+                n,
+            )
+        )
+
+    @abc.abstractmethod
+    def _cderivative(
+        self, first: complex, prev: complex, prev_control: complex, t: float, n: int = 1
+    ) -> complex: ...
+
+    def cunit_tangent(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t: Optional[float] = None,
+    ) -> complex:
+        """Returns the unit tangent of the segment at t as a complex number.
+
+        ..versionadded:: 1.4
+        """
+        return self._cunit_tangent(first, prev, prev_control, self.__check_t(t))
+
+    def unit_tangent(
+        self,
+        first: ComplexLike,
+        prev: ComplexLike,
+        prev_control: ComplexLike,
+        t: Optional[float] = None,
+    ) -> Vector2d:
+        """Returns the unit tangent of the segment at t as a :class:`Vector2D`.
+
+        ..versionadded:: 1.4
+        """
+        return Vector2d(
+            self.cunit_tangent(
+                complex(first or 0), complex(prev or 0), complex(prev_control or 0), t
+            )
+        )
+
+    def _cunit_tangent(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        dseg = self._cderivative(first, prev, t, 1)
+        return dseg / abs(dseg)
+
+    def cnormal(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t: Optional[float] = None,
+    ) -> complex:
+        """Returns the (right-hand-rule) normal vector of the segment at t as a complex
+        number.
+
+        ..versionadded:: 1.4
+        """
+        return self.cunit_tangent(first, prev, prev_control, t) * 1j
+
+    def normal(
+        self,
+        first: ComplexLike,
+        prev: ComplexLike,
+        prev_control: ComplexLike,
+        t: Optional[float] = None,
+    ) -> Vector2d:
+        """Returns the (right-hand-rule) normal vector of the segment at t as
+        :class:`Vector2D`.
+
+        ..versionadded:: 1.4
+        """
+        return Vector2d(
+            self.cnormal(
+                complex(first or 0), complex(prev or 0), complex(prev_control or 0), t
+            )
+        )
+
+    def curvature(
+        self,
+        first: ComplexLike,
+        prev: ComplexLike,
+        prev_control: ComplexLike,
+        t: Optional[float] = None,
+    ) -> float:
+        """Returns the curvature of the segment at t.
+
+        ..versionadded:: 1.4
+        """
+        # pylint: disable=protected-access
+        return self._curvature(
+            complex(first or 0),
+            complex(prev or 0),
+            complex(prev_control or 0),
+            self.__check_t(t),
+        )
+
+    @abc.abstractmethod
+    def _curvature(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> float: ...
+
+    # Point evaluation, splitting
+    def cpoint(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        """Returns the coordinates of the Bezier curve evaluated at t as complex number.
+
+        .. versionadded:: 1.4"""
+        return self._cpoint(first, prev, prev_control, self.__check_t(t, False))
+
+    def point(
+        self, first: ComplexLike, prev: ComplexLike, prev_control: ComplexLike, t: float
+    ) -> Vector2d:
+        """Returns the coordinates of the Bezier curve evaluated at t as :class:`Vector2d`.
+
+        .. versionadded:: 1.4"""
+        return Vector2d(
+            self.cpoint(
+                complex(first or 0), complex(prev or 0), complex(prev_control or 0), t
+            )
+        )
+
+    @abc.abstractmethod
+    def _cpoint(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex: ...
+
+    def split(
+        self, first: ComplexLike, prev: ComplexLike, prev_control: ComplexLike, t: float
+    ) -> Tuple[PathCommand, PathCommand]:
+        """Returns two segments, whose union is this segment and which join at
+        self.point(t).
+
+        .. versionadded:: 1.4"""
+        # no simplification here, we want to preserve the original type
+        return self._split(
+            complex(first),
+            complex(prev),
+            complex(prev_control),
+            self.__check_t(t, False),
+        )
+
+    @abc.abstractmethod
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[PathCommand, PathCommand]: ...
+
+    # Line integration
+
+    def length(
+        self,
+        first: ComplexLike,
+        prev: ComplexLike,
+        prev_control: ComplexLike,
+        t0: float = 0,
+        t1: float = 1,
+        settings=LengthSettings(),
+    ) -> float:
+        """Returns the length of the segment between t0 and t1.
+
+        .. versionadded:: 1.4"""
+        # pylint: disable=protected-access
+        return self._length(
+            complex(first),
+            complex(prev),
+            complex(prev_control),
+            self.__check_t(t0, False),
+            self.__check_t(t1, False),
+            settings,
+        )
+
+    @abc.abstractmethod
+    def _length(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t0: float = 0,
+        t1: float = 1,
+        settings=LengthSettings(),
+    ) -> float: ...
+
+    def ilength(
+        self,
+        first: ComplexLike,
+        prev: ComplexLike,
+        prev_control: ComplexLike,
+        length: float,
+        settings: ILengthSettings = ILengthSettings(),
+    ):
+        """Returns a float ``t``, such that ``self.length(0, t)`` is approximately
+        ``length``.
+
+        .. versionadded:: 1.4"""
+        # pylint: disable=protected-access
+        return self._ilength(
+            complex(first), complex(prev), complex(prev_control), length, settings
+        )
+
+    @abc.abstractmethod
+    def _ilength(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        length: float,
+        settings: ILengthSettings = ILengthSettings(),
+    ): ...
+
+
+class RelativePathCommand(PathCommand):
+    """
+    Abstract base class for relative path commands.
+
+    Implements most of methods of :py:class:`PathCommand` through
+    conversion to :py:class:`AbsolutePathCommand`
+    """
+
+    @property
+    def is_relative(self):
+        return True
+
+    @property
+    def is_absolute(self):
+        return False
+
+    def to_relative(self, prev: ComplexLike) -> RelativePathCommand:
+        return self.__class__(*self.args)
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        self.to_absolute(last_two_points[-1]).update_bounding_box(
+            first, last_two_points, bbox
+        )
+
+
+class AbsolutePathCommand(PathCommand):
+    """Absolute path command. Unlike :py:class:`RelativePathCommand` can be transformed
+    directly."""
+
+    @property
+    def is_relative(self):
+        return False
+
+    @property
+    def is_absolute(self):
+        return True
+
+    def to_absolute(self, prev: ComplexLike) -> AbsolutePathCommand:
+        return self.__class__(*self.args)
+
+    @abc.abstractmethod
+    def transform(self, transform: Transform) -> AbsolutePathCommand:
+        """Returns new transformed segment
+
+        :param transform: a transformation to apply
+        """
+
+    def rotate(self, degrees: float, center: Vector2d) -> AbsolutePathCommand:
+        """
+        Returns new transformed segment
+
+        :param degrees: rotation angle in degrees
+        :param center: invariant point of rotation
+        """
+        return self.transform(Transform(rotate=(degrees, center[0], center[1])))
+
+    def translate(self, dr: Vector2d) -> AbsolutePathCommand:
+        """Translate or scale this path command by dr"""
+        return self.transform(Transform(translate=dr))
+
+    def scale(self, factor: Union[float, Tuple[float, float]]) -> AbsolutePathCommand:
+        """Returns new transformed segment
+
+        :param factor: scale or (scale_x, scale_y)
+        """
+        return self.transform(Transform(scale=factor))
+
+
+class BezierArcComputationMixin:
+    """Functionality that works the same way for Arcs, Cubic and Quadratic
+
+    .. versionadded:: 1.4"""
+
+    _cpoint: Callable[[complex, complex, complex, float], complex]
+    _cderivative: Callable[..., complex]
+    poly: Callable[[complex, complex, complex, Optional[bool]], np.poly1d]
+
+    def inv_arclength(self, prev, prev_control, s, settings=ILengthSettings()):
+        """Ported from https://github.com/mathandy/svgpathtools/blob/19df25b99b405ec4fc7616b58384eca7879b6fd4/svgpathtools/path.py#L541
+        (MIT Licensed)"""
+        t_upper = 1
+        t_lower = 0
+        iteration = 0
+        while iteration < settings.maxits:
+            iteration += 1
+            t = (t_lower + t_upper) / 2
+            s_t = self._length(0j, prev, prev_control, t1=t, settings=settings)
+            if abs(s_t - s) < settings.length_tol:
+                return t
+            elif s_t < s:  # t too small
+                t_lower = t
+            else:  # s < s_t, t too big
+                t_upper = t
+            if t_upper == t_lower:
+                # warn("t is as close as a float can be to the correct value, "
+                #        "but |s(t) - s| = {} > s_tol".format(abs(s_t-s)))
+                return t
+        raise Exception(f"Maximum iterations reached with s(t) - s = {s_t - s}.")
+
+    def segment_length(
+        self,
+        start,
+        end,
+        start_point,
+        end_point,
+        pos_eval,
+        settings=LengthSettings(),
+        depth=0,
+    ):
+        """
+        Ported from https://github.com/mathandy/svgpathtools/blob/19df25b99b405ec4fc7616b58384eca7879b6fd4/svgpathtools/path.py#L479
+        (MIT licensed)
+        # TODO better treatment of degenerate beziers from
+        # https://github.com/linebender/kurbo/blob/c229a914d303c5989c9e6b1d766def2df27a8185/src/cubicbez.rs#L431
+        """
+        mid = (start + end) / 2
+        mid_point = pos_eval(mid)
+        length = abs(end_point - start_point)
+        first_half = abs(mid_point - start_point)
+        second_half = abs(end_point - mid_point)
+
+        length2 = first_half + second_half
+        if (length2 - length > settings.error) or (depth < settings.min_depth):
+            # Calculate the length of each segment:
+            depth += 1
+            return self.segment_length(
+                start, mid, start_point, mid_point, pos_eval, settings, depth
+            ) + self.segment_length(
+                mid, end, mid_point, end_point, pos_eval, settings, depth
+            )
+        # This is accurate enough.
+        return length2
+
+    def segment_curvature(self, prev: complex, prev_prev: complex, t: float):
+        """Returns the curvature of the segment at t.
+
+        Ported from https://github.com/mathandy/svgpathtools/blob/19df25b99b405ec4fc7616b58384eca7879b6fd4/svgpathtools/path.py#L386
+        (MIT licensed)
+        """
+
+        dz = self._cderivative(0j, prev, prev_prev, t)
+        ddz = self._cderivative(0j, prev, prev_prev, t, n=2)
+        dx, dy = dz.real, dz.imag
+        ddx, ddy = ddz.real, ddz.imag
+        try:
+            kappa = abs(dx * ddy - dy * ddx) / math.sqrt(dx * dx + dy * dy) ** 3
+        except (ZeroDivisionError, FloatingPointError):
+            # tangent vector is zero at t, use polytools to find limit
+            p = self.poly(0j, prev, prev_prev, False)
+            dp = p.deriv()
+            ddp = dp.deriv()
+            dx2, dy2 = np.real(dp), np.imag(dp)
+            ddx2, ddy2 = np.real(ddp), np.imag(ddp)
+            f2 = (dx2 * ddy2 - dy2 * ddx2) ** 2
+            g2 = (dx2 * dx2 + dy2 * dy2) ** 3
+            lim2 = rational_limit(f2, g2, t)
+            if lim2 < 0:  # impossible, must be numerical error
+                return 0
+            kappa = math.sqrt(lim2)
+        return kappa
+
+    def _length(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t0=0,
+        t1=1,
+        settings=LengthSettings(),
+    ) -> float:
+        return self.segment_length(
+            t0,
+            t1,
+            self._cpoint(first, prev, prev_control, t0),
+            self._cpoint(first, prev, prev_control, t1),
+            lambda t: self._cpoint(first, prev, prev_control, t),
+            settings,
+            0,
+        )
+
+    def _ilength(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        length,
+        settings=ILengthSettings(),
+    ):
+        return self.inv_arclength(prev, prev_control, length, settings)
+
+    def _curvature(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> float:
+        return self.segment_curvature(prev, prev_control, t)
+
+
+class BezierComputationMixin:
+    """Functionality that works the same for all Beziers (Quadratic, Cubic)
+
+    .. versionadded:: 1.4"""
+
+    def _bpoints(self, prev, prev_prev):
+        return (prev,) + self.ccontrol_points(0j, prev, prev_prev)
+
+    def bezier_unit_tangent(self, prev, prev_prev, t):
+        """Returns the unit tangent of the segment at t.
+
+        Ported from https://github.com/mathandy/svgpathtools/blob/19df25b99b405ec4fc7616b58384eca7879b6fd4/svgpathtools/path.py#L348
+        (MIT licensed)"""
+
+        dseg = self._cderivative(0j, prev, prev_prev, t)
+
+        try:
+            unit_tangent = dseg / abs(dseg)
+        except (ZeroDivisionError, FloatingPointError):
+            # This may be a removable singularity, if so we just need to compute
+            # the limit.
+            # Note: limit{{dseg / abs(dseg)} = sqrt(limit{dseg**2 / abs(dseg)**2})
+            dseg_poly = self.poly(prev, prev_prev).deriv()
+            dseg_abs_squared_poly = np.real(dseg_poly) ** 2 + np.imag(dseg_poly) ** 2
+            try:
+                unit_tangent = np.sqrt(
+                    rational_limit(dseg_poly**2, dseg_abs_squared_poly, t)
+                )
+            except ValueError:
+                bef = self.poly(prev, prev_prev).deriv()(t - 1e-4)
+                aft = self.poly(prev, prev_prev).deriv()(t + 1e-4)
+                mes = (
+                    "Unit tangent appears to not be well-defined at "
+                    f"t = {t}, \n"
+                    f"seg.poly().deriv()(t - 1e-4) = {bef}\n"
+                    f"seg.poly().deriv()(t + 1e-4) = {aft}"
+                )
+                raise ValueError(mes)
+        return unit_tangent

extensions/botbox3000/deps/inkex/paths/lines.py

@@ -0,0 +1,601 @@
+# coding=utf-8
+#
+# Copyright (C) 2018 Martin Owens <doctormo@gmail.com>
+# Copyright (C) 2023 Jonathan Neuhauser <jonathan.neuhauser@outlook.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.
+#
+"""Line-like path commands (Line, Horz, Vert, ZoneClose and their relative siblings)"""
+
+from __future__ import annotations
+
+from typing import overload, Tuple, Optional, TYPE_CHECKING, Callable, Union
+
+from inkex.paths.interfaces import ILengthSettings, LengthSettings
+
+from ..transforms import Transform, BoundingBox, ComplexLike
+
+from .interfaces import AbsolutePathCommand, RelativePathCommand, ILengthSettings
+
+if TYPE_CHECKING:
+    from .curves import Curve
+
+
+class LineMixin:
+    """Common Line functions"""
+
+    # pylint: disable=unused-argument
+
+    arg1: complex
+
+    cend_point: Callable[[complex, complex], complex]
+
+    def ccurve_points(self, first: complex, prev: complex, prev_prev: complex):
+        """Common implementation of ccurve_points for Lines"""
+        arg1 = self.cend_point(first, prev)
+        return prev, arg1, arg1
+
+    def ccontrol_points(
+        self,
+        first: complex,
+        prev: complex,
+        prev_prev: complex,  # pylint: disable=unused-argument
+    ) -> Tuple[complex, ...]:
+        """Common implementation of ccontrol_points for Lines"""
+        return (self.cend_point(first, prev),)
+
+    def _cderivative(
+        self, first: complex, prev: complex, prev_control: complex, t: float, n: int = 1
+    ) -> complex:
+        start = self.cend_point(first, prev)
+        if prev == start:
+            raise ValueError("Derivative is not defined for zero-length segments")
+        if n == 1:
+            return start - prev
+        return 0j
+
+    def _curvature(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> float:
+        return 0
+
+    def _cpoint(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        return self.cend_point(first, prev) * t + (1 - t) * prev
+
+    def _length(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t0: float = 0,
+        t1: float = 1,
+        settings=LengthSettings(),
+    ) -> float:
+        return abs(self.cend_point(first, prev) - prev) * (t1 - t0)
+
+    def _ilength(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        length: float,
+        settings: ILengthSettings = ILengthSettings(),
+    ):
+        return length / self._length(first, prev, prev_control)
+
+
+class Line(LineMixin, AbsolutePathCommand):
+    """Line segment"""
+
+    letter = "L"
+    nargs = 2
+
+    arg1: complex
+    """The (absolute) end points of the line."""
+
+    @property
+    def x(self):
+        """x coordinate of the line's (absolute) end point."""
+        return self.arg1.real
+
+    @property
+    def y(self):
+        """y coordinate of the line's (absolute) end point."""
+        return self.arg1.imag
+
+    @property
+    def args(self):
+        return self.x, self.y
+
+    @overload
+    def __init__(self, x: ComplexLike): ...
+
+    @overload
+    def __init__(self, x: float, y: float): ...
+
+    def __init__(self, x, y=None):
+        if y is not None:
+            self.arg1 = x + y * 1j
+        else:
+            self.arg1 = complex(x)
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        bbox += BoundingBox(
+            (last_two_points[-1].real, self.x), (last_two_points[-1].imag, self.y)
+        )
+
+    def to_relative(self, prev: ComplexLike) -> line:
+        return line(self.arg1 - prev)
+
+    def transform(self, transform) -> Line:
+        return Line(transform.capply_to_point(self.arg1))
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return self.arg1
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Line:
+        return Line(prev)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Line, Line]:
+        return Line(self._cpoint(first, prev, prev_control, t)), Line(self.arg1)
+
+
+class line(LineMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative line segment"""
+
+    letter = "l"
+    nargs = 2
+
+    arg1: complex
+    """The (relative) end points of the line."""
+
+    @property
+    def dx(self):
+        """x coordinate of the line's (relative) end point."""
+        return self.arg1.real
+
+    @property
+    def dy(self):
+        """y coordinate of the line's (relative) end point."""
+        return self.arg1.imag
+
+    @property
+    def args(self):
+        return self.dx, self.dy
+
+    @overload
+    def __init__(self, dx: ComplexLike): ...
+
+    @overload
+    def __init__(self, dx: float, dy: float): ...
+
+    def __init__(self, dx, dy=None):
+        if dy is not None:
+            self.arg1 = dx + dy * 1j
+        else:
+            self.arg1 = complex(dx)
+
+    def to_absolute(self, prev: ComplexLike) -> Line:
+        return Line(prev + self.arg1)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return self.arg1 + prev
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> line:
+        return line(-self.arg1)
+
+    def to_curve(
+        self, prev: ComplexLike, prev_prev: Optional[ComplexLike] = 0j
+    ) -> Curve:
+        raise ValueError("Move segments can not be changed into curves.")
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[line, line]:
+        dx1 = self.cpoint(first, prev, prev_control, t) - prev
+        return line(dx1), line(self.arg1 - dx1)
+
+
+class MoveMixin:
+    """Disable derivative / length method for Move command."""
+
+    def _cderivative(
+        self, first: complex, prev: complex, prev_control: complex, t: float, n: int = 1
+    ) -> complex:
+        raise ValueError("Derivative is not supported for move/Move")
+
+    def _cunit_tangent(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        raise ValueError("Unit Tangent is not supported for move/Move")
+
+    def _curvature(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> float:
+        raise ValueError("Curvature is not supported for move/Move")
+
+    def _cpoint(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        raise ValueError("Point is not supported for move/Move")
+
+    def _length(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t0: float = 0,
+        t1: float = 1,
+        settings=LengthSettings(),
+    ) -> float:
+        raise ValueError("Length is not supported for move/Move")
+
+    def _ilength(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        length: float,
+        settings: ILengthSettings = ILengthSettings(),
+    ):
+        raise ValueError("ILength is not supported for move/Move")
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Move, Move]:
+        raise ValueError("Split is not supported for move/Move")
+
+
+class Move(MoveMixin, AbsolutePathCommand):
+    """Move pen segment without a line"""
+
+    letter = "M"
+    nargs = 2
+    next_command = Line
+
+    arg1: complex
+    """The (absolute) end points of the Move command"""
+
+    @property
+    def x(self):
+        """x coordinate of the Moves's (absolute) end point."""
+        return self.arg1.real
+
+    @property
+    def y(self):
+        """y coordinate of the Move's (absolute) end point."""
+        return self.arg1.imag
+
+    @property
+    def args(self):
+        return self.x, self.y
+
+    @overload
+    def __init__(self, x: ComplexLike): ...
+
+    @overload
+    def __init__(self, x: float, y: float): ...
+
+    def __init__(self, x, y=None):
+        if y is not None:
+            self.arg1 = x + y * 1j
+        else:
+            self.arg1 = complex(x)
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        bbox += BoundingBox(self.x, self.y)
+
+    def ccurve_points(self, first: complex, prev: complex, prev_prev: complex):
+        return prev, self.arg1, self.arg1
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (self.arg1,)
+
+    def to_relative(self, prev: ComplexLike) -> move:
+        return move(self.arg1 - prev)
+
+    def transform(self, transform: Transform) -> Move:
+        return Move(transform.capply_to_point(self.arg1))
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg1
+
+    def to_curve(
+        self, prev: ComplexLike, prev_prev: Optional[ComplexLike] = 0j
+    ) -> Curve:
+        raise ValueError("Move segments can not be changed into curves.")
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Move:
+        return Move(prev)
+
+
+class move(MoveMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative move segment"""
+
+    letter = "m"
+    nargs = 2
+    next_command = line
+
+    @property
+    def dx(self):
+        """x coordinate of the moves's (relative) end point."""
+        return self.arg1.real
+
+    @property
+    def dy(self):
+        """y coordinate of the move's (relative) end point."""
+        return self.arg1.imag
+
+    @property
+    def args(self):
+        return self.dx, self.dy
+
+    @overload
+    def __init__(self, dx: ComplexLike): ...
+
+    @overload
+    def __init__(self, dx: float, dy: float): ...
+
+    def __init__(self, dx, dy=None):
+        if dy is not None:
+            self.arg1 = dx + dy * 1j
+        else:
+            self.arg1 = complex(dx)
+
+    def ccurve_points(self, first: complex, prev: complex, prev_prev: complex):
+        return prev, self.arg1 + prev, self.arg1 + prev
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (self.arg1 + prev,)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg1 + prev
+
+    def to_absolute(self, prev: ComplexLike) -> Move:
+        return Move(prev + self.arg1)
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> move:
+        return move(prev - first)
+
+    def to_curve(
+        self, prev: ComplexLike, prev_prev: Optional[ComplexLike] = 0j
+    ) -> Curve:
+        raise ValueError("Move segments can not be changed into curves.")
+
+
+class ZoneClose(LineMixin, AbsolutePathCommand):
+    """Close segment to finish a path"""
+
+    letter = "Z"
+    nargs = 0
+    next_command = Move
+
+    @property
+    def args(self):
+        return ()
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        pass
+
+    def transform(self, transform: Transform) -> ZoneClose:
+        return ZoneClose()
+
+    def to_relative(self, prev: ComplexLike) -> zoneClose:
+        return zoneClose()
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return first
+
+    def to_curve(
+        self, prev: ComplexLike, prev_prev: Optional[ComplexLike] = 0j
+    ) -> Curve:
+        raise ValueError("ZoneClose segments can not be changed into curves.")
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Line:
+        return Line(prev)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Line, ZoneClose]:
+        return Line(self._cpoint(first, prev, prev_control, t)), ZoneClose()
+
+
+class zoneClose(LineMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Same as above (svg says no difference)"""
+
+    letter = "z"
+    nargs = 0
+    next_command = Move
+
+    @property
+    def args(self):
+        return ()
+
+    def to_absolute(self, prev: ComplexLike):
+        return ZoneClose()
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> line:
+        return line(prev - first)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return first
+
+    def to_curve(
+        self, prev: ComplexLike, prev_prev: Optional[ComplexLike] = 0j
+    ) -> Curve:
+        raise ValueError("ZoneClose segments can not be changed into curves.")
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[line, zoneClose]:
+        return line(self.cpoint(first, prev, prev_control, t) - prev), zoneClose()
+
+
+class Horz(LineMixin, AbsolutePathCommand):
+    """Horizontal Line segment"""
+
+    letter = "H"
+    nargs = 1
+
+    @property
+    def args(self):
+        return (self.x,)
+
+    def __init__(self, x):
+        self.x = x
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        bbox += BoundingBox(
+            (last_two_points[-1].real, self.x), last_two_points[-1].imag
+        )
+
+    def to_relative(self, prev: ComplexLike) -> horz:
+        return horz(self.x - complex(prev).real)
+
+    def to_non_shorthand(self, prev: ComplexLike, prev_control: ComplexLike) -> Line:
+        return self.to_line(prev)
+
+    def transform(self, transform: Transform) -> AbsolutePathCommand:
+        raise ValueError("Horizontal lines can't be transformed directly.")
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return self.x + prev.imag * 1j
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Horz:
+        return Horz(complex(prev).real)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Horz, Horz]:
+        return Horz(self.cpoint(first, prev, prev_control, t).real), Horz(self.x)
+
+
+class horz(LineMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative horz line segment"""
+
+    letter = "h"
+    nargs = 1
+
+    @property
+    def args(self):
+        return (self.dx,)
+
+    def __init__(self, dx):
+        self.dx = dx
+
+    def to_absolute(self, prev: ComplexLike) -> Horz:
+        return Horz(complex(prev).real + self.dx)
+
+    def to_non_shorthand(self, prev: ComplexLike, prev_control: ComplexLike) -> Line:
+        return self.to_line(prev)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return (self.dx + prev.real) + prev.imag * 1j
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> horz:
+        return horz(-self.dx)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[horz, horz]:
+        dx1 = (self.cpoint(first, prev, prev_control, t) - prev).real
+        return horz(dx1), horz(self.dx - dx1)
+
+
+class Vert(LineMixin, AbsolutePathCommand):
+    """Vertical Line segment"""
+
+    letter = "V"
+    nargs = 1
+
+    @property
+    def args(self):
+        return (self.y,)
+
+    def __init__(self, y):
+        self.y = y
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        bbox += BoundingBox(
+            last_two_points[-1].real, (last_two_points[-1].imag, self.y)
+        )
+
+    def transform(self, transform: Transform) -> AbsolutePathCommand:
+        raise ValueError("Vertical lines can't be transformed directly.")
+
+    def to_non_shorthand(self, prev: ComplexLike, prev_control: ComplexLike) -> Line:
+        return self.to_line(prev)
+
+    def to_relative(self, prev: ComplexLike) -> vert:
+        return vert(self.y - complex(prev).imag)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return prev.real + self.y * 1j
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Vert:
+        return Vert(complex(prev).imag)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Vert, Vert]:
+        return Vert(self.cpoint(first, prev, prev_control, t).imag), Vert(self.y)
+
+
+class vert(LineMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative vertical line segment"""
+
+    letter = "v"
+    nargs = 1
+
+    @property
+    def args(self):
+        return (self.dy,)
+
+    def __init__(self, dy):
+        self.dy = dy
+
+    def to_absolute(self, prev: ComplexLike) -> Vert:
+        return Vert(complex(prev).imag + self.dy)
+
+    def to_non_shorthand(self, prev: ComplexLike, prev_control: ComplexLike) -> Line:
+        return self.to_line(prev)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        # pylint: disable=unused-argument
+        return prev.real + (prev.imag + self.dy) * 1j
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> vert:
+        return vert(-self.dy)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[vert, vert]:
+        dy1 = (self.cpoint(first, prev, prev_control, t) - prev).imag
+        return vert(dy1), vert(self.dy - dy1)

extensions/botbox3000/deps/inkex/paths/path.py

@@ -0,0 +1,937 @@
+# coding=utf-8
+#
+# Copyright (C) 2018 Martin Owens <doctormo@gmail.com>
+# Copyright (C) 2023 Jonathan Neuhauser <jonathan.neuhauser@outlook.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.
+#
+"""
+Path and CubicSuperPath classes
+"""
+
+from __future__ import annotations
+
+import re
+import copy
+import warnings
+from cmath import isclose
+
+from typing import Optional, Tuple, List, TypeVar, Iterator, Callable, Union
+from ..transforms import (
+    Transform,
+    BoundingBox,
+    Vector2d,
+    ComplexLike,
+)
+from ..utils import strargs
+
+from .lines import Line, Move, move, ZoneClose, zoneClose
+from .curves import Curve
+from .interfaces import (
+    ILengthSettings,
+    LengthSettings,
+    PathCommand,
+    AbsolutePathCommand,
+)
+
+Pathlike = TypeVar("Pathlike", bound="PathCommand")
+AbsolutePathlike = TypeVar("AbsolutePathlike", bound="AbsolutePathCommand")
+
+LEX_REX = re.compile(r"([MLHVCSQTAZmlhvcsqtaz])([^MLHVCSQTAZmlhvcsqtaz]*)")
+
+
+class InvalidPath(ValueError):
+    """Raised when given an invalid path string"""
+
+
+class Path(list):
+    """A list of segment commands which combine to draw a shape"""
+
+    callback: Optional[Callable] = None
+
+    class PathCommandProxy:
+        """
+        A handy class for Path traverse and coordinate access
+
+        Reduces number of arguments in user code compared to bare
+        :class:`PathCommand` methods
+        """
+
+        def __init__(
+            self,
+            command: PathCommand,
+            first_point: ComplexLike,
+            previous_end_point: ComplexLike,
+            prev2_control_point: ComplexLike,
+        ):
+            self.command = command
+            self.cfirst_point = complex(first_point)
+            self.cprevious_end_point = complex(previous_end_point)
+            self.cprev2_control_point = complex(prev2_control_point)
+
+        @property
+        def first_point(self) -> Vector2d:
+            """First point of the current subpath"""
+            return Vector2d(self.cfirst_point)
+
+        @property
+        def previous_end_point(self) -> Vector2d:
+            """End point of the previous command"""
+            return Vector2d(self.cprevious_end_point)
+
+        @property
+        def prev2_control_point(self) -> Vector2d:
+            """Last control point of the previous command"""
+            return Vector2d(self.cprev2_control_point)
+
+        @property
+        def name(self) -> str:
+            """The full name of the segment (i.e. Line, Arc, etc)"""
+            return self.command.name
+
+        @property
+        def letter(self) -> str:
+            """The single letter representation of this command (i.e. L, A, etc)"""
+            return self.command.letter
+
+        @property
+        def next_command(self):
+            """The implicit next command."""
+            return self.command.next_command
+
+        @property
+        def is_relative(self) -> bool:
+            """Whether the command is defined in relative coordinates, i.e. relative to
+            the previous endpoint (lower case path command letter)"""
+            return self.command.is_relative
+
+        @property
+        def is_absolute(self) -> bool:
+            """Whether the command is defined in absolute coordinates (upper case path
+            command letter)"""
+            return self.command.is_absolute
+
+        @property
+        def args(self) -> List[float]:
+            """Returns path command arguments as tuple of floats"""
+            return self.command.args
+
+        @property
+        def control_points(self) -> List[Vector2d]:
+            """Returns list of path command control points"""
+            return list(
+                self.command.control_points(
+                    self.cfirst_point,
+                    self.cprevious_end_point,
+                    self.cprev2_control_point,
+                )
+            )
+
+        @property
+        def end_point(self) -> Vector2d:
+            """Returns last control point of path command"""
+            return Vector2d(self.cend_point)
+
+        @property
+        def cend_point(self) -> complex:
+            """Returns last control point of path command (in complex form)"""
+            return self.command.cend_point(self.cfirst_point, self.cprevious_end_point)
+
+        def reverse(self) -> PathCommand:
+            """Reverse path command"""
+            return self.command.reverse(self.cend_point, self.cprevious_end_point)
+
+        def to_curve(self) -> Curve:
+            """Convert command to :py:class:`Curve`
+            Curve().to_curve() returns a copy
+            """
+            return self.command.to_curve(
+                self.cprevious_end_point, self.cprev2_control_point
+            )
+
+        def to_curves(self) -> List[Curve]:
+            """Convert command to list of :py:class:`Curve` commands"""
+            return self.command.to_curves(
+                self.cprevious_end_point, self.cprev2_control_point
+            )
+
+        def to_absolute(self) -> AbsolutePathCommand:
+            """Return relative counterpart for relative commands or copy for absolute"""
+            return self.command.to_absolute(self.cprevious_end_point)
+
+        def to_non_shorthand(self) -> AbsolutePathCommand:
+            """Returns an absolute non-shorthand command
+
+            .. versionadded:: 1.4"""
+            return self.command.to_non_shorthand(
+                self.cprevious_end_point, self.cprev2_control_point
+            )
+
+        def split(self, time) -> Tuple[Path.PathCommandProxy, Path.PathCommandProxy]:
+            """Split this path command into two PathCommandProxy segments.
+            Raises ValueError for Move commands.
+
+            .. versionadded:: 1.4"""
+            result = self.command.split(
+                self.cfirst_point,
+                self.cprevious_end_point,
+                self.cprev2_control_point,
+                time,
+            )
+            p1 = Path.PathCommandProxy(
+                result[0],
+                self.cfirst_point,
+                self.previous_end_point,
+                self.prev2_control_point,
+            )
+            prev2: ComplexLike = (
+                0j if len(p1.control_points) < 2 else p1.control_points[-2]
+            )
+            p2 = Path.PathCommandProxy(
+                result[1], self.cfirst_point, p1.end_point, prev2
+            )
+            return (p1, p2)
+
+        def cpoint(self, time) -> complex:
+            """Returns the coordinates of the Bezier curve evaluated at t as complex number.
+
+            .. versionadded:: 1.4"""
+            return self.command.cpoint(
+                self.cfirst_point,
+                self.cprevious_end_point,
+                self.cprev2_control_point,
+                time,
+            )
+
+        def point(self, time) -> Vector2d:
+            """Returns the coordinates of the Bezier curve evaluated at t as :class:`Vector2d`.
+
+            .. versionadded:: 1.4"""
+            return self.command.point(
+                self.cfirst_point,
+                self.cprevious_end_point,
+                self.cprev2_control_point,
+                time,
+            )
+
+        def length(self, t0=0, t1=1, settings=LengthSettings()) -> float:
+            """Get the length of the command between t0 and t1 in user units
+
+            .. versionadded:: 1.4"""
+            return self.command.length(
+                self.cfirst_point,
+                self.cprevious_end_point,
+                self.cprev2_control_point,
+                t0,
+                t1,
+                settings,
+            )
+
+        def ilength(self, length, settings=ILengthSettings()) -> float:
+            """Tries to compute the time t at which the path segment has the given
+            length along its trajectory
+
+            .. versionadded:: 1.4"""
+            return self.command.ilength(
+                self.cfirst_point,
+                self.cprevious_end_point,
+                self.cprev2_control_point,
+                length,
+                settings,
+            )
+
+        def cunit_tangent(self, t) -> complex:
+            """Returns the unit tangent at t as complex number
+
+            .. versionadded:: 1.4"""
+            return self.command.cunit_tangent(
+                self.cfirst_point,
+                self.cprevious_end_point,
+                self.cprev2_control_point,
+                t,
+            )
+
+        def unit_tangent(self, t) -> Vector2d:
+            """Returns the unit tangent at t as :class:`inkex.Vector2D`
+
+            .. versionadded::  1.4"""
+            return self.command.unit_tangent(
+                self.cfirst_point,
+                self.cprevious_end_point,
+                self.cprev2_control_point,
+                t,
+            )
+
+        def __str__(self):
+            return str(self.command)
+
+        def __repr__(self):
+            return "<" + self.__class__.__name__ + ">" + repr(self.command)
+
+    def __init__(self, path_d=None) -> None:
+        super().__init__()
+        if isinstance(path_d, str):
+            # Returns a generator returning PathCommand objects
+            path_d = self.parse_string(path_d)
+        elif isinstance(path_d, CubicSuperPath):
+            path_d = path_d.to_path()
+
+        for item in path_d or ():
+            if isinstance(item, PathCommand):
+                self.append(item)
+            elif isinstance(item, (list, tuple)) and len(item) == 2:
+                if isinstance(item[1], (list, tuple)):
+                    self.append(PathCommand.letter_to_class(item[0])(*item[1]))
+                else:
+                    if len(self) == 0:
+                        self.append(Move(*item))
+                    else:
+                        self.append(Line(*item))
+            else:
+                raise TypeError(
+                    f"Bad path type: {type(path_d).__name__}"
+                    f"({type(item).__name__}, ...): {item}"
+                )
+
+    @classmethod
+    def parse_string(cls, path_d):
+        """Parse a path string and generate segment objects"""
+        for cmd, numbers in LEX_REX.findall(path_d):
+            args = list(strargs(numbers))
+            cmd = PathCommand.letter_to_class(cmd)
+            i = 0
+            while i < len(args) or cmd.nargs == 0:
+                if len(args[i : i + cmd.nargs]) != cmd.nargs:
+                    return
+                seg = cmd(*args[i : i + cmd.nargs])
+                i += cmd.nargs
+                cmd = seg.next_command
+                yield seg
+
+    def bounding_box(self) -> Optional[BoundingBox]:
+        """Return bounding box of the Path"""
+        if not self:
+            return None
+        iterator = self.proxy_iterator()
+        proxy = next(iterator)
+        bbox = BoundingBox(proxy.first_point.x, proxy.first_point.y)
+        try:
+            while True:
+                proxy = next(iterator)
+                proxy.command.update_bounding_box(
+                    complex(proxy.first_point),
+                    [
+                        proxy.cprev2_control_point,
+                        proxy.cprevious_end_point,
+                    ],
+                    bbox,
+                )
+        except StopIteration:
+            return bbox
+
+    def append(self, cmd):
+        """Append a command to this path."""
+        try:
+            cmd.letter  # pylint: disable=pointless-statement
+            super().append(cmd)
+        except AttributeError:
+            self.extend(cmd)
+            warnings.warn(
+                "Passing a list to Path.add is deprecated, please use Path.extend",
+                category=DeprecationWarning,
+            )
+
+    def translate(self, x, y, inplace=False):  # pylint: disable=invalid-name
+        """Move all coords in this path by the given amount"""
+        return self.transform(Transform(translate=(x, y)), inplace=inplace)
+
+    def scale(self, x, y, inplace=False):  # pylint: disable=invalid-name
+        """Scale all coords in this path by the given amounts"""
+        return self.transform(Transform(scale=(x, y)), inplace=inplace)
+
+    def rotate(self, deg, center=None, inplace=False):
+        """Rotate the path around the given point"""
+        if center is None:
+            # Default center is center of bbox
+            bbox = self.bounding_box()
+            if bbox:
+                center = bbox.center
+            else:
+                center = Vector2d()
+        center = Vector2d(center)
+        return self.transform(
+            Transform(rotate=(deg, center.x, center.y)), inplace=inplace
+        )
+
+    @property
+    def control_points(self) -> Iterator[Vector2d]:
+        """Returns all control points of the Path"""
+        prev: complex = 0
+        prev_prev: complex = 0
+        first: complex = 0
+
+        seg: PathCommand
+        for seg in self:
+            cpts = seg.ccontrol_points(first, prev, prev_prev)
+            if seg.letter in "zZmM":
+                first = cpts[-1]
+            for cpt in cpts:
+                prev_prev = prev
+                prev = cpt
+                yield Vector2d(cpt)
+
+    @property
+    def cend_points(self) -> Iterator[complex]:
+        """Complex version of end_points"""
+        prev = 0j
+        first = 0j
+
+        seg: PathCommand
+        for seg in self:
+            end_point = seg.cend_point(first, prev)
+            if seg.letter in "zZmM":
+                first = end_point
+            prev = end_point
+            yield end_point
+
+    @property
+    def end_points(self) -> Iterator[Vector2d]:
+        """Returns all endpoints of all path commands (i.e. the nodes)"""
+        for i in self.cend_points:
+            yield Vector2d(i)
+
+    def transform(self, transform, inplace=False):
+        """Convert to new path"""
+        result = Path()
+        previous = 0j
+        previous_new = 0j
+        start_zone = True
+        first = 0j
+        first_new = 0j
+
+        seg: PathCommand
+        for i, seg in enumerate(self):
+            if start_zone:
+                first = seg.cend_point(first, previous)
+
+            if seg.letter in "hHVv":
+                seg = seg.to_line(previous)
+
+            if seg.is_relative:
+                new_seg = (
+                    seg.to_absolute(previous)
+                    .transform(transform)
+                    .to_relative(previous_new)
+                )
+            else:
+                new_seg = seg.transform(transform)
+
+            if start_zone:
+                first_new = new_seg.cend_point(first_new, previous_new)
+
+            if inplace:
+                self[i] = new_seg
+            else:
+                result.append(new_seg)
+            previous = seg.cend_point(first, previous)
+            previous_new = new_seg.cend_point(first_new, previous_new)
+            start_zone = seg.letter in "zZ"
+        if inplace:
+            return self
+        return result
+
+    def reverse(self):
+        """Returns a reversed path"""
+        result = Path()
+        try:
+            *_, first = self.cend_points
+        except ValueError:
+            # Empty path, return empty path
+            return result
+        closer = None
+
+        # Go through the path in reverse order
+        for index, prcom in reversed(list(enumerate(self.proxy_iterator()))):
+            if prcom.letter in "MmZz":
+                if closer is not None:
+                    if len(result) > 0 and result[-1].letter in "LlVvHh":
+                        result.pop()  # We can replace simple lines with Z
+                    result.append(closer)  # replace with same type (rel or abs)
+                if prcom.letter in "Zz":
+                    closer = prcom.command
+                else:
+                    closer = None
+
+            if index == 0:
+                if prcom.letter == "M":
+                    result.insert(0, Move(first))
+                elif prcom.letter == "m":
+                    result.insert(0, move(first))
+            else:
+                result.append(prcom.reverse())
+
+        return result
+
+    def break_apart(self) -> List[Path]:
+        """Breaks apart a path into its subpaths
+
+        .. versionadded:: 1.3"""
+        result = [Path()]
+        current = result[0]
+
+        for cmnd in self.proxy_iterator():
+            if cmnd.letter.lower() == "m":
+                current = Path()
+                result.append(current)
+                current.append(Move(cmnd.cend_point))
+            else:
+                current.append(cmnd.command)
+        # Remove all subpaths that are empty or only contain move commands
+        return [
+            i
+            for i in result
+            if len(i) != 0 and not all(j.letter.lower() == "m" for j in i)
+        ]
+
+    def close(self):
+        """Attempt to close the last path segment"""
+        if self and not self[-1].letter in "zZ":
+            self.append(ZoneClose())
+
+    def proxy_iterator(self) -> Iterator[PathCommandProxy]:
+        """
+        Yields :py:class:`AugmentedPathIterator`
+
+        :rtype: Iterator[ Path.PathCommandProxy ]
+        """
+
+        previous = 0j
+        prev_prev = 0j
+        first = 0j
+        seg: PathCommand
+        for seg in self:
+            if seg.letter in "zZmM":
+                first = seg.cend_point(first, previous)
+            yield Path.PathCommandProxy(seg, first, previous, prev_prev)
+            if seg.letter in "ctqsCTQS":
+                prev_prev = seg.ccontrol_points(first, previous, prev_prev)[-2]
+            previous = seg.cend_point(first, previous)
+
+    def subpath_iterator(self):
+        """Yield Path for each subpath."""
+        start_id = 0
+
+        for i, seg in enumerate(self):
+            if isinstance(seg, (move, Move)):
+                if start_id > -1 and i > 0:  # add previous path (open path)
+                    yield Path(self[start_id:i])
+                start_id = i
+            elif isinstance(seg, (zoneClose, ZoneClose)):  # add current path (closed)
+                yield Path(self[start_id : i + 1])
+                start_id = -1
+            elif i == len(self) - 1 and start_id > -1:  # add last path (open)
+                yield Path(self[start_id:])
+
+    def to_absolute(self):
+        """Convert this path to use only absolute coordinates"""
+        return self._to_absolute(True)
+
+    def to_non_shorthand(self) -> Path:
+        """Convert this path to use only absolute non-shorthand coordinates
+
+        .. versionadded:: 1.1"""
+        return self._to_absolute(False)
+
+    def _to_absolute(self, shorthand: bool) -> Path:
+        """Make entire Path absolute.
+
+        Args:
+            shorthand (bool): If false, then convert all shorthand commands to
+                non-shorthand.
+
+        Returns:
+            Path: the input path, converted to absolute coordinates.
+        """
+
+        abspath = Path()
+
+        previous = 0j
+        first = 0j
+        seg: PathCommand
+        for seg in self:
+            if seg.letter in "mM":
+                first = seg.cend_point(first, previous)
+
+            if shorthand:
+                abspath.append(seg.to_absolute(previous))
+            else:
+                if abspath and abspath[-1].letter in "QC":
+                    prev_control = list(abspath[-1].control_points(0, 0, 0))[-2]
+                else:
+                    prev_control = previous
+
+                abspath.append(seg.to_non_shorthand(previous, prev_control))
+
+            previous = seg.cend_point(first, previous)
+
+        return abspath
+
+    def to_relative(self):
+        """Convert this path to use only relative coordinates"""
+        abspath = Path()
+
+        previous = 0j
+        first = 0j
+        seg: PathCommand
+        for seg in self:
+            if seg.letter in "mM":
+                first = seg.cend_point(first, previous)
+
+            abspath.append(seg.to_relative(previous))
+            previous = seg.cend_point(first, previous)
+
+        return abspath
+
+    def __str__(self):
+        return " ".join([str(seg) for seg in self])
+
+    @staticmethod
+    def __add_helper__(other):
+        """Prepare a path for adding (either add or iadd)"""
+        if isinstance(other, str):
+            other = Path(other)
+        return other
+
+    def __iadd__(self, value):
+        return super().__iadd__(self.__add_helper__(value))
+
+    def __add__(self, other):
+        acopy = copy.deepcopy(self)
+        other = self.__add_helper__(other)
+        if isinstance(other, list):
+            acopy.extend(other)
+        return acopy
+
+    def to_arrays(self):
+        """Returns path in format of parsePath output, returning arrays of absolute
+        command data
+
+        .. deprecated:: 1.0
+            This is compatibility function for older API. Should not be used in new code
+
+        """
+        return [[seg.letter, list(seg.args)] for seg in self.to_non_shorthand()]
+
+    def to_superpath(self):
+        """Convert this path into a cubic super path"""
+        return CubicSuperPath(self)
+
+    def copy(self):
+        """Make a copy"""
+        return copy.deepcopy(self)
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, type, value, traceback):
+        if self.callback is not None:
+            self.callback(self)  # pylint: disable=not-callable
+
+
+class CubicSuperPath(list):
+    """
+    A conversion of a path into a predictable list of cubic curves which
+    can be operated on as a list of simplified instructions.
+
+    When converting back into a path, all lines, arcs etc will be converted
+    to curve instructions.
+
+    Structure is held as [SubPath[(point_a, bezier, point_b), ...], ...]
+    """
+
+    def __init__(self, items):
+        super().__init__()
+        self._closed = True
+        self._prev = 0j
+        self._prev_prev = 0j
+
+        if isinstance(items, str):
+            items = Path(items)
+
+        if isinstance(items, Path):
+            for item in items:
+                self.append_path_command(item)
+            return
+
+        for item in items:
+            self.append(item)
+
+    def __str__(self):
+        return str(self.to_path())
+
+    def append_node_with_handles(self, command: List[Tuple[float, float]]):
+        """First item: left handle, second item: node coords,
+        third item: right handle"""
+        if self._closed:
+            # Closed means that the previous segment is closed so we need a new one
+            # We always append to the last open segment. CSP starts out closed.
+            self._closed = False
+            super().append([])
+
+        self[-1].append(command)
+        self._prev_prev = command[0][0] + command[0][1] * 1j
+        self._prev = command[1][0] + command[1][1] * 1j
+
+    def append_path_command(self, command: PathCommand):
+        """Append a path command.
+
+        For ordinary commands:
+
+        ..code ::
+
+            old last entry -> [[.., ..], [.., ..], [x1, y1]]
+            new last entry -> [[x2, y2], [x3, y3], [x3, y3]]
+
+        The last tuple is duplicated (retracted handle): either it's the last command
+        of the subpath, then the handle will stay retracted, or it will be replaced
+        with the next path command.
+        """
+        if command.letter in "mM":
+            carg = command.cend_point(self._first, self._prev)
+            arg = Vector2d.c2t(carg)
+            super().append([[arg[:], arg[:], arg[:]]])
+            self._prev = self._prev_prev = carg
+            self._closed = False
+            return
+        if command.letter in "zZ" and self:
+            # This duplicates the first segment to 'close' the path
+            self[-1].append([self[-1][0][0][:], self[-1][0][1][:], self[-1][0][2][:]])
+            # Then adds a new subpath for the next shape (if any)
+            # self._closed = True
+            self._prev = self._first
+            return
+        if command.letter in "aA":
+            # Arcs are made up of (possibly) more than one curve, depending on their
+            # angle (approximated)
+            for arc_curve in command.to_curves(self._prev, self._prev_prev):
+                self.append_path_command(arc_curve)
+            return
+        # Handle regular curves.
+
+        if self._closed:
+            # Previous segment is closed. Append a new segment first.
+            self._closed = False
+            super().append([])
+
+        cp1, cp2, cp3 = command.ccurve_points(0j, self._prev, self._prev_prev)
+
+        item = [Vector2d.c2t(cp1), Vector2d.c2t(cp2), Vector2d.c2t(cp3)]
+        self._prev = cp3
+        if not command.letter in "QT":
+            self._prev_prev = cp2
+        else:
+            self._prev_prev = command.ccontrol_points(0j, self._prev, self._prev_prev)[
+                0
+            ]
+
+        if self[-1]:  # There exists a previous segment, replace its outgoing handle.
+            self[-1][-1][-1] = item[0]
+        # Append the segment with the last coordinate (node pos) repeated.
+        self[-1].append(item[1:] + [item[-1][:]])
+
+    def append(self, item):
+        """Append a segment/node to the superpath and update the internal state.
+
+        item may be specified in any of the following formats:
+
+        - PathCommand
+        - [str, List[float]] - A path command letter and its arguments
+        - [[float, float], [float, float], [float, float]] - Incoming handle, node,
+           outgoing handle.
+        - List[[float, float], [float, float], [float, float]] - An entire subpath.
+
+
+        """
+        if isinstance(item, list) and len(item) == 2 and isinstance(item[0], str):
+            item = PathCommand.letter_to_class(item[0])(*item[1])
+        if isinstance(item, PathCommand):
+            self.append_path_command(item)
+            return
+
+        if isinstance(item, list):
+            # Item is a subpath: List[Handle, node, Handle]. Just append the
+            # subpath, and update the prev/ prev_prev positions.
+            if (
+                (len(item) != 3 or not all(len(bit) == 2 for bit in item))
+                and len(item[0]) == 3
+                and all(len(bit) == 2 for bit in item[0])
+            ):
+                super().append(self._clean(item))
+
+            elif len(item) == 3 and all(len(bit) == 2 for bit in item):
+                # Item is already a csp segment [Handle, node, Handle].
+                if self._closed:
+                    # Closed means that the previous segment is closed so we need a new
+                    # one.
+                    # We always append to the last open segment. CSP starts out closed.
+                    self._closed = False
+                    super().append([])
+
+                # Item is already a csp segment and has already been shifted.
+                self[-1].append([i.copy() for i in item])
+            else:
+                raise ValueError(f"Unknown super curve list format: {item}")
+
+            self._prev_prev = Vector2d.t2c(self[-1][-1][0])
+            self._prev = Vector2d.t2c(self[-1][-1][1])
+        else:
+            raise ValueError(f"Unknown super curve list format: {item}")
+
+    def _clean(self, lst):
+        """Recursively clean lists so they have the same type"""
+        if isinstance(lst, (tuple, list)):
+            return [self._clean(child) for child in lst]
+        return lst
+
+    @property
+    def _first(self):
+        try:
+            return self[-1][0][0][0] + self[-1][0][0][1] * 1j
+        except IndexError:
+            return 0 + 0j
+
+    def to_path(self, curves_only=False, rtol=1e-5, atol=1e-8):
+        """Convert the super path back to an svg path
+
+        Arguments: see :func:`to_segments` for parameters"""
+        return Path(list(self.to_segments(curves_only, rtol, atol)))
+
+    def to_segments(self, curves_only=False, rtol=1e-5, atol=1e-8):
+        """Generate a set of segments for this cubic super path
+
+        Arguments:
+            curves_only (bool, optional): If False, curves that can be represented
+                by Lineto / ZoneClose commands, will be. Defaults to False.
+            rtol (float, optional): relative tolerance, passed to :func:`is_line` and
+                :func:`inkex.transforms.ImmutableVector2d.is_close` for checking if a
+                line can be replaced by a ZoneClose command. Defaults to 1e-5.
+
+                .. versionadded:: 1.2
+            atol: absolute tolerance, passed to :func:`is_line` and
+                :func:`inkex.transforms.ImmutableVector2d.is_close`. Defaults to 1e-8.
+
+                .. versionadded:: 1.2"""
+        for subpath in self:
+            previous = []
+            for segment in subpath:
+                if not previous:
+                    yield Move(Vector2d(segment[1]))
+                elif self.is_line(previous, segment, rtol, atol) and not curves_only:
+                    if segment is subpath[-1] and Vector2d(segment[1]).is_close(
+                        Vector2d(subpath[0][1]), rtol, atol
+                    ):
+                        yield ZoneClose()
+                    else:
+                        yield Line(Vector2d(segment[1]))
+                else:
+                    yield Curve(
+                        Vector2d(previous[2]),
+                        Vector2d(segment[0]),
+                        Vector2d(segment[1]),
+                    )
+                previous = segment
+
+    def transform(self, transform):
+        """Apply a transformation matrix to this super path"""
+        return self.to_path().transform(transform).to_superpath()
+
+    @staticmethod
+    def is_on(pt_a, pt_b, pt_c, tol=1e-8):
+        """Checks if point pt_a is on the line between points pt_b and pt_c
+
+        .. versionadded:: 1.2"""
+        return CubicSuperPath.collinear(pt_a, pt_b, pt_c, tol) and (
+            CubicSuperPath.within(pt_a[0], pt_b[0], pt_c[0])
+            if abs(pt_a[0] - pt_b[0]) > 1e-13
+            else CubicSuperPath.within(pt_a[1], pt_b[1], pt_c[1])
+        )
+
+    @staticmethod
+    def collinear(pt_a, pt_b, pt_c, tol=1e-8):
+        """Checks if points pt_a, pt_b, pt_c lie on the same line,
+        i.e. that the cross product (b-a) x (c-a) < tol
+
+        .. versionadded:: 1.2"""
+        return (
+            abs(
+                (pt_b[0] - pt_a[0]) * (pt_c[1] - pt_a[1])
+                - (pt_c[0] - pt_a[0]) * (pt_b[1] - pt_a[1])
+            )
+            < tol
+        )
+
+    @staticmethod
+    def within(val_b, val_a, val_c):
+        """Checks if float val_b is between val_a and val_c
+
+        .. versionadded:: 1.2"""
+        return val_a <= val_b <= val_c or val_c <= val_b <= val_a
+
+    @staticmethod
+    def is_line(previous, segment, rtol=1e-5, atol=1e-8):
+        """Check whether csp segment (two points) can be expressed as a line has
+        retracted handles or the handles can be retracted without loss of information
+        (i.e. both handles lie on the line)
+
+        .. versionchanged:: 1.2
+            Previously, it was only checked if both control points have retracted
+            handles. Now it is also checked if the handles can be retracted without
+            (visible) loss of information (i.e. both handles lie on the line connecting
+            the nodes).
+
+        Arguments:
+            previous: first node in superpath notation
+            segment: second node in superpath notation
+            rtol (float, optional): relative tolerance, passed to
+                :func:`inkex.transforms.ImmutableVector2d.is_close` for checking handle
+                retraction. Defaults to 1e-5.
+
+                .. versionadded:: 1.2
+            atol (float, optional): absolute tolerance, passed to
+                :func:`inkex.transforms.ImmutableVector2d.is_close` for checking handle
+                retraction and
+                :func:`inkex.paths.CubicSuperPath.is_on` for checking if all points
+                (nodes + handles) lie on a line. Defaults to 1e-8.
+
+                .. versionadded:: 1.2
+        """
+
+        retracted = isclose(
+            Vector2d(previous[1]), Vector2d(previous[2]), rel_tol=rtol, abs_tol=atol
+        ) and isclose(
+            Vector2d(segment[0]), Vector2d(segment[1]), rel_tol=rtol, abs_tol=atol
+        )
+
+        if retracted:
+            return True
+
+        # Can both handles be retracted without loss of information?
+        # Definitely the case if the handles lie on the same line as the two nodes and
+        # in the correct order
+        # E.g. cspbezsplitatlength outputs non-retracted handles when splitting a
+        # straight line
+        return CubicSuperPath.is_on(
+            segment[0], segment[1], previous[2], atol
+        ) and CubicSuperPath.is_on(previous[2], previous[1], segment[0], atol)

extensions/botbox3000/deps/inkex/paths/quadratic.py

@@ -0,0 +1,456 @@
+# coding=utf-8
+#
+# Copyright (C) 2018 Martin Owens <doctormo@gmail.com>
+# Copyright (C) 2023 Jonathan Neuhauser <jonathan.neuhauser@outlook.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.
+#
+"""Quadratic and TepidQuadratic path commands"""
+
+from __future__ import annotations
+
+from typing import overload, Tuple, Callable, Union
+from math import sqrt
+
+import numpy as np
+
+from ..transforms import quadratic_extrema, Transform, ComplexLike
+
+from .interfaces import (
+    AbsolutePathCommand,
+    RelativePathCommand,
+    BezierComputationMixin,
+    BezierArcComputationMixin,
+    LengthSettings,
+)
+
+
+class QuadraticMixin(BezierComputationMixin, BezierArcComputationMixin):
+    # pylint: disable=unused-argument
+    ccontrol_points: Callable[[complex, complex, complex], Tuple[complex, ...]]
+
+    def _cderivative(
+        self, first: complex, prev: complex, prev_control: complex, t: float, n: int = 1
+    ) -> complex:
+        points = self.ccontrol_points(first, prev, prev_control)
+        if n == 1:
+            return 2 * ((points[0] - prev) * (1 - t) + (points[1] - points[0]) * t)
+        if n == 2:
+            return 2 * (prev - 2 * points[0] + points[1])
+        if n > 2:
+            return 0j
+        raise ValueError("n should be a positive integer.")
+
+    def _cunit_tangent(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        return self.bezier_unit_tangent(prev, prev_control, t)
+
+    def _cpoint(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> complex:
+        control, end = self.ccontrol_points(first, prev, prev_control)
+        return (1 - t) ** 2 * prev + 2 * t * (1 - t) * control + t**2 * end
+
+    # TODO maybe better treatment of degenerate beziers from
+    # https://github.com/linebender/kurbo/blob/c229a914d303c5989c9e6b1d766def2df27a8185/src/quadbez.rs#L239
+    # Ported from https://github.com/mathandy/svgpathtools/blob/19df25b99b405ec4fc7616b58384eca7879b6fd4/svgpathtools/path.py#L919
+    # (MIT licensed)
+    def _length(
+        self,
+        first: complex,
+        prev: complex,
+        prev_control: complex,
+        t0: float = 0,
+        t1: float = 1,
+        settings=LengthSettings(),
+    ) -> float:
+        control, end = self.ccontrol_points(first, prev, prev_control)
+        a = prev - 2 * control + end
+        b = 2 * (control - prev)
+
+        if abs(a) < 1e-12:
+            s = abs(b) * (t1 - t0)
+        else:
+            c2 = 4 * (a.real**2 + a.imag**2)
+            c1 = 4 * (a.real * b.real + a.imag * b.imag)
+            c0 = b.real**2 + b.imag**2
+
+            beta = c1 / (2 * c2)
+            gamma = c0 / c2 - beta**2
+
+            dq1_mag = sqrt(c2 * t1**2 + c1 * t1 + c0)
+            dq0_mag = sqrt(c2 * t0**2 + c1 * t0 + c0)
+            # this implicitly handles division by zero
+            try:
+                logarand = (sqrt(c2) * (t1 + beta) + dq1_mag) / (
+                    sqrt(c2) * (t0 + beta) + dq0_mag
+                )
+
+                s = (
+                    (t1 + beta) * dq1_mag
+                    - (t0 + beta) * dq0_mag
+                    + gamma * sqrt(c2) * np.log(logarand)
+                ) / 2
+            except ZeroDivisionError:
+                s = np.nan
+            if np.isnan(s):
+                tstar = abs(b) / (2 * abs(a))
+                if t1 < tstar:
+                    return abs(a) * (t0**2 - t1**2) - abs(b) * (t0 - t1)
+                elif tstar < t0:
+                    return abs(a) * (t1**2 - t0**2) - abs(b) * (t1 - t0)
+                else:
+                    return (
+                        abs(a) * (t1**2 + t0**2)
+                        - abs(b) * (t1 + t0)
+                        + abs(b) ** 2 / (2 * abs(a))
+                    )
+        return s
+
+    def _abssplit(
+        self, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Quadratic, Quadratic]:
+        """Split this Quadratic and return two Quadratics using DeCasteljau's algorithm"""
+        p1, p2 = self.ccontrol_points(0j, prev, prev_control)
+        p1_1 = (1 - t) * prev + t * p1
+        p1_2 = (1 - t) * p1 + t * p2
+        p2_1 = (1 - t) * p1_1 + t * p1_2
+        return Quadratic(p1_1, p2_1), Quadratic(p1_2, p2)
+
+    def _relsplit(self, prev: complex, prev_control: complex, t: float):
+        """Split this curve and return two curves"""
+        c1abs, c2abs = self._abssplit(prev, prev_control, t)
+        return c1abs.to_relative(prev), c2abs.to_relative(c1abs.arg2)
+
+
+class Quadratic(QuadraticMixin, AbsolutePathCommand):
+    """Absolute Quadratic Curved Line segment"""
+
+    letter = "Q"
+    nargs = 4
+
+    arg1: complex
+    """The (absolute) control point"""
+
+    arg2: complex
+    """The (absolute) end point"""
+
+    @property
+    def x2(self) -> float:
+        """x coordinate of the (absolute) control point"""
+        return self.arg1.real
+
+    @property
+    def y2(self) -> float:
+        """y coordinate of the (absolute) control point"""
+        return self.arg1.imag
+
+    @property
+    def x3(self) -> float:
+        """x coordinate of the (absolute) end point"""
+        return self.arg2.real
+
+    @property
+    def y3(self) -> float:
+        """y coordinate of the (absolute) end point"""
+        return self.arg2.imag
+
+    @property
+    def args(self):
+        return self.x2, self.y2, self.x3, self.y3
+
+    @overload
+    def __init__(self, x2: ComplexLike, x3: ComplexLike): ...
+
+    @overload
+    def __init__(self, x2: float, y2: float, x3: float, y3: float): ...
+
+    def __init__(self, x2, y2, x3=None, y3=None):
+        if x3 is not None:
+            self.arg1 = x2 + y2 * 1j
+            self.arg2 = x3 + y3 * 1j
+        else:
+            self.arg1, self.arg2 = complex(x2), complex(y2)
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        x1, x2, x3 = last_two_points[-1].real, self.x2, self.x3
+        y1, y2, y3 = last_two_points[-1].imag, self.y2, self.y3
+
+        if not (x1 in bbox.x and x2 in bbox.x and x3 in bbox.x):
+            bbox.x += quadratic_extrema(x1, x2, x3)
+
+        if not (y1 in bbox.y and y2 in bbox.y and y3 in bbox.y):
+            bbox.y += quadratic_extrema(y1, y2, y3)
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (self.arg1, self.arg2)
+
+    def to_relative(self, prev: ComplexLike) -> quadratic:
+        return quadratic(self.arg1 - prev, self.arg2 - prev)
+
+    def transform(self, transform: Transform) -> Quadratic:
+        return Quadratic(
+            transform.capply_to_point(self.arg1), transform.capply_to_point(self.arg2)
+        )
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg2
+
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        pt1 = 1.0 / 3 * prev + 2.0 / 3 * self.arg1
+        pt2 = 2.0 / 3 * self.arg1 + 1.0 / 3 * self.arg2
+        return pt1, pt2, self.arg2
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> Quadratic:
+        prev = complex(prev)
+        return Quadratic(self.x2, self.y2, prev.real, prev.imag)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Quadratic, Quadratic]:
+        return self._abssplit(prev, prev_control, t)
+
+
+class quadratic(QuadraticMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative quadratic line segment"""
+
+    letter = "q"
+    nargs = 4
+
+    arg1: complex
+    """The (relative) control point"""
+
+    arg2: complex
+    """The (relative) end point"""
+
+    @property
+    def dx2(self) -> float:
+        """x coordinate of the (relative) control point"""
+        return self.arg1.real
+
+    @property
+    def dy2(self) -> float:
+        """y coordinate of the (relative) control point"""
+        return self.arg1.imag
+
+    @property
+    def dx3(self) -> float:
+        """x coordinate of the (relative) end point"""
+        return self.arg2.real
+
+    @property
+    def dy3(self) -> float:
+        """y coordinate of the (relative) end point"""
+        return self.arg2.imag
+
+    @property
+    def args(self):
+        return self.dx2, self.dy2, self.dx3, self.dy3
+
+    @overload
+    def __init__(self, dx2: ComplexLike, dx3: ComplexLike): ...
+
+    @overload
+    def __init__(self, dx2: float, dy2: float, dx3: float, dy3: float): ...
+
+    def __init__(self, dx2, dy2, dx3=None, dy3=None):
+        if dx3 is not None:
+            self.arg1 = dx2 + dy2 * 1j
+            self.arg2 = dx3 + dy3 * 1j
+        else:
+            self.arg1, self.arg2 = complex(dx2), complex(dy2)
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (self.arg1 + prev, self.arg2 + prev)
+
+    def to_absolute(self, prev: ComplexLike) -> Quadratic:
+        return Quadratic(self.arg1 + prev, self.arg2 + prev)
+
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        pt1 = 1.0 / 3 * prev + 2.0 / 3 * (prev + self.arg1)
+        pt2 = 2.0 / 3 * (prev + self.arg1) + 1.0 / 3 * (prev + self.arg2)
+        return pt1, pt2, prev + self.arg2
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg2 + prev
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> quadratic:
+        return quadratic(-self.arg2 + self.arg1, -self.arg2)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[quadratic, quadratic]:
+        return self._relsplit(prev, prev_control, t)
+
+
+class TepidQuadratic(QuadraticMixin, AbsolutePathCommand):
+    """Continued Quadratic Line segment"""
+
+    letter = "T"
+    nargs = 2
+
+    arg1: complex
+    """The (absolute) control point"""
+
+    @property
+    def x3(self) -> float:
+        """x coordinate of the (absolute) end point"""
+        return self.arg1.real
+
+    @property
+    def y3(self) -> float:
+        """y coordinate of the (absolute) end point"""
+        return self.arg1.imag
+
+    @property
+    def args(self):
+        return self.x3, self.y3
+
+    @overload
+    def __init__(self, x3: ComplexLike): ...
+
+    @overload
+    def __init__(self, x3: float, y3: float): ...
+
+    def __init__(self, x3, y3=None):
+        if y3 is not None:
+            self.arg1 = x3 + y3 * 1j
+        else:
+            self.arg1 = complex(x3)
+
+    def update_bounding_box(self, first, last_two_points, bbox):
+        self.to_quadratic(last_two_points[-1], last_two_points[-2]).update_bounding_box(
+            first, last_two_points, bbox
+        )
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (2 * prev - prev_prev, self.arg1)
+
+    def to_non_shorthand(
+        self, prev: ComplexLike, prev_control: ComplexLike
+    ) -> Quadratic:
+        return self.to_quadratic(prev, prev_control)
+
+    def to_relative(self, prev: ComplexLike) -> tepidQuadratic:
+        return tepidQuadratic(self.arg1 - prev)
+
+    def transform(self, transform: Transform) -> TepidQuadratic:
+        return TepidQuadratic(transform.capply_to_point(self.arg1))
+
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        qp1 = 2 * prev - prev_prev
+        qp2 = self.arg1
+        pt1 = 1.0 / 3 * prev + 2.0 / 3 * qp1
+        pt2 = 2.0 / 3 * qp1 + 1.0 / 3 * qp2
+        return pt1, pt2, qp2
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg1
+
+    def to_quadratic(self, prev: ComplexLike, prev_prev: ComplexLike) -> Quadratic:
+        """Convert this continued quadratic into a full quadratic"""
+        return Quadratic(
+            *self.ccontrol_points(complex(prev), complex(prev), complex(prev_prev))
+        )
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> TepidQuadratic:
+        return TepidQuadratic(prev)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[Quadratic, Quadratic]:
+        return self._abssplit(prev, prev_control, t)
+
+
+class tepidQuadratic(QuadraticMixin, RelativePathCommand):  # pylint: disable=invalid-name
+    """Relative continued quadratic line segment"""
+
+    letter = "t"
+    nargs = 2
+
+    arg1: complex
+    """The (relative) control point"""
+
+    @property
+    def dx3(self) -> float:
+        """x coordinate of the (relative) end point"""
+        return self.arg1.real
+
+    @property
+    def dy3(self) -> float:
+        """y coordinate of the (relative) end point"""
+        return self.arg1.imag
+
+    @property
+    def args(self):
+        return self.dx3, self.dy3
+
+    @overload
+    def __init__(self, dx3: ComplexLike): ...
+
+    @overload
+    def __init__(self, dx3: float, dy3: float): ...
+
+    def __init__(self, dx3, dy3=None):
+        if dy3 is not None:
+            self.arg1 = dx3 + dy3 * 1j
+        else:
+            self.arg1 = complex(dx3)
+
+    def ccontrol_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        return (2 * prev - prev_prev, self.arg1 + prev)
+
+    def ccurve_points(
+        self, first: complex, prev: complex, prev_prev: complex
+    ) -> Tuple[complex, ...]:
+        qp1 = 2 * prev - prev_prev
+        qp2 = self.arg1 + prev
+        pt1 = 1.0 / 3 * prev + 2.0 / 3 * qp1
+        pt2 = 2.0 / 3 * qp1 + 1.0 / 3 * qp2
+        return pt1, pt2, qp2
+
+    def to_absolute(self, prev: ComplexLike) -> TepidQuadratic:
+        return TepidQuadratic(self.arg1 + prev)
+
+    def to_non_shorthand(
+        self, prev: ComplexLike, prev_control: ComplexLike
+    ) -> Quadratic:
+        return self.to_absolute(prev).to_non_shorthand(prev, prev_control)
+
+    def cend_point(self, first: complex, prev: complex) -> complex:
+        return self.arg1 + prev
+
+    def reverse(self, first: ComplexLike, prev: ComplexLike) -> tepidQuadratic:
+        return tepidQuadratic(-self.arg1)
+
+    def _split(
+        self, first: complex, prev: complex, prev_control: complex, t: float
+    ) -> Tuple[quadratic, quadratic]:
+        return self._relsplit(prev, prev_control, t)