svgpath2mpl.py

# -*- coding: utf-8 -*-
"""
SVGPATH2MPL
~~~~~~~~~~~
Parse SVG path definition strings into matplotlib Path objects.
A path in SVG is defined by a 'path' element which contains a
``d="(path data)"`` attribute that contains moveto, line, curve (both
cubic and quadratic Béziers), arc and closepath instructions. See the SVG
Path specification at <https://www.w3.org/TR/SVG/paths.html>.

:copyright: (c) 2016, Nezar Abdennur.
:license: BSD.

"""
from __future__ import division, print_function
from math import sin, cos, sqrt, degrees, radians, acos
import re

from matplotlib.path import Path
import matplotlib.transforms as transforms
import numpy as np

__version__ = '1.0.0'
__all__ = ['parse_path']


COMMANDS = set('MmZzLlHhVvCcSsQqTtAa')
UPPERCASE = set('MZLHVCSQTA')

COMMAND_RE = re.compile(r"([MmZzLlHhVvCcSsQqTtAa])")
FLOAT_RE = re.compile(r"[-+]?[0-9]*\.?[0-9]+(?:[eE][-+]?[0-9]+)?")

COMMAND_CODES = {
    'M': (Path.MOVETO,),    # moveto
    'L': (Path.LINETO,),    # line
    'H': (Path.LINETO,),    # shorthand for horizontal line
    'V': (Path.LINETO,),    # shorthand for vertical line
    'Q': (Path.CURVE3,)*2,  # quadratic bezier
    'T': (Path.CURVE3,)*2,  # shorthand for smooth quadratic bezier
    'C': (Path.CURVE4,)*3,  # cubic bezier
    'S': (Path.CURVE4,)*3,  # shorthand for smooth cubic bezier
    'Z': (Path.CLOSEPOLY,), # closepath
    'A': None               # arc
}

PARAMS = {
    'M': 2, # moveto
    'L': 2, # line
    'H': 1, # shorthand for horizontal line
    'V': 1, # shorthand for vertical line
    'Q': 4, # quadratic bezier
    'T': 4, # shorthand for smooth quadratic bezier
    'C': 6, # cubic bezier
    'S': 6, # shorthand for smooth cubic bezier
    'Z': 0, # closepath
    'A': 7  # arc
}


def endpoint_to_center(start, radius, rotation, large, sweep, end):
    """
    Translates the "endpoint" parameterization of an elliptical arc used by
    the SVG spec to the "center" parameterization.

    Parameters
    ----------
    start : complex
        Starting point (x1, y1).
    radius : complex
        Two elliptical radii (rx, ry).
    rotation : float
        Angle from the x-axis of the current coordinate system to the x-axis of
        the ellipse.
    large : bool
        False if an arc spanning < 180 degrees is to be drawn, True if an arc
        spanning >= 180 degrees is to be drawn.
    sweep : bool
        If sweep-flag is True, then the arc will be drawn in a "positive-angle"
        direction from start to end.
    end : complex
        End point (x2, y2).

    Returns
    -------
    radius : complex
        Radii of the ellipse (rx, ry), potentially corrected if out-of-range.
    center : complex
        Center of the ellipse (xc, yc).
    theta1, theta2 : float
        Start and end angles of an arc on the unit circle prior to being
        stretched and rotated into an elliptical arc.

    Notes
    -----
    See [1]_, `svg.path <https://github.com/regebro/svg.path>`_, and this
    `SO question <https://stackoverflow.com/q/197649>`_.

    References
    ----------

    .. [1] http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes

    """
    # Step 1: compute x1prim, y1prim
    cosr = cos(radians(rotation))
    sinr = sin(radians(rotation))
    dx = (start.real - end.real) / 2
    dy = (start.imag - end.imag) / 2
    x1prim = cosr * dx + sinr * dy
    y1prim = -sinr * dx + cosr * dy
    x1prim_sq = x1prim * x1prim
    y1prim_sq = y1prim * y1prim

    rx = abs(radius.real)
    ry = abs(radius.imag)
    rx_sq = rx * rx
    ry_sq = ry * ry

    # Correct out of range radii
    radius_scale = (x1prim_sq / rx_sq) + (y1prim_sq / ry_sq)
    if radius_scale > 1:
        radius_scale = sqrt(radius_scale)
        rx *= radius_scale
        ry *= radius_scale
        rx_sq = rx * rx
        ry_sq = ry * ry
    else:
        # SVG spec only scales UP
        radius_scale = 1
    radius = rx + ry * 1j

    # Step 2: compute cxprim, cyprim
    t1 = rx_sq * y1prim_sq
    t2 = ry_sq * x1prim_sq
    c = sqrt(abs((rx_sq * ry_sq - t1 - t2) / (t1 + t2)))
    if large == sweep:
        c = -c
    cxprim = c * rx * y1prim / ry
    cyprim = -c * ry * x1prim / rx

    # Step 3: compute the center from cxprim, cyprim
    center = complex(
        (cosr * cxprim - sinr * cyprim) + ((start.real + end.real) / 2),
        (sinr * cxprim + cosr * cyprim) + ((start.imag + end.imag) / 2),
    )

    # Step 4: compute theta and delta_theta
    ux = (x1prim - cxprim) / rx
    uy = (y1prim - cyprim) / ry
    vx = (-x1prim - cxprim) / rx
    vy = (-y1prim - cyprim) / ry
    n = sqrt(ux * ux + uy * uy)
    p = ux
    theta = degrees(acos(p / n))
    if uy < 0:
        theta = -theta
    theta = theta % 360

    n = sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy))
    p = ux * vx + uy * vy
    d = p / n
    # In certain cases the above calculation can through inaccuracies
    # become just slightly out of range, f ex -1.0000000000000002.
    d = np.clip(d, -1.0, 1.0)

    delta = degrees(acos(d))
    if (ux * vy - uy * vx) < 0:
        delta = -delta
    delta = delta % 360
    if not sweep:
        if delta > 0:
            delta -= 360

    return radius, center, theta, theta + delta


def arc_path(start, radius, rotation, large, sweep, end):
    """
    Generate an elliptical arc path given an endpoint parameterization.

    Uses matplotlib to draw the arc using quadratic Bezier curves.

    Parameters
    ----------
    start : complex
        Starting point (x1, y1).
    radius : complex
        Two elliptical radii (rx, ry).
    rotation : float
        Angle from the x-axis of the current coordinate system to the x-axis of
        the ellipse.
    large : bool
        False if an arc spanning < 180 degrees is to be drawn, True if an arc
        spanning >= 180 degrees is to be drawn.
    sweep : bool
        If sweep-flag is True, then the arc will be drawn in a "positive-angle"
        direction from start to end.
    end : complex
        End point (x2, y2).

    Returns
    -------
    codes : array (n,)
        Command codes
    verts : array (n,2)
        Vertices

    Notes
    -----
    We first perform a conversion to center parameterization and generate
    a circular arc at the origin. Then we apply scaling, translation and
    rotation.

    One can think of an ellipse as a circle that has been stretched and then
    rotated. Start by making an arc along the unit circle from `theta1` to
    `theta2`, centered at `center`. Then scale the circle along the x and y
    axes according to the given radii. Finally, rotate the arc around the
    center through the given angle `rotation`.

    """
    radius, center, theta1, theta2 = endpoint_to_center(
        start,
        radius,
        rotation,
        large,
        sweep,
        end
    )

    # Create an arc on the unit circle
    # Matplotlib does this using CURVE4 operations
    # https://matplotlib.org/stable/_modules/matplotlib/path.html#Path.arc
    if theta2 > theta1:
        arc = Path.arc(theta1=theta1, theta2=theta2)
        reverse_path = False
    else:
        arc = Path.arc(theta1=theta2, theta2=theta1)
        reverse_path = True

    # Transform it into an elliptical arc:
    # * scale the minor and major axes
    # * translate it to the center
    # * rotate the x-axis of the ellipse from the x-axis of the current
    #   coordinate system
    trans = (
        transforms.Affine2D()
        .scale(radius.real, radius.imag)
        .translate(center.real, center.imag)
        .rotate_deg_around(center.real, center.imag, rotation)
    )
    arc = trans.transform_path(arc)
    codes = np.array(arc.codes)
    verts = np.array(arc.vertices)

    # Make sure we are drawing from start to end
    if reverse_path:
        verts = verts[::-1, :]

    # Change the initial MOVETO operation into a LINETO to connect to the
    # previous path
    codes[0] = Path.LINETO

    return codes, verts


def _tokenize_path(pathdef):
    for x in COMMAND_RE.split(pathdef):
        if x in COMMANDS:
            yield x
        for token in FLOAT_RE.findall(x):
            yield token


def _next_pos(elements):
    return float(elements.pop()) + float(elements.pop()) * 1j


def _parse_path(pathdef, current_pos):
    # In the SVG specs, initial movetos are absolute, even if specified as 'm'.
    # This is the default behavior here as well. But if you pass in a
    # current_pos variable, the initial moveto will be relative to that
    # current_pos. This is useful.
    elements = list(_tokenize_path(pathdef))
    # Reverse for easy use of .pop()
    elements.reverse()

    start_pos = None
    command = None

    while elements:

        # 1. Determine the current command

        if elements[-1] in COMMANDS:
            # New command.
            last_command = command  # Used by S and T
            command = elements.pop()
            absolute = command in UPPERCASE
            command = command.upper()
        else:
            # Implicit command.
            # If this element starts with numbers, it is an implicit command
            # and we don't change the command. Check that it's allowed:
            if command is None:
                raise ValueError(
                    "Unallowed implicit command in {}, position {}".format(
                        pathdef, len(pathdef.split()) - len(elements))
                    )
            last_command = command  # Used by S and T

        # 2. Parse the current command

        # MOVETO
        if command == 'M':
            pos = _next_pos(elements)
            if absolute:
                current_pos = pos
            else:
                current_pos += pos

            # when M is called, reset start_pos
            # This behavior of Z is defined in svg spec:
            # http://www.w3.org/TR/SVG/paths.html#PathDataClosePathCommand
            start_pos = current_pos

            yield COMMAND_CODES['M'], [(current_pos.real, current_pos.imag)]

            # Implicit moveto commands are treated as lineto commands.
            # So we set command to lineto here, in case there are
            # further implicit commands after this moveto.
            command = 'L'

        # CLOSEPATH
        elif command == 'Z':
            # path closure
            if current_pos != start_pos:
                verts = [(start_pos.real, start_pos.imag)]
                yield COMMAND_CODES['L'], verts

            # mpl.Path: a point is required but ignored
            verts = [(start_pos.real, start_pos.imag)]
            yield COMMAND_CODES['Z'], verts

            current_pos = start_pos
            start_pos = None
            command = None  # You can't have implicit commands after closing.

        # LINETO
        elif command == 'L':
            pos = _next_pos(elements)
            if not absolute:
                pos += current_pos
            verts = [(pos.real, pos.imag)]
            yield COMMAND_CODES['L'], verts
            current_pos = pos

        # HORIZONTAL_PATHTO
        elif command == 'H':
            x = elements.pop()
            pos = float(x) + current_pos.imag * 1j
            if not absolute:
                pos += current_pos.real
            verts = [(pos.real, pos.imag)]
            yield COMMAND_CODES['H'], verts
            current_pos = pos

        # VERTICAL_PATHTO
        elif command == 'V':
            y = elements.pop()
            pos = current_pos.real + float(y) * 1j
            if not absolute:
                pos += current_pos.imag * 1j
            verts = [(pos.real, pos.imag)]
            yield COMMAND_CODES['V'], verts
            current_pos = pos

        # CUBIC_BEZIER
        elif command == 'C':
            control1 = _next_pos(elements)
            control2 = _next_pos(elements)
            end = _next_pos(elements)
            if not absolute:
                control1 += current_pos
                control2 += current_pos
                end += current_pos
            verts = [
                 (control1.real, control1.imag),
                 (control2.real, control2.imag),
                 (end.real, end.imag)
            ]
            yield COMMAND_CODES['C'], verts
            current_pos = end

        # SMOOTH_CUBIC_BEZIER
        elif command == 'S':
            # Smooth curve. First control point is the "reflection" of
            # the second control point in the previous path.
            if last_command not in 'CS':
                # If there is no previous command or if the previous command
                # was not an C, c, S or s, assume the first control point is
                # coincident with the current point.
                control1 = current_pos
            else:
                # The first control point is assumed to be the reflection of
                # the second control point on the previous command relative
                # to the current point.
                last_control = control2
                control1 = current_pos + current_pos - last_control
            control2 = _next_pos(elements)
            end = _next_pos(elements)
            if not absolute:
                control2 += current_pos
                end += current_pos
            verts = [
                (control1.real, control1.imag),
                (control2.real, control2.imag),
                (end.real, end.imag)
            ]
            yield COMMAND_CODES['S'], verts
            current_pos = end

        # QUADRATIC_BEZIER
        elif command == 'Q':
            control = _next_pos(elements)
            end = _next_pos(elements)
            if not absolute:
                control += current_pos
                end += current_pos
            verts = [
                (control.real, control.imag),
                (end.real, end.imag)
            ]
            yield COMMAND_CODES['Q'], verts
            current_pos = end

        # SMOOTH_QUADRATIC_BEZIER
        elif command == 'T':
            # Smooth curve. Control point is the "reflection" of
            # the second control point in the previous path.
            if last_command not in 'QT':
                # If there is no previous command or if the previous command
                # was not an Q, q, T or t, assume the first control point is
                # coincident with the current point.
                control = current_pos
            else:
                # The control point is assumed to be the reflection of
                # the control point on the previous command relative
                # to the current point.
                last_control = control
                control = current_pos + current_pos - last_control
            end = _next_pos(elements)
            if not absolute:
                end += current_pos
            verts = [
                (control.real, control.imag),
                (end.real, end.imag)
            ]
            yield COMMAND_CODES['T'], verts
            current_pos = end

        # ELLIPTICAL_ARC
        elif command == 'A':
            radius = _next_pos(elements)
            rotation = float(elements.pop())
            large = float(elements.pop())
            sweep = float(elements.pop())
            end = _next_pos(elements)

            if not absolute:
                end += current_pos

            if current_pos == end:
                # This is equivalent of omitting the segment, so do nothing
                continue
            elif radius.real == 0 or radius.imag == 0:
                # This should be treated as a straight line
                verts = [(end.real, end.imag)]
                yield COMMAND_CODES['L'], verts
            else:
                codes, verts = arc_path(
                    current_pos, radius, rotation, large, sweep, end
                )
                yield codes, verts

            current_pos = end


def parse_path(pathdef, current_pos=0 + 0j):
    """
    Parse an SVG path definition string into a matplotlib Path object.

    Parameters
    ----------
    pathdef : str
        SVG path 'd' attribute, e.g. 'M 100 100 L 300 100 L 200 300 z'.
    current_pos : complex, optional
        Coordinates of the starting position of the path, given as a complex
        number. When provided, an initial moveto operation will be intepreted
        as relative to this position even if given as M.

    Returns
    -------
    :class:`matplotlib.path.Path` instance

    See also
    --------
    matplotlib.path.Path
    matplotlib.patches.PathPatch
    matplotlib.collections.PathCollection
    matplotlib.transforms

    """
    codes = []
    verts = []
    for c, v in _parse_path(pathdef, current_pos):
        codes.extend(c)
        verts.extend(v)
    return Path(verts, codes)