"""

code_type = np.uint8

# Path codes

STOP = code_type(0) # 1 vertex

MOVETO = code_type(1) # 1 vertex

LINETO = code_type(2) # 1 vertex

CURVE3 = code_type(3) # 2 vertices

CURVE4 = code_type(4) # 3 vertices

CLOSEPOLY = code_type(79) # 1 vertex

#: A dictionary mapping Path codes to the number of vertices that the

#: code expects.

NUM_VERTICES_FOR_CODE = {STOP: 1,

MOVETO: 1,

LINETO: 1,

CURVE3: 2,

CURVE4: 3,

CLOSEPOLY: 1}

def __init__(self, vertices, codes=None, _interpolation_steps=1,

closed=False, readonly=False):

"""

vertices = _to_unmasked_float_array(vertices)

_api.check_shape((None, 2), vertices=vertices)

if codes is not None and len(vertices):

codes = np.asarray(codes, self.code_type)

if codes.ndim != 1 or len(codes) != len(vertices):

raise ValueError("'codes' must be a 1D list or array with the "

"same length of 'vertices'. "

f"Your vertices have shape {vertices.shape} "

f"but your codes have shape {codes.shape}")

if len(codes) and codes[0] != self.MOVETO:

raise ValueError("The first element of 'code' must be equal "

f"to 'MOVETO' ({self.MOVETO}). "

f"Your first code is {codes[0]}")

elif closed and len(vertices):

codes = np.empty(len(vertices), dtype=self.code_type)

codes[0] = self.MOVETO

codes[1:-1] = self.LINETO

codes[-1] = self.CLOSEPOLY

self._vertices = vertices

self._codes = codes

self._interpolation_steps = _interpolation_steps

self._update_values()

if readonly:

self._vertices.flags.writeable = False

if self._codes is not None:

self._codes.flags.writeable = False

self._readonly = True

else:

self._readonly = False

@classmethod

def _fast_from_codes_and_verts(cls, verts, codes, internals_from=None):

"""

pth = cls.__new__(cls)

pth._vertices = _to_unmasked_float_array(verts)

pth._codes = codes

pth._readonly = False

if internals_from is not None:

pth._should_simplify = internals_from._should_simplify

pth._simplify_threshold = internals_from._simplify_threshold

pth._interpolation_steps = internals_from._interpolation_steps

else:

pth._should_simplify = True

pth._simplify_threshold = mpl.rcParams['path.simplify_threshold']

pth._interpolation_steps = 1

return pth

@classmethod

def _create_closed(cls, vertices):

"""

v = _to_unmasked_float_array(vertices)

return cls(np.concatenate([v, v[:1]]), closed=True)

def _update_values(self):

self._simplify_threshold = mpl.rcParams['path.simplify_threshold']

self._should_simplify = (

self._simplify_threshold > 0 and

mpl.rcParams['path.simplify'] and

len(self._vertices) >= 128 and

(self._codes is None or np.all(self._codes <= Path.LINETO))

)

@property

def vertices(self):

"""The vertices of the `Path` as an (N, 2) array."""

return self._vertices

@vertices.setter

def vertices(self, vertices):

if self._readonly:

raise AttributeError("Can't set vertices on a readonly Path")

self._vertices = vertices

self._update_values()

@property

def codes(self):

"""

return self._codes

@codes.setter

def codes(self, codes):

if self._readonly:

raise AttributeError("Can't set codes on a readonly Path")

self._codes = codes

self._update_values()

@property

def simplify_threshold(self):

"""

return self._simplify_threshold

@simplify_threshold.setter

def simplify_threshold(self, threshold):

self._simplify_threshold = threshold

@property

def should_simplify(self):

"""

return self._should_simplify

@should_simplify.setter

def should_simplify(self, should_simplify):

self._should_simplify = should_simplify

@property

def readonly(self):

"""

return self._readonly

def copy(self):

"""

return copy.copy(self)

def __deepcopy__(self, memo):

"""

# Deepcopying arrays (vertices, codes) strips the writeable=False flag.

cls = type(self)

memo[id(self)] = p = cls.__new__(cls)

for k, v in self.__dict__.items():

setattr(p, k, copy.deepcopy(v, memo))

p._readonly = False

return p

def deepcopy(self, memo=None):

"""

return copy.deepcopy(self, memo)

@classmethod

def make_compound_path_from_polys(cls, XY):

"""

# for each poly: 1 for the MOVETO, (numsides-1) for the LINETO, 1 for

# the CLOSEPOLY; the vert for the closepoly is ignored but we still

# need it to keep the codes aligned with the vertices

numpolys, numsides, two = XY.shape

if two != 2:

raise ValueError("The third dimension of 'XY' must be 2")

stride = numsides + 1

nverts = numpolys * stride

verts = np.zeros((nverts, 2))

codes = np.full(nverts, cls.LINETO, dtype=cls.code_type)

codes[0::stride] = cls.MOVETO

codes[numsides::stride] = cls.CLOSEPOLY

for i in range(numsides):

verts[i::stride] = XY[:, i]

return cls(verts, codes)

@classmethod

def make_compound_path(cls, *args):

r"""

if not args:

return Path(np.empty([0, 2], dtype=np.float32))

vertices = np.concatenate([path.vertices for path in args])

codes = np.empty(len(vertices), dtype=cls.code_type)

i = 0

for path in args:

size = len(path.vertices)

if path.codes is None:

if size:

codes[i] = cls.MOVETO

codes[i+1:i+size] = cls.LINETO

else:

codes[i:i+size] = path.codes

i += size

not_stop_mask = codes != cls.STOP # Remove STOPs, as internal STOPs are a bug.

return cls(vertices[not_stop_mask], codes[not_stop_mask])

def __repr__(self):

return f"Path({self.vertices!r}, {self.codes!r})"

def __len__(self):

return len(self.vertices)

def iter_segments(self, transform=None, remove_nans=True, clip=None,

snap=False, stroke_width=1.0, simplify=None,

curves=True, sketch=None):

"""

if not len(self):

return

cleaned = self.cleaned(transform=transform,

remove_nans=remove_nans, clip=clip,

snap=snap, stroke_width=stroke_width,

simplify=simplify, curves=curves,

sketch=sketch)

# Cache these object lookups for performance in the loop.

NUM_VERTICES_FOR_CODE = self.NUM_VERTICES_FOR_CODE

STOP = self.STOP

vertices = iter(cleaned.vertices)

codes = iter(cleaned.codes)

for curr_vertices, code in zip(vertices, codes):

if code == STOP:

break

extra_vertices = NUM_VERTICES_FOR_CODE[code] - 1

if extra_vertices:

for i in range(extra_vertices):

next(codes)

curr_vertices = np.append(curr_vertices, next(vertices))

yield curr_vertices, code

def iter_bezier(self, **kwargs):

"""

first_vert = None

prev_vert = None

for verts, code in self.iter_segments(**kwargs):

if first_vert is None:

if code != Path.MOVETO:

raise ValueError("Malformed path, must start with MOVETO.")

if code == Path.MOVETO: # a point is like "CURVE1"

first_vert = verts

yield BezierSegment(np.array([first_vert])), code

elif code == Path.LINETO: # "CURVE2"

yield BezierSegment(np.array([prev_vert, verts])), code

elif code == Path.CURVE3:

yield BezierSegment(np.array([prev_vert, verts[:2],

verts[2:]])), code

elif code == Path.CURVE4:

yield BezierSegment(np.array([prev_vert, verts[:2],

verts[2:4], verts[4:]])), code

elif code == Path.CLOSEPOLY:

yield BezierSegment(np.array([prev_vert, first_vert])), code

elif code == Path.STOP:

return

else:

raise ValueError(f"Invalid Path.code_type: {code}")

prev_vert = verts[-2:]

def _iter_connected_components(self):

"""Return subpaths split at MOVETOs."""

if self.codes is None:

yield self

else:

idxs = np.append((self.codes == Path.MOVETO).nonzero()[0], len(self.codes))

for sl in map(slice, idxs, idxs[1:]):

yield Path._fast_from_codes_and_verts(

self.vertices[sl], self.codes[sl], self)

def cleaned(self, transform=None, remove_nans=False, clip=None,

*, simplify=False, curves=False,

stroke_width=1.0, snap=False, sketch=None):

"""

vertices, codes = _path.cleanup_path(

self, transform, remove_nans, clip, snap, stroke_width, simplify,

curves, sketch)

pth = Path._fast_from_codes_and_verts(vertices, codes, self)

if not simplify:

pth._should_simplify = False

return pth

def transformed(self, transform):

"""

return Path(transform.transform(self.vertices), self.codes,

self._interpolation_steps)

def contains_point(self, point, transform=None, radius=0.0):

"""

if transform is not None:

transform = transform.frozen()

# `point_in_path` does not handle nonlinear transforms, so we

# transform the path ourselves. If *transform* is affine, letting

# `point_in_path` handle the transform avoids allocating an extra

# buffer.

if transform and not transform.is_affine:

self = transform.transform_path(self)

transform = None

return _path.point_in_path(point[0], point[1], radius, self, transform)

def contains_points(self, points, transform=None, radius=0.0):

"""

if transform is not None:

transform = transform.frozen()

result = _path.points_in_path(points, radius, self, transform)

return result.astype('bool')

def contains_path(self, path, transform=None):

"""

if transform is not None:

transform = transform.frozen()

return _path.path_in_path(self, None, path, transform)

def get_extents(self, transform=None, **kwargs):

"""

from .transforms import Bbox

if transform is not None:

self = transform.transform_path(self)

if self.codes is None:

xys = self.vertices

elif len(np.intersect1d(self.codes, [Path.CURVE3, Path.CURVE4])) == 0:

# Optimization for the straight line case.

# Instead of iterating through each curve, consider

# each line segment's end-points

# (recall that STOP and CLOSEPOLY vertices are ignored)

xys = self.vertices[np.isin(self.codes,

[Path.MOVETO, Path.LINETO])]

else:

xys = []

for curve, code in self.iter_bezier(**kwargs):

# places where the derivative is zero can be extrema

_, dzeros = curve.axis_aligned_extrema()

# as can the ends of the curve

xys.append(curve([0, *dzeros, 1]))

xys = np.concatenate(xys)

if len(xys):

return Bbox([xys.min(axis=0), xys.max(axis=0)])

else:

return Bbox.null()

def intersects_path(self, other, filled=True):

"""

return _path.path_intersects_path(self, other, filled)

def intersects_bbox(self, bbox, filled=True):

"""

return _path.path_intersects_rectangle(

self, bbox.x0, bbox.y0, bbox.x1, bbox.y1, filled)

def interpolated(self, steps):

"""

if steps == 1 or len(self) == 0:

return self

if self.codes is not None and self.MOVETO in self.codes[1:]:

return self.make_compound_path(

*(p.interpolated(steps) for p in self._iter_connected_components()))

if self.codes is not None and self.CLOSEPOLY in self.codes and not np.all(

self.vertices[self.codes == self.CLOSEPOLY] == self.vertices[0]):

vertices = self.vertices.copy()

vertices[self.codes == self.CLOSEPOLY] = vertices[0]

else:

vertices = self.vertices

vertices = simple_linear_interpolation(vertices, steps)

codes = self.codes

if codes is not None:

new_codes = np.full((len(codes) - 1) * steps + 1, Path.LINETO,

dtype=self.code_type)

new_codes[0::steps] = codes

else:

new_codes = None

return Path(vertices, new_codes)

def to_polygons(self, transform=None, width=0, height=0, closed_only=True):

"""

if len(self.vertices) == 0:

return []

if transform is not None:

transform = transform.frozen()

if self.codes is None and (width == 0 or height == 0):

vertices = self.vertices

if closed_only:

if len(vertices) < 3:

return []

elif np.any(vertices[0] != vertices[-1]):

vertices = [*vertices, vertices[0]]

if transform is None:

return [vertices]

else:

return [transform.transform(vertices)]

# Deal with the case where there are curves and/or multiple

# subpaths (using extension code)

return _path.convert_path_to_polygons(

self, transform, width, height, closed_only)

_unit_rectangle = None

@classmethod

def unit_rectangle(cls):

"""

if cls._unit_rectangle is None:

cls._unit_rectangle = cls([[0, 0], [1, 0], [1, 1], [0, 1], [0, 0]],

closed=True, readonly=True)

return cls._unit_rectangle

_unit_regular_polygons = WeakValueDictionary()

@classmethod

def unit_regular_polygon(cls, numVertices):

"""

if numVertices <= 16:

path = cls._unit_regular_polygons.get(numVertices)

else:

path = None

if path is None:

theta = ((2 * np.pi / numVertices) * np.arange(numVertices + 1)

# This initial rotation is to make sure the polygon always

# "points-up".

+ np.pi / 2)

verts = np.column_stack((np.cos(theta), np.sin(theta)))

path = cls(verts, closed=True, readonly=True)

if numVertices <= 16:

cls._unit_regular_polygons[numVertices] = path

return path

_unit_regular_stars = WeakValueDictionary()

@classmethod

def unit_regular_star(cls, numVertices, innerCircle=0.5):

"""

if numVertices <= 16:

path = cls._unit_regular_stars.get((numVertices, innerCircle))

else:

path = None

if path is None:

ns2 = numVertices * 2

theta = (2*np.pi/ns2 * np.arange(ns2 + 1))

# This initial rotation is to make sure the polygon always

# "points-up"

theta += np.pi / 2.0

r = np.ones(ns2 + 1)

r[1::2] = innerCircle

verts = (r * np.vstack((np.cos(theta), np.sin(theta)))).T

path = cls(verts, closed=True, readonly=True)

if numVertices <= 16:

cls._unit_regular_stars[(numVertices, innerCircle)] = path

return path

@classmethod

def unit_regular_asterisk(cls, numVertices):

"""

return cls.unit_regular_star(numVertices, 0.0)

_unit_circle = None

@classmethod

def unit_circle(cls):

"""

if cls._unit_circle is None:

cls._unit_circle = cls.circle(center=(0, 0), radius=1,

readonly=True)

return cls._unit_circle

@classmethod

def circle(cls, center=(0., 0.), radius=1., readonly=False):

"""

MAGIC = 0.2652031

SQRTHALF = np.sqrt(0.5)

MAGIC45 = SQRTHALF * MAGIC

vertices = np.array([[0.0, -1.0],

[MAGIC, -1.0],

[SQRTHALF-MAGIC45, -SQRTHALF-MAGIC45],

[SQRTHALF, -SQRTHALF],

[SQRTHALF+MAGIC45, -SQRTHALF+MAGIC45],

[1.0, -MAGIC],

[1.0, 0.0],

[1.0, MAGIC],

[SQRTHALF+MAGIC45, SQRTHALF-MAGIC45],

[SQRTHALF, SQRTHALF],

[SQRTHALF-MAGIC45, SQRTHALF+MAGIC45],

[MAGIC, 1.0],

[0.0, 1.0],

[-MAGIC, 1.0],

[-SQRTHALF+MAGIC45, SQRTHALF+MAGIC45],

[-SQRTHALF, SQRTHALF],

[-SQRTHALF-MAGIC45, SQRTHALF-MAGIC45],

[-1.0, MAGIC],

[-1.0, 0.0],

[-1.0, -MAGIC],

[-SQRTHALF-MAGIC45, -SQRTHALF+MAGIC45],

[-SQRTHALF, -SQRTHALF],

[-SQRTHALF+MAGIC45, -SQRTHALF-MAGIC45],

[-MAGIC, -1.0],

[0.0, -1.0],

[0.0, -1.0]],

dtype=float)

codes = [cls.CURVE4] * 26

codes[0] = cls.MOVETO

codes[-1] = cls.CLOSEPOLY

return Path(vertices * radius + center, codes, readonly=readonly)

_unit_circle_righthalf = None

@classmethod

def unit_circle_righthalf(cls):

"""

if cls._unit_circle_righthalf is None:

MAGIC = 0.2652031

SQRTHALF = np.sqrt(0.5)

MAGIC45 = SQRTHALF * MAGIC

vertices = np.array(

[[0.0, -1.0],

[MAGIC, -1.0],

[SQRTHALF-MAGIC45, -SQRTHALF-MAGIC45],

[SQRTHALF, -SQRTHALF],

[SQRTHALF+MAGIC45, -SQRTHALF+MAGIC45],

[1.0, -MAGIC],

[1.0, 0.0],

[1.0, MAGIC],

[SQRTHALF+MAGIC45, SQRTHALF-MAGIC45],

[SQRTHALF, SQRTHALF],

[SQRTHALF-MAGIC45, SQRTHALF+MAGIC45],

[MAGIC, 1.0],

[0.0, 1.0],

[0.0, -1.0]],

float)

codes = np.full(14, cls.CURVE4, dtype=cls.code_type)

codes[0] = cls.MOVETO

codes[-1] = cls.CLOSEPOLY

cls._unit_circle_righthalf = cls(vertices, codes, readonly=True)

return cls._unit_circle_righthalf

@classmethod

def arc(cls, theta1, theta2, n=None, is_wedge=False):

"""

halfpi = np.pi * 0.5

eta1 = theta1

n_turns = (theta2 - theta1) / 360

nearest_turn = np.rint(n_turns)

is_full_circle = nearest_turn != 0 and abs(n_turns - nearest_turn) <= 1e-12

# We unwrap *theta2* to the shortest arc within 360 degrees.

# Full circles need special handling as floating point errors can