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path.py

00001 """
Contains a class for managing paths (polylines).
"""

import math
from weakref import WeakValueDictionary

import numpy as np
from numpy import ma

from matplotlib._path import point_in_path, get_path_extents, \
    point_in_path_collection, get_path_collection_extents, \
    path_in_path, path_intersects_path, convert_path_to_polygons
from matplotlib.cbook import simple_linear_interpolation

00016 class Path(object):
    """
    Path represents a series of possibly disconnected, possibly
    closed, line and curve segments.

    The underlying storage is made up of two parallel numpy arrays:
      - vertices: an Nx2 float array of vertices
      - codes: an N-length uint8 array of vertex types

    These two arrays always have the same length in the first
    dimension.  For example, to represent a cubic curve, you must
    provide three vertices as well as three codes "CURVE3".

    The code types are:

       - ``STOP``   :  1 vertex (ignored)
           A marker for the end of the entire path (currently not
           required and ignored)

       - ``MOVETO`` :  1 vertex
            Pick up the pen and move to the given vertex.

       - ``LINETO`` :  1 vertex
            Draw a line from the current position to the given vertex.

       - ``CURVE3`` :  1 control point, 1 endpoint
          Draw a quadratic Bezier curve from the current position,
          with the given control point, to the given end point.

       - ``CURVE4`` :  2 control points, 1 endpoint
          Draw a cubic Bezier curve from the current position, with
          the given control points, to the given end point.

       - ``CLOSEPOLY`` : 1 vertex (ignored)
          Draw a line segment to the start point of the current
          polyline.

    Users of Path objects should not access the vertices and codes
    arrays directly.  Instead, they should use :meth:`iter_segments`
    to get the vertex/code pairs.  This is important since many Paths,
    as an optimization, do not store a codes array at all, but have a
    default one provided for them by :meth:`iter_segments`.
    """

    # Path codes
    STOP      = 0 # 1 vertex
    MOVETO    = 1 # 1 vertex
    LINETO    = 2 # 1 vertex
    CURVE3    = 3 # 2 vertices
    CURVE4    = 4 # 3 vertices
    CLOSEPOLY = 5 # 1 vertex

    NUM_VERTICES = [1, 1, 1, 2, 3, 1]

    code_type = np.uint8

00072     def __init__(self, vertices, codes=None):
        """
        Create a new path with the given vertices and codes.

        vertices is an Nx2 numpy float array, masked array or Python
        sequence.

        codes is an N-length numpy array or Python sequence of type
        Path.code_type.

        These two arrays must have the same length in the first
        dimension.

        If codes is None, vertices will be treated as a series of line
        segments.  If vertices contains masked values, the resulting
        path will be compressed, with MOVETO codes inserted in the
        correct places to jump over the masked regions.
        """
        if ma.isMaskedArray(vertices):
            is_mask = True
            mask = ma.getmask(vertices)
        else:
            is_mask = False
            vertices = np.asarray(vertices, np.float_)
            mask = ma.nomask

        if codes is not None:
            codes = np.asarray(codes, self.code_type)
            assert codes.ndim == 1
            assert len(codes) == len(vertices)

        # The path being passed in may have masked values.  However,
        # the backends (and any affine transformations in matplotlib
        # itself), are not expected to deal with masked arrays, so we
        # must remove them from the array (using compressed), and add
        # MOVETO commands to the codes array accordingly.
        if is_mask:
            if mask is not ma.nomask:
                mask1d = np.logical_or.reduce(mask, axis=1)
                gmask1d = np.invert(mask1d)
                if codes is None:
                    codes = np.empty((len(vertices)), self.code_type)
                    codes.fill(self.LINETO)
                    codes[0] = self.MOVETO
                vertices = vertices[gmask1d].filled() # ndarray
                codes[np.roll(mask1d, 1)] = self.MOVETO
                codes = codes[gmask1d] # np.compress is much slower
            else:
                vertices = np.asarray(vertices, np.float_)

        assert vertices.ndim == 2
        assert vertices.shape[1] == 2

        self.codes = codes
        self.vertices = vertices

    #@staticmethod
00129     def make_compound_path(*args):
        """
        (staticmethod) Make a compound path from a list of Path
        objects.  Only polygons (not curves) are supported.
        """
        for p in args:
            assert p.codes is None

        lengths = [len(x) for x in args]
        total_length = sum(lengths)

        vertices = np.vstack([x.vertices for x in args])
        vertices.reshape((total_length, 2))

        codes = Path.LINETO * np.ones(total_length)
        i = 0
        for length in lengths:
            codes[i] = Path.MOVETO
            i += length

        return Path(vertices, codes)
    make_compound_path = staticmethod(make_compound_path)

    def __repr__(self):
        return "Path(%s, %s)" % (self.vertices, self.codes)

    def __len__(self):
        return len(self.vertices)

00158     def iter_segments(self):
        """
        Iterates over all of the curve segments in the path.  Each
        iteration returns a 2-tuple (*vertices*, *code*), where
        *vertices* is a sequence of 1 - 3 coordinate pairs, and *code* is
        one of the :class:`Path` codes.
        """
        vertices = self.vertices
        if not len(vertices):
            return

        codes = self.codes
        len_vertices = len(vertices)
        isnan = np.isnan
        any = np.any

        NUM_VERTICES = self.NUM_VERTICES
        MOVETO = self.MOVETO
        LINETO = self.LINETO
        CLOSEPOLY = self.CLOSEPOLY
        STOP = self.STOP

        if codes is None:
            next_code = MOVETO
            for v in vertices:
                if any(isnan(v)):
                    next_code = MOVETO
                else:
                    yield v, next_code
                    next_code = LINETO
        else:
            i = 0
            was_nan = False
            while i < len_vertices:
                code = codes[i]
                if code == CLOSEPOLY:
                    yield [], code
                    i += 1
                elif code == STOP:
                    return
                else:
                    num_vertices = NUM_VERTICES[int(code)]
                    curr_vertices = vertices[i:i+num_vertices].flatten()
                    if any(isnan(curr_vertices)):
                        was_nan = True
                    elif was_nan:
                        yield curr_vertices[-2:], MOVETO
                        was_nan = False
                    else:
                        yield curr_vertices, code
                    i += num_vertices

00210     def transformed(self, transform):
        """
        Return a transformed copy of the path.

        See :class:`matplotlib.transforms.TransformedPath` for a path
        that will cache the transformed result and automatically
        update when the transform changes.
        """
        return Path(transform.transform(self.vertices), self.codes)

00220     def contains_point(self, point, transform=None):
        """
        Returns True if the path contains the given point.

        If transform is not None, the path will be transformed before
        performing the test.
        """
        if transform is not None:
            transform = transform.frozen()
        return point_in_path(point[0], point[1], self, transform)

00231     def contains_path(self, path, transform=None):
        """
        Returns True if this path completely contains the given path.

        If transform is not None, the path will be transformed before
        performing the test.
        """
        if transform is not None:
            transform = transform.frozen()
        return path_in_path(self, None, path, transform)

00242     def get_extents(self, transform=None):
        """
        Returns the extents (xmin, ymin, xmax, ymax) of the path.

        Unlike computing the extents on the vertices alone, this
        algorithm will take into account the curves and deal with
        control points appropriately.
        """
        from transforms import Bbox
        if transform is not None:
            transform = transform.frozen()
        return Bbox(get_path_extents(self, transform))

00255     def intersects_path(self, other):
        """
        Returns True if this path intersects another given path.
        """
        return path_intersects_path(self, other)

00261     def intersects_bbox(self, bbox):
        """
        Returns True if this path intersects a given
        :class:`~matplotlib.transforms.Bbox`.
        """
        from transforms import BboxTransformTo
        rectangle = self.unit_rectangle().transformed(
            BboxTransformTo(bbox))
        result = self.intersects_path(rectangle)
        return result

00272     def interpolated(self, steps):
        """
        Returns a new path resampled to length N x steps.
        Does not currently handle interpolating curves.
        """
        vertices = simple_linear_interpolation(self.vertices, steps)
        codes = self.codes
        if codes is not None:
            new_codes = Path.LINETO * np.ones(((len(codes) - 1) * steps + 1, ))
            new_codes[0::steps] = codes
        else:
            new_codes = None
        return Path(vertices, new_codes)

00286     def to_polygons(self, transform=None, width=0, height=0):
        """
        Convert this path to a list of polygons.  Each polygon is an
        Nx2 array of vertices.  In other words, each polygon has no
        ``MOVETO`` instructions or curves.  This is useful for
        displaying in backends that do not support compound paths or
        Bezier curves, such as GDK.

        If width and height are both non-zero then the lines will be
        simplified so that vertices outside of (0, 0), (width, height)
        will be clipped.
        """
        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):
            if transform is None:
                return [self.vertices]
            else:
                return [transform.transform(self.vertices)]

        # Deal with the case where there are curves and/or multiple
        # subpaths (using extension code)
        return convert_path_to_polygons(self, transform, width, height)

    _unit_rectangle = None
    #@classmethod
00316     def unit_rectangle(cls):
        """
        (staticmethod) Returns a :class:`Path` of the unit rectangle
        from (0, 0) to (1, 1).
        """
        if cls._unit_rectangle is None:
            cls._unit_rectangle = \
                Path([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0], [0.0, 0.0]])
        return cls._unit_rectangle
    unit_rectangle = classmethod(unit_rectangle)

    _unit_regular_polygons = WeakValueDictionary()
    #@classmethod
00329     def unit_regular_polygon(cls, numVertices):
        """
        (staticmethod) Returns a :class:`Path` for a unit regular
        polygon with the given numVertices and radius of 1.0, centered
        at (0, 0).
        """
        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).reshape((numVertices + 1, 1)))
            # This initial rotation is to make sure the polygon always
            # "points-up"
            theta += np.pi / 2.0
            verts = np.concatenate((np.cos(theta), np.sin(theta)), 1)
            path = Path(verts)
            cls._unit_regular_polygons[numVertices] = path
        return path
    unit_regular_polygon = classmethod(unit_regular_polygon)

    _unit_regular_stars = WeakValueDictionary()
    #@classmethod
00353     def unit_regular_star(cls, numVertices, innerCircle=0.5):
        """
        (staticmethod) Returns a :class:`Path` for a unit regular star
        with the given numVertices and radius of 1.0, centered at (0,
        0).
        """
        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 = np.vstack((r*np.cos(theta), r*np.sin(theta))).transpose()
            path = Path(verts)
            cls._unit_regular_polygons[(numVertices, innerCircle)] = path
        return path
    unit_regular_star = classmethod(unit_regular_star)

    #@classmethod
00378     def unit_regular_asterisk(cls, numVertices):
        """
        (staticmethod) Returns a :class:`Path` for a unit regular
        asterisk with the given numVertices and radius of 1.0,
        centered at (0, 0).
        """
        return cls.unit_regular_star(numVertices, 0.0)
    unit_regular_asterisk = classmethod(unit_regular_asterisk)

    _unit_circle = None
    #@classmethod
00389     def unit_circle(cls):
        """
        (staticmethod) Returns a :class:`Path` of the unit circle.
        The circle is approximated using cubic Bezier curves.  This
        uses 8 splines around the circle using the approach presented
        here:

          Lancaster, Don.  `Approximating a Circle or an Ellipse Using Four
          Bezier Cubic Splines <http://www.tinaja.com/glib/ellipse4.pdf>`_.
        """
        if cls._unit_circle is None:
            MAGIC = 0.2652031
            SQRTHALF = np.sqrt(0.5)
            MAGIC45 = np.sqrt((MAGIC*MAGIC) / 2.0)

            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]],
                np.float_)

            codes = cls.CURVE4 * np.ones(26)
            codes[0] = cls.MOVETO
            codes[-1] = cls.CLOSEPOLY

            cls._unit_circle = Path(vertices, codes)
        return cls._unit_circle
    unit_circle = classmethod(unit_circle)

    #@classmethod
00451     def arc(cls, theta1, theta2, n=None, is_wedge=False):
        """
        (staticmethod) Returns an arc on the unit circle from angle
        theta1 to angle theta2 (in degrees).

        If n is provided, it is the number of spline segments to make.
        If n is not provided, the number of spline segments is
        determined based on the delta between theta1 and theta2.

           Masionobe, L.  2003.  `Drawing an elliptical arc using
           polylines, quadratic or cubic Bezier curves
           <http://www.spaceroots.org/documents/ellipse/index.html>`_.
        """
        # degrees to radians
        theta1 *= np.pi / 180.0
        theta2 *= np.pi / 180.0

        twopi  = np.pi * 2.0
        halfpi = np.pi * 0.5

        eta1 = np.arctan2(np.sin(theta1), np.cos(theta1))
        eta2 = np.arctan2(np.sin(theta2), np.cos(theta2))
        eta2 -= twopi * np.floor((eta2 - eta1) / twopi)
        if (theta2 - theta1 > np.pi) and (eta2 - eta1 < np.pi):
            eta2 += twopi

        # number of curve segments to make
        if n is None:
            n = int(2 ** np.ceil((eta2 - eta1) / halfpi))
        if n < 1:
            raise ValueError("n must be >= 1 or None")

        deta = (eta2 - eta1) / n
        t = np.tan(0.5 * deta)
        alpha = np.sin(deta) * (np.sqrt(4.0 + 3.0 * t * t) - 1) / 3.0

        steps = np.linspace(eta1, eta2, n + 1, True)
        cos_eta = np.cos(steps)
        sin_eta = np.sin(steps)

        xA = cos_eta[:-1]
        yA = sin_eta[:-1]
        xA_dot = -yA
        yA_dot = xA

        xB = cos_eta[1:]
        yB = sin_eta[1:]
        xB_dot = -yB
        yB_dot = xB

        if is_wedge:
            length = n * 3 + 4
            vertices = np.zeros((length, 2), np.float_)
            codes = Path.CURVE4 * np.ones((length, ), Path.code_type)
            vertices[1] = [xA[0], yA[0]]
            codes[0:2] = [Path.MOVETO, Path.LINETO]
            codes[-2:] = [Path.LINETO, Path.CLOSEPOLY]
            vertex_offset = 2
            end = length - 2
        else:
            length = n * 3 + 1
            vertices = np.zeros((length, 2), np.float_)
            codes = Path.CURVE4 * np.ones((length, ), Path.code_type)
            vertices[0] = [xA[0], yA[0]]
            codes[0] = Path.MOVETO
            vertex_offset = 1
            end = length

        vertices[vertex_offset  :end:3, 0] = xA + alpha * xA_dot
        vertices[vertex_offset  :end:3, 1] = yA + alpha * yA_dot
        vertices[vertex_offset+1:end:3, 0] = xB - alpha * xB_dot
        vertices[vertex_offset+1:end:3, 1] = yB - alpha * yB_dot
        vertices[vertex_offset+2:end:3, 0] = xB
        vertices[vertex_offset+2:end:3, 1] = yB

        return Path(vertices, codes)
    arc = classmethod(arc)

    #@classmethod
00530     def wedge(cls, theta1, theta2, n=None):
        """
        (staticmethod) Returns a wedge of the unit circle from angle
        theta1 to angle theta2 (in degrees).
        """
        return cls.arc(theta1, theta2, n, True)
    wedge = classmethod(wedge)

_get_path_collection_extents = get_path_collection_extents
00539 def get_path_collection_extents(*args):
    """
    Given a sequence of :class:`Path` objects, returns the bounding
    box that encapsulates all of them.
    """
    from transforms import Bbox
    if len(args[1]) == 0:
        raise ValueError("No paths provided")
    return Bbox.from_extents(*_get_path_collection_extents(*args))

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