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    # ##### BEGIN GPL LICENSE BLOCK #####
    #
    #  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.
    #
    # ##### END GPL LICENSE BLOCK #####
    
    # <pep8 compliant>
    
    """Convert an Art object to a list of PolyArea objects.
    """
    
    __author__ = "howard.trickey@gmail.com"
    
    import math
    from . import geom
    from . import vecfile
    import itertools
    
    
    class ConvertOptions(object):
        """Contains options used to control art to poly conversion.
    
        Attributes:
          subdiv_kind: int - one of a few 'enum' strings:
              'UNIFORM' - all curves subdivided the same amount
              'ADAPTIVE' - curves subdivided until flat enough
              'EVEN' - curves subdivided to make segments of uniform length
          smoothness: int - controls smoothness of curve conversion:
            usage depends on subdiv_kind:
              'UNIFORM': number of times to subdivide
              'ADAPTIVE': if subdivide a quarter circle bezier this many times,
                then that is the definition of 'flat enough'
              'EVEN': proportional to 1/uniform-length-of-segments
                (so higher numbers mean shorter segments)
    
          filled_only: bool - look only at filled faces
          combine_paths: bool - use union of all subpaths to find
            boundaries and holes instead of just looking for compound
            paths in the input file
          ignore_white: bool - ignore white-filled paths (background, probably)
        """
    
        def __init__(self):
            self.subdiv_kind = "UNIFORM"
            self.smoothness = 1
            self.filled_only = True
            self.combine_paths = False
            self.ignore_white = True
    
    
    def ArtToPolyAreas(art, options):
        """Convert Art object to PolyAreas.
    
        Each filled Path in the Art object will produce zero
        or more PolyAreas.  If options.filled_only is False, then stroked paths
        produce PolyAreas too.
    
        If options.ignore_white is True, we assume that white is the background
        color and not intended to produce polyareas (for example, sometimes there
        is a filled background rectangle for the entire page).
    
        If options.combine_paths is True, use the union of all subpaths of all
        Paths to look for outer boundaries and holes, else just look insdie each
        Path separately.
    
        Args:
          art: geom.Art - contains Paths to convert
          options: ConvertOptions
        Returns:
          geom.PolyAreas
        """
    
        ans = geom.PolyAreas()
        paths_to_convert = art.paths
        if options.filled_only:
            paths_to_convert = [p for p in paths_to_convert if p.filled]
        if options.ignore_white:
            paths_to_convert = [p for p in paths_to_convert \
                if p.fillpaint != geom.white_paint]
        # TODO: look for dup paths (both filled and stroked) and dedup
        # TODO (perhaps): look for a 'background rectangle' and remove
        if options.subdiv_kind == "EVEN":
            _SetEvenLength(options, paths_to_convert)
        if options.combine_paths:
            combinedpath = geom.Path()
            combinedpath.subpaths = _flatten([p.subpaths \
                for p in paths_to_convert])
            areas = PathToPolyAreas(combinedpath, options, ans.points)
        else:
            areas = _flatten([PathToPolyAreas(p, options, ans.points) \
                for p in paths_to_convert])
        ans.polyareas.extend(areas)
        return ans
    
    
    def PathToPolyAreas(path, options, points):
        """Convert Path object to list of PolyArea, sharing points.
    
        Like ArtToPolyAreas, but for a single Path in Art.
    
        Usually only one PolyArea will be in the returned list,
        but there may be zero if the path has zero area,
        and there may be more than one if it contains
        non-overlapping polygons.
        (TODO: or if it self-crosses)
    
        Args:
          path: geom.Path - the path to convert
          options: ConvertOptions
          points: geom.Points - use this shared points for all areas
        Returns:
          list of geom.PolyArea
        """
    
        subpolyareas = [
            _SubpathToPolyArea(sp, options, points, path.fillpaint.color) \
            for sp in path.subpaths]
        subpolyareas = [pa for pa in subpolyareas if len(pa.poly) > 0]
        return CombineSimplePolyAreas(subpolyareas)
    
    
    def CombineSimplePolyAreas(subpolyareas):
        """Combine PolyAreas without holes into ones that may have holes.
    
        Take the poly's in each argument PolyArea and find those that
        are contained in others, so returning a list of PolyAreas that may
        contain holes.
        The argument PolyAreas may be reused an modified in forming
        the result.
    
        Args:
          subpolyareas: list of geom.PolyArea
        Returns:
          list of geom.PolyArea
        """
    
        n = len(subpolyareas)
        areas = [geom.SignedArea(pa.poly, pa.points) for pa in subpolyareas]
        lens = list(map(lambda x: len(x.poly), subpolyareas))
        cls = dict()
        for i in range(n):
            for j in range(n):
                cls[(i, j)] = _ClassifyPathPairs(subpolyareas[i], subpolyareas[j])
        # calculate set cont where (i,j) is in cont if
        # subpolyareas[i] contains subpolyareas[j]
        cont = set()
        for i in range(n):
            for j in range(n):
                if i != j and _Contains(i, j, areas, lens, cls):
                    cont.add((i, j))
        # now make real PolyAreas, with holes assigned
        polyareas = []
        assigned = set()
        count = 0
        while len(assigned) < n and count < n:
            for i in range(n):
                if i in assigned:
                    continue
                if _IsBoundary(i, n, cont, assigned):
                    # have a new boundary area, i
                    assigned.add(i)
                    holes = _GetHoles(i, n, cont, assigned)
                    pa = subpolyareas[i]
                    for j in holes:
                        pa.AddHole(subpolyareas[j])
                    polyareas.append(pa)
            count += 1
        if len(assigned) < n:
            # shouldn't happen
            print("Whoops, PathToPolyAreas didn't assign all")
        return polyareas
    
    
    def _SubpathToPolyArea(subpath, options, points, color=(0.0, 0.0, 0.0)):
        """Return a PolyArea representing a single subpath.
    
        Converts curved segments into approximating line
        segments.
        For 'EVEN' subdiv_kind, divides lines too.
        Ignores zero-length or near zero-length segments.
        Ensures that face is CCW-oriented.
        Use the data field of the PolyArea to hold the filling color.
    
        Args:
          subpath: geom.Subpath - the subpath to convert
          options: ConvertOptions
          points: geom.Points - used this shared Points for area
          color: (float, float, float) - rgb of filling color
        Returns:
          geom.PolyArea
        """
    
        face = []
        prev = None
        ans = geom.PolyArea()
        ans.points = points
        ans.data = color
        for seg in subpath.segments:
            (ty, start, end) = seg[0:3]
            if not prev or prev != start:
                face.append(start)
            if ty == "L":
                if options.subdiv_kind == "EVEN":
                    lines = _EvenLineDivide(start, end, options)
                    face.extend(lines[1:])
                else:
                    face.append(end)
                prev = end
            elif ty == "B":
                approx = Bezier3Approx([start, seg[3], seg[4], end], options)
                # first point of approx should be current end of face
                face.extend(approx[1:])
                prev = end
            elif ty == "Q":
                print("unimplemented segment type Q")
            elif ty == "A":
                approx = ArcApprox(start, end, seg[3], seg[4], seg[5], seg[6],
                    options)
                face.extend(approx[1:])
                prev = end
            else:
                print("unexpected segment type", ty)
        # now make a cleaned face in a new PolyArea
        # with no two successive points approximately equal
        if len(face) <= 2:
            # degenerate face, return an empty PolyArea
            return ans
        previndex = -1
        for i in range(0, len(face)):
            point = face[i]
            newindex = ans.points.AddPoint(point)
            if newindex == previndex or \
                i == len(face) - 1 and newindex == ans.poly[0]:
                continue
            ans.poly.append(newindex)
            previndex = newindex
        # make sure that face is CCW oriented
        if geom.SignedArea(ans.poly, ans.points) < 0.0:
            ans.poly.reverse()
        return ans
    
    
    def Bezier3Approx(cps, options):
        """Compute a polygonal approximation to a cubic bezier segment.
    
        Args:
          cps: list of 4 coord tuples -
              (start, control point 1, control point 2, end)
          options: ConvertOptions
        Returns:
          list of tuples (coordinates) for straight line approximation of the
          bezier
        """
    
        if options.subdiv_kind == "EVEN":
            return _EvenBezier3Approx(cps, options)
        else:
            return _SubdivideBezier3Approx(cps, options, 0)
    
    
    def _SetEvenLength(options, paths):
        """Use the bounding box of paths to set even_length in options.
    
        We want the option.smoothness parameter to control the length
        of segments that we will try to divide Bezier curves into when
        using the EVEN method.  More smoothness -> shorter length.
        But the user should think of this in terms of the overall dimensions
        of their diagram, not in absolute terms.
        Let's say that smoothness==0 means the length should 1/4 the
        size of the longest size of the bounding box, and, for general
        smoothness:
    
                        longest_side_length
          even_length = -------------------
                        4 * (smoothness+1)
    
        Args:
          options: ConvertOptions
          paths: list of geom.Path
        Side effects:
          Sets options.even_length according to above formula
        """
    
        minx = 1e10
        maxx = -1e10
        miny = 1e10
        maxy = -1e10
        for p in paths:
            for sp in p.subpaths:
                for seg in sp.segments:
                    endi = 3 if seg[0] == 'A' else len(seg)
                    for (x, y) in seg[1:endi]:
                        minx = min(minx, x)
                        maxx = max(maxx, x)
                        miny = min(miny, y)
                        maxy = max(maxy, y)
        longest_side_length = max(maxx - minx, maxy - miny)
        if longest_side_length <= 0:
            longest_side_length = 1.0
        options.even_length = longest_side_length / \
            (4.0 * (options.smoothness + 1))
    
    
    def _EvenBezier3Approx(cps, options):
        """Use even segment lengths to approximate a cubic bezier segment.
    
        Args:
          cps: list of 4 coord tuples -
              (start, control point 1, control point 2, end)
          options: ConvertOptions
        Returns:
          list of tuples (coordinates) for straight line approximation of the
          bezier
        """
    
        # This could be made better by recursing a couple of times
        # but the average of the control polygon and chord length is a good
        # first order approximation.
        arc_length = 0.5 * (geom.VecLen(geom.VecSub(cps[3], cps[0])) + \
                     0.5 * (geom.VecLen(geom.VecSub(cps[1], cps[0])) + \
                            geom.VecLen(geom.VecSub(cps[2], cps[1])) + \
                            geom.VecLen(geom.VecSub(cps[3], cps[2]))))
        # make sure segment lengths are at least as short as even_length
        numsegs = math.ceil(arc_length / options.even_length)
        # unless smoothness is zero, make sure Beziers split at least once
        if options.smoothness > 0 and numsegs == 1:
            numsegs = 2
        ans = [cps[0]]
        for i in range(1, numsegs):
            t = i * (1.0 / numsegs)
            pt = _BezierEval(cps, t)
            ans.append(pt)
        ans.append(cps[3])
        return ans
    
    
    def _BezierEval(cps, t):
        """Evaluate a cubic Bezier at parameter t.
    
        Args:
          cps: list of 4 coord tuples -
              (start, control point 1, control point 2, end)
          t: float - parameter (0 -> start, 1 -> end)
        Returns:
          tuple (coordinates) of point at parameter t along the curve
        """
    
        b1 = _Bez3step(cps, 1, t)
        b2 = _Bez3step(b1, 2, t)
        b3 = _Bez3step(b2, 3, t)
        return b3[0]
    
    
    def _EvenLineDivide(start, end, options):
        """Like _EvenBezier3Approx, but for line segments.
    
        Args:
          start: tuple - coords of start point
          end: tuple - coords of end point
          options: ConvertOptions
        Returns:
          list of tuples (coordinates) for pieces of lines.
        """
    
        line_length = geom.VecLen(geom.VecSub(end, start))
        numsegs = math.ceil(line_length / options.even_length)
        ans = [start]
        for i in range(1, numsegs):
            t = i * (1.0 / numsegs)
            pt = _LinInterp(start, end, t)
            ans.append(pt)
        ans.append(end)
        return ans
    
    
    def _LinInterp(a, b, t):
        """Return the point that is t of the way from a to b.
    
        Args:
          a: tuple - coords of start point
          b: tuple - coords of end point
          t: float - interpolation parameter
        Returns:
          tuple (coordinates)
        """
    
        n = len(a)  # dimension of coordinates
        ans = [0.0] * n
        for i in range(n):
            ans[i] = (1.0 - t) * a[i] + t * b[i]
        return tuple(ans)
    
    
    # These ratios chosen so that a 4-bezier approximation
    # to a circle gets subdivided 0, 1, 2, etc. times
    # when using 'adaptive'.
    adaptive_ratios = [1.2286, 1.0531, 1.0136, 1.0124, 1.0030, 1.0007]
    
    
    def _SubdivideBezier3Approx(cps, options, recurse_count):
        """Use successive bisection to approximate a cubic bezier segment.
    
        Args:
          cps: list of 4 coord tuples -
              (start, control point 1, control point 2, end)
          options: ConvertOptions
          recurse_count: int - how deep have we recursed so far
        Returns:
          list of tuples (coordinates) for straight line approximation of
          the bezier
        """
    
        (vs, _, _, ve) = b0 = cps
        subdivide_num = options.smoothness
        adaptive = (options.subdiv_kind == "ADAPTIVE")
        if recurse_count >= subdivide_num and not adaptive:
            return [vs, ve]
        alpha = 0.5
        b1 = _Bez3step(b0, 1, alpha)
        b2 = _Bez3step(b1, 2, alpha)
        b3 = _Bez3step(b2, 3, alpha)
        if adaptive:
            straightlen = geom.VecLen(geom.VecSub(ve, vs))
            if straightlen < geom.DISTTOL:
                return [vs, ve]
            approxcurvelen = \
              geom.VecLen(geom.VecSub(cps[1], cps[0])) + \
              geom.VecLen(geom.VecSub(cps[2], cps[1])) + \
              geom.VecLen(geom.VecSub(cps[3], cps[2]))
            ratio = approxcurvelen / straightlen
            if subdivide_num < 0:
                subdivide_num = 0
            elif subdivide_num >= len(adaptive_ratios):
                subdivide_num = len(adaptive_ratios) - 1
            aratio = adaptive_ratios[subdivide_num]
            if ratio <= aratio:
                return [vs, ve]
        else:
            if subdivide_num - recurse_count == 1:
                # recursive case would do this too, but optimize a bit
                return [vs, b3[0], ve]
        left = [b0[0], b1[0], b2[0], b3[0]]
        right = [b3[0], b2[1], b1[2], b0[3]]
        ansleft = _SubdivideBezier3Approx(left, options, recurse_count + 1)
        ansright = _SubdivideBezier3Approx(right, options, recurse_count + 1)
        # ansleft ends with b3[0] and ansright starts with it
        return ansleft + ansright[1:]
    
    
    def _Bez3step(b, r, alpha):
        """Cubic bezier step r for interpolating at parameter alpha.
    
        Steps 1, 2, 3 are applied in succession to the 4 points
        representing a bezier segment, making a triangular arrangement
        of interpolating the previous step's output, so that after
        step 3 we have the point that is at parameter alpha of the segment.
        The left-half control points will be on the left side of the triangle
        and the right-half control points will be on the right side of the
        triangle.
    
        Args:
          b: list of tuples (coordinates), of length 5-r
          r: int - step number (0=orig points and cps)
          alpha: float - value in range 0..1 where want to divide at
        Returns:
          list of length 4-r, of vertex coordinates, giving linear interpolations
              at parameter alpha between successive pairs of points in b
        """
    
        ans = []
        n = len(b[0])  # dimension of coordinates
        beta = 1 - alpha
        for i in range(0, 4 - r):
            # find c, alpha of the way from b[i] to b[i+1]
            t = [0.0] * n
            for d in range(n):
                t[d] = b[i][d] * beta + b[i + 1][d] * alpha
            ans.append(tuple(t))
        return ans
    
    
    def ArcApprox(start, end, rad, xrot, large_arc, ccw, options):
        """Approximate an elliptical arc with line segments, according to options.
    
        Implementation follows notes in F.6 of SVG spec.
    
        Args:
          start: (float, float) - starting point
          end: (float, float) - ending point
          rad: (float, float) - x-radius, y-radius
          xrot: float - angle of rotation from x-axis, in degrees
          large_arc: bool - should we take a larger arc?
          ccw: bool - does arc proceed counter-clockwise?
          options: ConvertOptions
        Returns:
          list of tuples (coordinates) for straight line approximation of arc
        """
    
        if start == end:
            return [start]
        (rx, ry) = rad
        if rx == 0.0 or ry == 0.0:
            # treat same as line
            if options.subdiv_kind == "EVEN":
                return _EvenLineDivide(start, end, options)
            else:
                return [start, end]
        rx = abs(rx)
        ry = abs(ry)
        (x1, y1) = start
        (x2, y2) = end
    
        # Convert to center parameterization.
        # Primed coords: origin at midpoint of (start, end)
        # followed by rotaiton to line up coord axes with ellipse axes
        x1p = (x1 - x2) / 2.0
        y1p = (y1 - y2) / 2.0
        phi = xrot * math.pi / 180.0
        cos_phi = math.cos(phi)
        sin_phi = math.sin(phi)
        (x1p, y1p) = (cos_phi * x1p + sin_phi * y1p, \
            -sin_phi * x1p + cos_phi * y1p)
        # perhaps scale up rx, ry to make ellipse achievable
        lam = (x1p ** 2) / rx ** 2 + (y1p ** 2) / ry ** 2
        if lam > 1.0:
            slam = math.sqrt(lam)
            rx *= slam
            ry *= slam
        cf2 = (rx ** 2 * ry ** 2 - rx ** 2 * y1p ** 2 - ry ** 2 * x1p ** 2) / \
            (rx ** 2 * y1p ** 2 + ry ** 2 * x1p ** 2)
        if cf2 <= 0.0:
            cfactor = 0.0
        else:
            cfactor = math.sqrt(cf2)
        if large_arc == ccw:
            cfactor = -cfactor
        cxp = cfactor * rx * y1p / ry
        cyp = -cfactor * ry * x1p / rx
        cx = cos_phi * cxp - sin_phi * cyp + (x1 + x2) / 2.0
        cy = sin_phi * cxp + cos_phi * cyp + (y1 + y2) / 2.0
        theta1 = _Angle((1.0, 0.0), ((x1p - cxp) / rx, (y1p - cyp) / ry))
        delta_theta = _Angle(((x1p - cxp) / rx, (y1p - cyp) / ry),
            ((-x1p - cxp) / rx, (-y1p - cyp) / ry))
        if not ccw and delta_theta > 0.0:
            delta_theta -= 2 * math.pi
        elif ccw and delta_theta < 0.0:
            delta_theta += 2 * math.pi
        if abs(delta_theta) < 1e-5:
            # shouldn't happen
            return [start, end]
    
        # Now arc is:
        #  (x, y) = M * col(rx * cos theta, ry * sin theta) + col(cx, cy)
        # where theta goes from theta1 to theta1 + delta_theta
        # and M is rotation matrix for phi
        # Let's ignore the fact that the axes may have different lengths
        # and just divide delta_theta into the right number of segments
        # to satisfy the smoothness options.
        if options.subdiv_kind == "EVEN":
            # arc_length = pi*d * fraction of circle represented by delta_theta
            arc_length = abs(delta_theta * (rx + ry) / 2.0)
            numsegs = math.ceil(arc_length / options.even_length)
        else:
            # for smoothness 0, have 1 segment per quarter circle
            # and double for each smoothness increment after that
            numsegs = (2 ** options.smoothness) * \
                math.ceil(abs(delta_theta) / (math.pi * 2.0))
        theta_incr = delta_theta / numsegs
        ans = start
        theta = theta1
        endtheta = theta1 + delta_theta
        ans = [start]
        # end condition should be theta ~== endtheta but also
        # should be no more than numsegs iters
        for i in range(numsegs):
            theta = theta + theta_incr
            if abs(theta - endtheta) < 1e-5:
                break
            cos_theta = math.cos(theta)
            sin_theta = math.sin(theta)
            x = cos_phi * rx * cos_theta - sin_phi * ry * sin_theta + cx
            y = sin_phi * rx * cos_theta + cos_phi * ry * sin_theta + cy
            ans.append((x, y))
        ans.append(end)
        return ans
    
    
    def _Angle(u, v):
        """Return angle between two vectors.
    
        Args:
          u: (float, float)
          v: (float, float)
        Returns:
          float - angle in radians between u and v, where
            it is +/- depending on sign of ux * vy - uy * vx
        """
    
        (ux, uy) = u
        (vx, vy) = v
        costheta = (ux * vx + uy * vy) / \
            (math.sqrt(ux ** 2 + uy ** 2) * math.sqrt(vx ** 2 + vy ** 2))
        if costheta > 1.0:
            costheta = 1.0
        if costheta < -1.0:
            costheta = -1.0
        theta = math.acos(costheta)
        if ux * vy - uy * vx < 0.0:
            theta = -theta
        return theta
    
    
    def _ClassifyPathPairs(a, b):
        """Classify vertices of path b with respect to path a.
    
        Args:
          a: geom.PolyArea - the test outer face (ignoring holes)
          b: geom.PolyArea - the test inner face (ignoring holes)
        Returns:
          (int, int) - first is #verts of b inside a, second is #verts of b on a
        """
    
        num_in = 0
        num_on = 0
        for v in b.poly:
            vp = b.points.pos[v]
            k = geom.PointInside(vp, a.poly, a.points)
            if k > 0:
                num_in += 1
            elif k == 0:
                num_on += 1
        return (num_in, num_on)
    
    
    def _Contains(i, j, areas, lens, cls):
        """Return True if path i contains majority of vertices of path j.
    
        Args:
          i: index of supposed containing path
          j: index of supposed contained path
          areas: list of floats - areas of all the paths
          lens: list of ints - lenths of each of the paths
          cls: dict - maps pairs to result of _ClassifyPathPairs
        Returns:
          bool - True if path i contains at least 55% of j's vertices
        """
    
        if i == j:
            return False
        (jinsidei, joni) = cls[(i, j)]
        if jinsidei == 0 or joni == lens[j] or \
           float(jinsidei) / float(lens[j]) < 0.55:
            return False
        else:
            (insidej, _) = cls[(j, i)]
            if float(insidej) / float(lens[i]) > 0.55:
                return areas[i] > areas[j]  # tie breaker
            else:
                return True
    
    
    def _IsBoundary(i, n, cont, assigned):
        """Is path i a boundary, given current assignment?
    
        Args:
          i: int - index of a path to test for boundary possiblity
          n: int - total number of paths
          cont: dict - maps path pairs (i,j) to _Contains(i,j,...) result
          assigned: set  of int - which paths are already assigned
        Returns:
          bool - True if there is no unassigned j, j!=i, such that
                 path j contains path i
        """
    
        for j in range(0, n):
            if j == i or j in assigned:
                continue
            if (j, i) in cont:
                return False
        return True
    
    
    def _GetHoles(i, n, cont, assigned):
        """Find holes for path i: i.e., unassigned paths directly inside it.
    
        Directly inside means there is not some other unassigned path k
        such that path such that path i contains k and path k contains j.
        (If such a k is already assigned, then its islands have been assigned too.)
    
        Args:
          i: int - index of a boundary path
          n: int - total number of paths
          cont: dict - maps path pairs (i,j) to _Contains(i,j,...) result
          assigned: set  of int - which paths are already assigned
        Returns:
          list of int - indices of paths that are islands
        Side Effect:
          Adds island indices to assigned set.
        """
    
        isls = []
        for j in range(0, n):
            if j in assigned:
                continue   # catches i==j too, since i is assigned by now
            if (i, j) in cont:
                directly = True
                for k in range(0, n):
                    if k == j or k in assigned:
                        continue
                    if (i, k) in cont and (k, j) in cont:
                        directly = False
                        break
                if directly:
                    isls.append(j)
                    assigned.add(j)
        return isls
    
    
    def _flatten(l):
        """Return a flattened shallow list.
    
        Args:
          l : list of lists
        Returns:
          list - concatenation of sublists of l
    
        """
    
        return list(itertools.chain.from_iterable(l))