# Source code for fontTools.varLib.interpolatable

    """
    Tool to find wrong contour order between different masters, and
    other interpolatability (or lack thereof) issues.

    Call as:
    $ fonttools varLib.interpolatable font1 font2 ...
    """

    from fontTools.pens.basePen import AbstractPen, BasePen
    from fontTools.pens.pointPen import SegmentToPointPen
    from fontTools.pens.recordingPen import RecordingPen
    from fontTools.pens.statisticsPen import StatisticsPen
    from fontTools.pens.momentsPen import OpenContourError
    from collections import OrderedDict
    import itertools
    import sys

    def _rot_list(l, k):
        """Rotate list by k items forward.  Ie. item at position 0 will be
        at position k in returned list.  Negative k is allowed."""
        n = len(l)
        k %= n
        if not k: return l
        return l[n-k:] + l[:n-k]

    class PerContourPen(BasePen):
        def __init__(self, Pen, glyphset=None):
            BasePen.__init__(self, glyphset)
            self._glyphset = glyphset
            self._Pen = Pen
            self._pen = None
            self.value = []

        def _moveTo(self, p0):
            self._newItem()
            self._pen.moveTo(p0)

        def _lineTo(self, p1):
            self._pen.lineTo(p1)

        def _qCurveToOne(self, p1, p2):
            self._pen.qCurveTo(p1, p2)

        def _curveToOne(self, p1, p2, p3):
            self._pen.curveTo(p1, p2, p3)

        def _closePath(self):
            self._pen.closePath()
            self._pen = None

        def _endPath(self):
            self._pen.endPath()
            self._pen = None

        def _newItem(self):
            self._pen = pen = self._Pen()
            self.value.append(pen)

    class PerContourOrComponentPen(PerContourPen):
        def addComponent(self, glyphName, transformation):
            self._newItem()
            self.value[-1].addComponent(glyphName, transformation)

    class RecordingPointPen(BasePen):

        def __init__(self):
            self.value = []

        def beginPath(self, identifier = None, **kwargs):
            pass

        def endPath(self) -> None:
            pass

        def addPoint(self, pt, segmentType=None):
            self.value.append((pt, False if segmentType is None else True))

    def _vdiff(v0, v1):
        return tuple(b - a for a, b in zip(v0, v1))

    def _vlen(vec):
        v = 0
        for x in vec:
            v += x * x
        return v

    def _complex_vlen(vec):
        v = 0
        for x in vec:
            v += abs(x) * abs(x)
        return v

    def _matching_cost(G, matching):
        return sum(G[i][j] for i, j in enumerate(matching))

    def min_cost_perfect_bipartite_matching(G):
        n = len(G)
        try:
            from scipy.optimize import linear_sum_assignment

            rows, cols = linear_sum_assignment(G)
            assert (rows == list(range(n))).all()
            return list(cols), _matching_cost(G, cols)
        except ImportError:
            pass

        try:
            from munkres import Munkres

            cols = [None] * n
            for row, col in Munkres().compute(G):
                cols[row] = col
            return cols, _matching_cost(G, cols)
        except ImportError:
            pass

        if n > 6:
            raise Exception("Install Python module 'munkres' or 'scipy >= 0.17.0'")

        # Otherwise just brute-force
        permutations = itertools.permutations(range(n))
        best = list(next(permutations))
        best_cost = _matching_cost(G, best)
        for p in permutations:
            cost = _matching_cost(G, p)
            if cost < best_cost:
                best, best_cost = list(p), cost
        return best, best_cost

    def test(glyphsets, glyphs=None, names=None):

        if names is None:
            names = glyphsets
        if glyphs is None:
            glyphs = glyphsets[0].keys()

        hist = []
        problems = OrderedDict()

        def add_problem(glyphname, problem):
            problems.setdefault(glyphname, []).append(problem)

        for glyph_name in glyphs:
            # print()
            # print(glyph_name)

            try:
                allVectors = []
                allNodeTypes = []
                allContourIsomorphisms = []
                for glyphset, name in zip(glyphsets, names):
                    # print('.', end='')
                    if glyph_name not in glyphset:
                        add_problem(glyph_name, {"type": "missing", "master": name})
                        continue
                    glyph = glyphset[glyph_name]

                    perContourPen = PerContourOrComponentPen(
                        RecordingPen, glyphset=glyphset
                    )
                    try:
                        glyph.draw(perContourPen, outputImpliedClosingLine=True)
                    except TypeError:
                        glyph.draw(perContourPen)
                    contourPens = perContourPen.value
                    del perContourPen

                    contourVectors = []
                    contourIsomorphisms = []
                    nodeTypes = []
                    allNodeTypes.append(nodeTypes)
                    allVectors.append(contourVectors)
                    allContourIsomorphisms.append(contourIsomorphisms)
                    for ix, contour in enumerate(contourPens):

                        nodeVecs = tuple(instruction[0] for instruction in contour.value)
                        nodeTypes.append(nodeVecs)

                        stats = StatisticsPen(glyphset=glyphset)
                        try:
                            contour.replay(stats)
                        except OpenContourError as e:
                            add_problem(
                                glyph_name,
                                {"master": name, "contour": ix, "type": "open_path"},
                            )
                            continue
                        size = abs(stats.area) ** 0.5 * 0.5
                        vector = (
                            int(size),
                            int(stats.meanX),
                            int(stats.meanY),
                            int(stats.stddevX * 2),
                            int(stats.stddevY * 2),
                            int(stats.correlation * size),
                        )
                        contourVectors.append(vector)
                        # print(vector)

                        # Check starting point
                        if nodeVecs[0] == 'addComponent':
                            continue
                        assert nodeVecs[0] == 'moveTo'
                        assert nodeVecs[-1] in ('closePath', 'endPath')
                        points = RecordingPointPen()
                        converter = SegmentToPointPen(points, False)
                        contour.replay(converter)
                        # points.value is a list of pt,bool where bool is true if on-curve and false if off-curve;
                        # now check all rotations and mirror-rotations of the contour and build list of isomorphic
                        # possible starting points.
                        bits = 0
                        for pt,b in points.value:
                            bits = (bits << 1) | b
                        n = len(points.value)
                        mask = (1 << n ) - 1
                        isomorphisms = []
                        contourIsomorphisms.append(isomorphisms)
                        for i in range(n):
                            b = ((bits << i) & mask) | ((bits >> (n - i)))
                            if b == bits:
                                isomorphisms.append(_rot_list ([complex(*pt) for pt,bl in points.value], i))
                        # Add mirrored rotations
                        mirrored = list(reversed(points.value))
                        reversed_bits = 0
                        for pt,b in mirrored:
                            reversed_bits = (reversed_bits << 1) | b
                        for i in range(n):
                            b = ((reversed_bits << i) & mask) | ((reversed_bits >> (n - i)))
                            if b == bits:
                                isomorphisms.append(_rot_list ([complex(*pt) for pt,bl in mirrored], i))

                # Check each master against the first on in the list.
                m0 = allNodeTypes[0]
                for i,m1 in enumerate(allNodeTypes[1:]):
                    if len(m0) != len(m1):
                        add_problem(
                            glyph_name,
                            {
                                "type": "path_count",
                                "master_1": names[0],
                                "master_2": names[i + 1],
                                "value_1": len(m0),
                                "value_2": len(m1),
                            },
                        )
                    if m0 == m1:
                        continue
                    for pathIx, (nodes1, nodes2) in enumerate(zip(m0, m1)):
                        if nodes1 == nodes2:
                            continue
                        if len(nodes1) != len(nodes2):
                            add_problem(
                                glyph_name,
                                {
                                    "type": "node_count",
                                    "path": pathIx,
                                    "master_1": names[0],
                                    "master_2": names[i + 1],
                                    "value_1": len(nodes1),
                                    "value_2": len(nodes2),
                                },
                            )
                            continue
                        for nodeIx, (n1, n2) in enumerate(zip(nodes1, nodes2)):
                            if n1 != n2:
                                add_problem(
                                    glyph_name,
                                    {
                                        "type": "node_incompatibility",
                                        "path": pathIx,
                                        "node": nodeIx,
                                        "master_1": names[0],
                                        "master_2": names[i + 1],
                                        "value_1": n1,
                                        "value_2": n2,
                                    },
                                )
                                continue

                m0 = allVectors[0]
                for i, m1 in enumerate(allVectors[1:]):
                    if len(m0) != len(m1):
                        # We already reported this
                        continue
                    if not m0:
                        continue
                    costs = [[_vlen(_vdiff(v0, v1)) for v1 in m1] for v0 in m0]
                    matching, matching_cost = min_cost_perfect_bipartite_matching(costs)
                    identity_matching = list(range(len(m0)))
                    identity_cost = sum(costs[i][i] for i in range(len(m0)))
                    if matching != identity_matching and matching_cost < identity_cost * .95:
                        add_problem(
                            glyph_name,
                            {
                                "type": "contour_order",
                                "master_1": names[0],
                                "master_2": names[i + 1],
                                "value_1": list(range(len(m0))),
                                "value_2": matching,
                            },
                        )
                        break

                m0 = allContourIsomorphisms[0]
                for i, m1 in enumerate(allContourIsomorphisms[1:]):
                    if len(m0) != len(m1):
                        # We already reported this
                        continue
                    if not m0:
                        continue
                    for ix,(contour0,contour1) in enumerate(zip(m0,m1)):
                        c0 = contour0[0]
                        costs = [v for v in (_complex_vlen(_vdiff(c0, c1)) for c1 in contour1)]
                        min_cost = min(costs)
                        first_cost = costs[0]
                        if min_cost < first_cost * .95:
                            add_problem(
                                glyph_name,
                                {
                                    "type": "wrong_start_point",
                                    "contour": ix,
                                    "master_1": names[0],
                                    "master_2": names[i + 1],
                                },
                            )

            except ValueError as e:
                add_problem(
                    glyph_name,
                    {"type": "math_error", "master": name, "error": e},
                )
        return problems

    def main(args=None):
        """Test for interpolatability issues between fonts"""
        import argparse

        parser = argparse.ArgumentParser(
            "fonttools varLib.interpolatable",
            description=main.__doc__,
        )
        parser.add_argument(
            "--json",
            action="store_true",
            help="Output report in JSON format",
        )
        parser.add_argument(
            "inputs", metavar="FILE", type=str, nargs="+", help="Input TTF/UFO files"
        )

        args = parser.parse_args(args)
        glyphs = None
        # glyphs = ['uni08DB', 'uniFD76']
        # glyphs = ['uni08DE', 'uni0034']
        # glyphs = ['uni08DE', 'uni0034', 'uni0751', 'uni0753', 'uni0754', 'uni08A4', 'uni08A4.fina', 'uni08A5.fina']

        from os.path import basename

        fonts = []
        names = []

        if len(args.inputs) == 1:
            if args.inputs[0].endswith('.designspace'):
                from fontTools.designspaceLib import DesignSpaceDocument
                designspace = DesignSpaceDocument.fromfile(args.inputs[0])
                args.inputs = [master.path for master in designspace.sources]

            elif args.inputs[0].endswith('.glyphs'):
                from glyphsLib import GSFont, to_ufos
                gsfont = GSFont(args.inputs[0])
                fonts.extend(to_ufos(gsfont))
                names = ['%s-%s' % (f.info.familyName, f.info.styleName) for f in fonts]
                args.inputs = []

            elif args.inputs[0].endswith('.ttf'):
                from fontTools.ttLib import TTFont
                font = TTFont(args.inputs[0])
                if 'gvar' in font:
                    # Is variable font
                    gvar = font['gvar']
                    # Gather all "master" locations
                    locs = set()
                    for variations in gvar.variations.values():
                        for var in variations:
                            loc = []
                            for tag,val in sorted(var.axes.items()):
                                loc.append((tag,val[1]))
                            locs.add(tuple(loc))
                    # Rebuild locs as dictionaries
                    new_locs = [{}]
                    names.append("()")
                    for loc in sorted(locs, key=lambda v: (len(v), v)):
                        names.append(str(loc))
                        l = {}
                        for tag,val in loc:
                            l[tag] = val
                        new_locs.append(l)
                    locs = new_locs
                    del new_locs
                    # locs is all master locations now

                    for loc in locs:
                        fonts.append(font.getGlyphSet(location=loc, normalized=True))

                    args.inputs = []

        for filename in args.inputs:
            if filename.endswith(".ufo"):
                from fontTools.ufoLib import UFOReader
                fonts.append(UFOReader(filename))
            else:
                from fontTools.ttLib import TTFont
                fonts.append(TTFont(filename))

            names.append(basename(filename).rsplit(".", 1)[0])

        if hasattr(fonts[0], 'getGlyphSet'):
            glyphsets = [font.getGlyphSet() for font in fonts]
        else:
            glyphsets = fonts

        problems = test(glyphsets, glyphs=glyphs, names=names)
        if args.json:
            import json

            print(json.dumps(problems))
        else:
            for glyph, glyph_problems in problems.items():
                print(f"Glyph {glyph} was not compatible: ")
                for p in glyph_problems:
                    if p["type"] == "missing":
                        print("    Glyph was missing in master %s" % p["master"])
                    if p["type"] == "open_path":
                        print("    Glyph has an open path in master %s" % p["master"])
                    if p["type"] == "path_count":
                        print(
                            "    Path count differs: %i in %s, %i in %s"
                            % (p["value_1"], p["master_1"], p["value_2"], p["master_2"])
                        )
                    if p["type"] == "node_count":
                        print(
                            "    Node count differs in path %i: %i in %s, %i in %s"
                            % (
                                p["path"],
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                            )
                        )
                    if p["type"] == "node_incompatibility":
                        print(
                            "    Node %o incompatible in path %i: %s in %s, %s in %s"
                            % (
                                p["node"],
                                p["path"],
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                            )
                        )
                    if p["type"] == "contour_order":
                        print(
                            "    Contour order differs: %s in %s, %s in %s"
                            % (
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                            )
                        )
                    if p["type"] == "wrong_start_point":
                        print(
                            "    Contour %d start point differs: %s, %s"
                            % (
                                p["contour"],
                                p["master_1"],
                                p["master_2"],
                            )
                        )
        if problems:
            return problems

    if __name__ == "__main__":
        import sys

        problems = main()
        sys.exit(int(bool(problems)))