fonttools/Lib/fontTools/varLib/interpolatable.py

"""
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 AbstractPointPen, SegmentToPointPen
from fontTools.pens.recordingPen import RecordingPen
from fontTools.pens.statisticsPen import StatisticsPen
from fontTools.pens.momentsPen import OpenContourError
from fontTools.varLib.models import piecewiseLinearMap, normalizeLocation
from fontTools.misc.fixedTools import floatToFixedToStr
from collections import defaultdict, deque
from functools import wraps
from pprint import pformat
from math import sqrt, copysign
import itertools
import logging

log = logging.getLogger("fontTools.varLib.interpolatable")


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."""
    return l[-k:] + l[:-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(AbstractPointPen):
    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_hypot2(v0, v1):
    s = 0
    for x0, x1 in zip(v0, v1):
        d = x1 - x0
        s += d * d
    return s


def _vdiff_hypot2_complex(v0, v1):
    s = 0
    for x0, x1 in zip(v0, v1):
        d = x1 - x0
        s += d.real * d.real + d.imag * d.imag
    return s


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


def min_cost_perfect_bipartite_matching_scipy(G):
    n = len(G)
    rows, cols = linear_sum_assignment(G)
    assert (rows == list(range(n))).all()
    return list(cols), _matching_cost(G, cols)


def min_cost_perfect_bipartite_matching_munkres(G):
    n = len(G)
    cols = [None] * n
    for row, col in Munkres().compute(G):
        cols[row] = col
    return cols, _matching_cost(G, cols)


def min_cost_perfect_bipartite_matching_bruteforce(G):
    n = len(G)

    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


try:
    from scipy.optimize import linear_sum_assignment

    min_cost_perfect_bipartite_matching = min_cost_perfect_bipartite_matching_scipy
except ImportError:
    try:
        from munkres import Munkres

        min_cost_perfect_bipartite_matching = (
            min_cost_perfect_bipartite_matching_munkres
        )
    except ImportError:
        min_cost_perfect_bipartite_matching = (
            min_cost_perfect_bipartite_matching_bruteforce
        )


def _contour_vector_from_stats(stats):
    size = sqrt(abs(stats.area))
    return (
        copysign((size), stats.area),
        stats.meanX,
        stats.meanY,
        stats.stddevX * 2,
        stats.stddevY * 2,
        stats.correlation * size,
    )


def _points_characteristic_bits(points):
    bits = 0
    for pt, b in points:
        bits = (bits << 1) | b
    return bits


def _points_complex_vector(points):
    vector = []
    points = [complex(*pt) for pt, _ in points]
    n = len(points)
    points.extend(points[:2])
    for i in range(n):
        p0 = points[i]

        # The point itself
        vector.append(p0)

        # The distance to the next point;
        # Emphasized by 2 empirically
        p1 = points[i + 1]
        d0 = p1 - p0
        vector.append(d0 * 2)

        """
        # The angle to the next point, as a cross product;
        # Square root of, to match dimentionality of distance.
        p2 = points[i + 2]
        d1 = p2 - p1
        cross = d0.real * d1.imag - d0.imag * d1.real
        cross = copysign(sqrt(abs(cross)), cross)
        vector.append(cross)
        """

    return vector


def _add_isomorphisms(points, reference_bits, isomorphisms, reverse):
    n = len(points)

    bits = _points_characteristic_bits(points)
    vector = _points_complex_vector(points)

    assert len(vector) % n == 0
    mult = len(vector) // n
    mask = (1 << n) - 1

    for i in range(n):
        b = ((bits << i) & mask) | ((bits >> (n - i)))
        if b == reference_bits:
            isomorphisms.append((_rot_list(vector, i * mult), i, reverse))


def _find_parents_and_order(glyphsets, locations):
    parents = [None] + list(range(len(glyphsets) - 1))
    order = list(range(len(glyphsets)))
    if locations:
        # Order base master first
        bases = (i for i, l in enumerate(locations) if all(v == 0 for v in l.values()))
        if bases:
            base = next(bases)
            logging.info("Base master index %s, location %s", base, locations[base])
        else:
            base = 0
            logging.warning("No base master location found")

        # Form a minimum spanning tree of the locations
        try:
            from scipy.sparse.csgraph import minimum_spanning_tree

            graph = [[0] * len(locations) for _ in range(len(locations))]
            axes = set()
            for l in locations:
                axes.update(l.keys())
            axes = sorted(axes)
            vectors = [tuple(l.get(k, 0) for k in axes) for l in locations]
            for i, j in itertools.combinations(range(len(locations)), 2):
                graph[i][j] = _vdiff_hypot2(vectors[i], vectors[j])

            tree = minimum_spanning_tree(graph)
            rows, cols = tree.nonzero()
            graph = defaultdict(set)
            for row, col in zip(rows, cols):
                graph[row].add(col)
                graph[col].add(row)

            # Traverse graph from the base and assign parents
            parents = [None] * len(locations)
            order = []
            visited = set()
            queue = deque([base])
            while queue:
                i = queue.popleft()
                visited.add(i)
                order.append(i)
                for j in sorted(graph[i]):
                    if j not in visited:
                        parents[j] = i
                        queue.append(j)

        except ImportError:
            pass

        log.info("Parents: %s", parents)
        log.info("Order: %s", order)
    return parents, order


def test_gen(
    glyphsets,
    glyphs=None,
    names=None,
    ignore_missing=False,
    *,
    locations=None,
    tolerance=0.95,
):
    if names is None:
        names = glyphsets

    if glyphs is None:
        # `glyphs = glyphsets[0].keys()` is faster, certainly, but doesn't allow for sparse TTFs/OTFs given out of order
        # ... risks the sparse master being the first one, and only processing a subset of the glyphs
        glyphs = {g for glyphset in glyphsets for g in glyphset.keys()}

    parents, order = _find_parents_and_order(glyphsets, locations)

    def grand_parent(i, glyphname):
        if i is None:
            return None
        i = parents[i]
        if i is None:
            return None
        while parents[i] is not None and glyphsets[i][glyphname] is None:
            i = parents[i]
        return i

    for glyph_name in glyphs:
        log.info("Testing glyph %s", glyph_name)
        try:
            allVectors = []
            allNodeTypes = []
            allContourIsomorphisms = []
            allGlyphs = [glyphset[glyph_name] for glyphset in glyphsets]
            if len([1 for glyph in allGlyphs if glyph is not None]) <= 1:
                continue
            for glyph, glyphset, name in zip(allGlyphs, glyphsets, names):
                if glyph is None:
                    if not ignore_missing:
                        yield (glyph_name, {"type": "missing", "master": name})
                    allNodeTypes.append(None)
                    allVectors.append(None)
                    allContourIsomorphisms.append(None)
                    continue

                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):
                    contourOps = tuple(op for op, arg in contour.value)
                    nodeTypes.append(contourOps)

                    stats = StatisticsPen(glyphset=glyphset)
                    try:
                        contour.replay(stats)
                    except OpenContourError as e:
                        yield (
                            glyph_name,
                            {"master": name, "contour": ix, "type": "open_path"},
                        )
                        continue
                    contourVectors.append(_contour_vector_from_stats(stats))

                    # Check starting point
                    if contourOps[0] == "addComponent":
                        continue
                    assert contourOps[0] == "moveTo"
                    assert contourOps[-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.

                    isomorphisms = []
                    contourIsomorphisms.append(isomorphisms)

                    reference_bits = _points_characteristic_bits(points.value)
                    # Add rotations
                    _add_isomorphisms(points.value, reference_bits, isomorphisms, False)
                    # Add mirrored rotations
                    _add_isomorphisms(
                        list(reversed(points.value)), reference_bits, isomorphisms, True
                    )

            for m1idx in order:
                m1 = allNodeTypes[m1idx]
                if m1 is None:
                    continue
                m0idx = grand_parent(m1idx, glyph_name)
                if m0idx is None:
                    continue
                m0 = allNodeTypes[m0idx]
                if m0 is None:
                    continue
                if len(m0) != len(m1):
                    yield (
                        glyph_name,
                        {
                            "type": "path_count",
                            "master_1": names[m0idx],
                            "master_2": names[m1idx],
                            "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):
                        yield (
                            glyph_name,
                            {
                                "type": "node_count",
                                "path": pathIx,
                                "master_1": names[m0idx],
                                "master_2": names[m1idx],
                                "value_1": len(nodes1),
                                "value_2": len(nodes2),
                            },
                        )
                        continue
                    for nodeIx, (n1, n2) in enumerate(zip(nodes1, nodes2)):
                        if n1 != n2:
                            yield (
                                glyph_name,
                                {
                                    "type": "node_incompatibility",
                                    "path": pathIx,
                                    "node": nodeIx,
                                    "master_1": names[m0idx],
                                    "master_2": names[m1idx],
                                    "value_1": n1,
                                    "value_2": n2,
                                },
                            )
                            continue

            matchings = [None] * len(allVectors)
            for m1idx in order:
                m1 = allVectors[m1idx]
                if not m1:
                    continue
                m0idx = grand_parent(m1idx, glyph_name)
                if m0idx is None:
                    continue
                m0 = allVectors[m0idx]
                if m0 is None:
                    continue
                if len(m0) != len(m1):
                    # We already reported this
                    continue
                costs = [[_vdiff_hypot2(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 * tolerance
                ):
                    yield (
                        glyph_name,
                        {
                            "type": "contour_order",
                            "master_1": names[m0idx],
                            "master_2": names[m1idx],
                            "value_1": list(range(len(m0))),
                            "value_2": matching,
                        },
                    )
                    matchings[m1idx] = matching

            for m1idx in order:
                m1 = allContourIsomorphisms[m1idx]
                if m1 is None:
                    continue
                m0idx = grand_parent(m1idx, glyph_name)
                if m0idx is None:
                    continue
                m0 = allContourIsomorphisms[m0idx]
                if m0 is None:
                    continue
                if len(m0) != len(m1):
                    # We already reported this
                    continue
                for ix, (contour0, contour1) in enumerate(zip(m0, m1)):
                    if len(contour0) != len(contour1):
                        # We already reported this
                        continue
                    # If contour-order is wrong, don't try reporting starting-point
                    if matchings[m1idx] is not None and matchings[m1idx][ix] != ix:
                        continue
                    c0 = contour0[0]
                    costs = [_vdiff_hypot2_complex(c0[0], c1[0]) for c1 in contour1]
                    min_cost_idx, min_cost = min(enumerate(costs), key=lambda x: x[1])
                    first_cost = costs[0]
                    if min_cost < first_cost * tolerance:
                        yield (
                            glyph_name,
                            {
                                "type": "wrong_start_point",
                                "contour": ix,
                                "master_1": names[m0idx],
                                "master_2": names[m1idx],
                                "value_1": 0,
                                "value_2": contour1[min_cost_idx][1],
                                "reversed": contour1[min_cost_idx][2],
                            },
                        )

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


@wraps(test_gen)
def test(*args, **kwargs):
    problems = defaultdict(list)
    for glyphname, problem in test_gen(*args, **kwargs):
        problems[glyphname].append(problem)
    return problems


def recursivelyAddGlyph(glyphname, glyphset, ttGlyphSet, glyf):
    if glyphname in glyphset:
        return
    glyphset[glyphname] = ttGlyphSet[glyphname]

    for component in getattr(glyf[glyphname], "components", []):
        recursivelyAddGlyph(component.glyphName, glyphset, ttGlyphSet, glyf)


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

    parser = argparse.ArgumentParser(
        "fonttools varLib.interpolatable",
        description=main.__doc__,
    )
    parser.add_argument(
        "--glyphs",
        action="store",
        help="Space-separate name of glyphs to check",
    )
    parser.add_argument(
        "--tolerance",
        action="store",
        type=float,
        help="Error tolerance. Default 0.95",
    )
    parser.add_argument(
        "--json",
        action="store_true",
        help="Output report in JSON format",
    )
    parser.add_argument(
        "--pdf",
        action="store",
        help="Output report in PDF format",
    )
    parser.add_argument(
        "--html",
        action="store",
        help="Output report in HTML format",
    )
    parser.add_argument(
        "--quiet",
        action="store_true",
        help="Only exit with code 1 or 0, no output",
    )
    parser.add_argument(
        "--output",
        action="store",
        help="Output file for the problem report; Default: stdout",
    )
    parser.add_argument(
        "--ignore-missing",
        action="store_true",
        help="Will not report glyphs missing from sparse masters as errors",
    )
    parser.add_argument(
        "inputs",
        metavar="FILE",
        type=str,
        nargs="+",
        help="Input a single variable font / DesignSpace / Glyphs file, or multiple TTF/UFO files",
    )
    parser.add_argument("-v", "--verbose", action="store_true", help="Run verbosely.")

    args = parser.parse_args(args)

    from fontTools import configLogger

    configLogger(level=("INFO" if args.verbose else "ERROR"))

    glyphs = args.glyphs.split() if args.glyphs else None

    from os.path import basename

    fonts = []
    names = []
    locations = []

    if len(args.inputs) == 1:
        designspace = None
        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]
            locations = [master.location for master in designspace.sources]
            axis_triples = {
                a.name: (a.minimum, a.default, a.maximum) for a in designspace.axes
            }
            axis_mappings = {a.name: a.map for a in designspace.axes}
            axis_triples = {
                k: tuple(piecewiseLinearMap(v, dict(axis_mappings[k])) for v in vv)
                for k, vv in axis_triples.items()
            }

        elif args.inputs[0].endswith(".glyphs"):
            from glyphsLib import GSFont, to_designspace

            gsfont = GSFont(args.inputs[0])
            designspace = to_designspace(gsfont)
            fonts = [source.font for source in designspace.sources]
            names = ["%s-%s" % (f.info.familyName, f.info.styleName) for f in fonts]
            args.inputs = []
            locations = [master.location for master in designspace.sources]
            axis_triples = {
                a.name: (a.minimum, a.default, a.maximum) for a in designspace.axes
            }
            axis_mappings = {a.name: a.map for a in designspace.axes}
            axis_triples = {
                k: tuple(piecewiseLinearMap(v, dict(axis_mappings[k])) for v in vv)
                for k, vv in axis_triples.items()
            }

        elif args.inputs[0].endswith(".ttf"):
            from fontTools.ttLib import TTFont

            font = TTFont(args.inputs[0])
            if "gvar" in font:
                # Is variable font

                axisMapping = {}
                fvar = font["fvar"]
                for axis in fvar.axes:
                    axisMapping[axis.axisTag] = {
                        -1: axis.minValue,
                        0: axis.defaultValue,
                        1: axis.maxValue,
                    }
                if "avar" in font:
                    avar = font["avar"]
                    for axisTag, segments in avar.segments.items():
                        fvarMapping = axisMapping[axisTag].copy()
                        for location, value in segments.items():
                            axisMapping[axisTag][value] = piecewiseLinearMap(
                                location, fvarMapping
                            )

                gvar = font["gvar"]
                glyf = font["glyf"]
                # Gather all glyphs at their "master" locations
                ttGlyphSets = {}
                glyphsets = defaultdict(dict)

                if glyphs is None:
                    glyphs = sorted(gvar.variations.keys())
                for glyphname in glyphs:
                    for var in gvar.variations[glyphname]:
                        locDict = {}
                        loc = []
                        for tag, val in sorted(var.axes.items()):
                            locDict[tag] = val[1]
                            loc.append((tag, val[1]))

                        locTuple = tuple(loc)
                        if locTuple not in ttGlyphSets:
                            ttGlyphSets[locTuple] = font.getGlyphSet(
                                location=locDict, normalized=True
                            )

                        recursivelyAddGlyph(
                            glyphname, glyphsets[locTuple], ttGlyphSets[locTuple], glyf
                        )

                names = ["''"]
                fonts = [font.getGlyphSet()]
                locations = [{}]
                axis_triples = {a: (-1, 0, +1) for a in sorted(axisMapping.keys())}
                for locTuple in sorted(glyphsets.keys(), key=lambda v: (len(v), v)):
                    name = (
                        "'"
                        + " ".join(
                            "%s=%s"
                            % (
                                k,
                                floatToFixedToStr(
                                    piecewiseLinearMap(v, axisMapping[k]), 14
                                ),
                            )
                            for k, v in locTuple
                        )
                        + "'"
                    )
                    names.append(name)
                    fonts.append(glyphsets[locTuple])
                    locations.append(dict(locTuple))
                args.ignore_missing = True
                args.inputs = []

    if not locations:
        locations = [{} for _ in fonts]

    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])

    glyphsets = []
    for font in fonts:
        if hasattr(font, "getGlyphSet"):
            glyphset = font.getGlyphSet()
        else:
            glyphset = font
        glyphsets.append({k: glyphset[k] for k in glyphset.keys()})

    if len(glyphsets) == 1:
        return None

    if not glyphs:
        glyphs = sorted(set([gn for glyphset in glyphsets for gn in glyphset.keys()]))

    glyphsSet = set(glyphs)
    for glyphset in glyphsets:
        glyphSetGlyphNames = set(glyphset.keys())
        diff = glyphsSet - glyphSetGlyphNames
        if diff:
            for gn in diff:
                glyphset[gn] = None

    # Normalize locations
    locations = [normalizeLocation(loc, axis_triples) for loc in locations]

    log.info("Running on %d glyphsets", len(glyphsets))
    log.info("Locations: %s", pformat(locations))
    problems_gen = test_gen(
        glyphsets,
        glyphs=glyphs,
        names=names,
        locations=locations,
        ignore_missing=args.ignore_missing,
        tolerance=args.tolerance or 0.95,
    )
    problems = defaultdict(list)

    f = sys.stdout if args.output is None else open(args.output, "w")

    if not args.quiet:
        if args.json:
            import json

            for glyphname, problem in problems_gen:
                problems[glyphname].append(problem)

            print(json.dumps(problems), file=f)
        else:
            last_glyphname = None
            for glyphname, p in problems_gen:
                problems[glyphname].append(p)

                if glyphname != last_glyphname:
                    print(f"Glyph {glyphname} was not compatible: ", file=f)
                    last_glyphname = glyphname

                if p["type"] == "missing":
                    print("    Glyph was missing in master %s" % p["master"], file=f)
                if p["type"] == "open_path":
                    print(
                        "    Glyph has an open path in master %s" % p["master"], file=f
                    )
                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"]),
                        file=f,
                    )
                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"],
                        ),
                        file=f,
                    )
                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"],
                        ),
                        file=f,
                    )
                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"],
                        ),
                        file=f,
                    )
                if p["type"] == "wrong_start_point":
                    print(
                        "    Contour %d start point differs: %s in %s, %s in %s; reversed: %s"
                        % (
                            p["contour"],
                            p["value_1"],
                            p["master_1"],
                            p["value_2"],
                            p["master_2"],
                            p["reversed"],
                        ),
                        file=f,
                    )
                if p["type"] == "math_error":
                    print(
                        "    Miscellaneous error in %s: %s"
                        % (
                            p["master"],
                            p["error"],
                        ),
                        file=f,
                    )
    else:
        for glyphname, problem in problems_gen:
            problems[glyphname].append(problem)

    if args.pdf:
        log.info("Writing PDF to %s", args.pdf)
        from .interpolatablePlot import InterpolatablePDF

        with InterpolatablePDF(args.pdf, glyphsets=glyphsets, names=names) as pdf:
            pdf.add_problems(problems)
            if not problems and not args.quiet:
                pdf.draw_cupcake()

    if args.html:
        log.info("Writing HTML to %s", args.html)
        from .interpolatablePlot import InterpolatableSVG

        svgs = []
        with InterpolatableSVG(svgs, glyphsets=glyphsets, names=names) as svg:
            svg.add_problems(problems)
            if not problems and not args.quiet:
                svg.draw_cupcake()

        import base64

        with open(args.html, "wb") as f:
            f.write(b"<!DOCTYPE html>\n")
            f.write(b"<html><body align=center>\n")
            for svg in svgs:
                f.write("<img src='data:image/svg+xml;base64,".encode("utf-8"))
                f.write(base64.b64encode(svg))
                f.write(b"' />\n")
                f.write(b"<hr>\n")
            f.write(b"</body></html>\n")

    if problems:
        return problems


if __name__ == "__main__":
    import sys

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