io_export_paper_model.py

            bottom = min(min(seg.bottom for seg in self.boundary), min(vertex.co.y for vertex in phantoms))
            top = max(max(seg.top for seg in self.boundary), max(vertex.co.y for vertex in phantoms))
            bbox_width = right - left
            bbox_height = top - bottom
            if min(bbox_width, bbox_height)**2 > size_limit.x**2 + size_limit.y**2:
                return False
            if (bbox_width > size_limit.x or bbox_height > size_limit.y) and (bbox_height > size_limit.x or bbox_width > size_limit.y):
                # further checks (TODO!)
                # for the time being, just throw this piece away
                return False

        distance_limit = edge.vector.length_squared * epsilon
        # try and merge UVVertices closer than sqrt(distance_limit)
        merged_uvedges = set()
        merged_uvedge_pairs = list()

        # merge all uvvertices that are close enough using a union-find structure
        # uvvertices will be merged only in cases other->self and self->self
        # all resulting groups are merged together to a uvvertex of self
        is_merged_mine = False
        shared_vertices = self.uvverts_by_id.keys() & other.uvverts_by_id.keys()
        for vertex_id in shared_vertices:
            uvs = self.uvverts_by_id[vertex_id] + other.uvverts_by_id[vertex_id]
            len_mine = len(self.uvverts_by_id[vertex_id])
            merged = dict()
            for i, a in enumerate(uvs[:len_mine]):
                i = root_find(i, merged)
                for j, b in enumerate(uvs[i+1:], i+1):
                    b = b if j < len_mine else phantoms[b]
                    j = root_find(j, merged)
                    if i == j:
                        continue
                    i, j = (j, i) if j < i else (i, j)
                    if (a.co - b.co).length_squared < distance_limit:
                        merged[j] = i
            for source, target in merged.items():
                target = root_find(target, merged)
                phantoms[uvs[source]] = uvs[target]
                is_merged_mine |= (source < len_mine)  # remember that a vertex of this island has been merged

        for uvedge in (chain(self.boundary, other.boundary) if is_merged_mine else other.boundary):
            for partner in uvedge.edge.uvedges:
                if partner is not uvedge:
                    paired_a, paired_b = phantoms.get(partner.vb, partner.vb), phantoms.get(partner.va, partner.va)
                    if (partner.uvface.flipped ^ flipped) != uvedge.uvface.flipped:
                        paired_a, paired_b = paired_b, paired_a
                    if phantoms.get(uvedge.va, uvedge.va) is paired_a and phantoms.get(uvedge.vb, uvedge.vb) is paired_b:
                        # if these two edges will get merged, add them both to the set
                        merged_uvedges.update((uvedge, partner))
                        merged_uvedge_pairs.append((uvedge, partner))
                        break

        if uvedge_b not in merged_uvedges:
            raise UnfoldError("Export failed. Please report this error, including the model if you can.")

        boundary_other = [
            PhantomUVEdge(phantoms[uvedge.va], phantoms[uvedge.vb], flipped ^ uvedge.uvface.flipped)
            for uvedge in other.boundary if uvedge not in merged_uvedges]
        # TODO: if is_merged_mine, it might make sense to create a similar list from self.boundary as well

        incidence = {vertex.tup for vertex in phantoms.values()}.intersection(vertex.tup for vertex in self.vertices)
        incidence = {position: list() for position in incidence}  # from now on, 'incidence' is a dict
        for uvedge in chain(boundary_other, self.boundary):
            if uvedge.va.co == uvedge.vb.co:
                continue
            for vertex in (uvedge.va, uvedge.vb):
                site = incidence.get(vertex.tup)
                if site is not None:
                    site.append(uvedge)
        for position, segments in incidence.items():
            if len(segments) <= 2:
                continue
            segments.sort(key=slope_from(position))
            for right, left in pairs(segments):
                is_left_ccw = left.is_uvface_upwards() ^ (left.max.tup == position)
                is_right_ccw = right.is_uvface_upwards() ^ (right.max.tup == position)
                if is_right_ccw and not is_left_ccw and type(right) is not type(left) and right not in merged_uvedges and left not in merged_uvedges:
                    return False
                if (not is_right_ccw and right not in merged_uvedges) ^ (is_left_ccw and left not in merged_uvedges):
                    return False

        # check for self-intersections
        try:
            try:
                sweepline = QuickSweepline() if self.has_safe_geometry and other.has_safe_geometry else BruteSweepline()
                sweep(sweepline, (uvedge for uvedge in chain(boundary_other, self.boundary)))
                self.has_safe_geometry &= other.has_safe_geometry
            except GeometryError:
                sweep(BruteSweepline(), (uvedge for uvedge in chain(boundary_other, self.boundary)))
                self.has_safe_geometry = False
        except Intersection:
            return False

        # mark all edges that connect the islands as not cut
        for uvedge in merged_uvedges:
            uvedge.edge.is_main_cut = False

        # include all trasformed vertices as mine
        self.vertices.update(phantoms.values())

        # update the uvverts_by_id dictionary
        for source, target in phantoms.items():
            present = self.uvverts_by_id.get(target.vertex.index)
            if not present:
                self.uvverts_by_id[target.vertex.index] = [target]
            else:
                # emulation of set behavior... sorry, it is faster
                if source in present:
                    present.remove(source)
                if target not in present:
                    present.append(target)

        # re-link uvedges and uvfaces to their transformed locations
        for uvedge in other.edges:
            uvedge.island = self
            uvedge.va = phantoms[uvedge.va]
            uvedge.vb = phantoms[uvedge.vb]
            uvedge.update()
        if is_merged_mine:
            for uvedge in self.edges:
                uvedge.va = phantoms.get(uvedge.va, uvedge.va)
                uvedge.vb = phantoms.get(uvedge.vb, uvedge.vb)
        self.edges.update(other.edges)

        for uvface in other.faces:
            uvface.island = self
            uvface.vertices = [phantoms[uvvertex] for uvvertex in uvface.vertices]
            uvface.uvvertex_by_id = {
                index: phantoms[uvvertex]
                for index, uvvertex in uvface.uvvertex_by_id.items()}
            uvface.flipped ^= flipped
        if is_merged_mine:
            # there may be own uvvertices that need to be replaced by phantoms
            for uvface in self.faces:
                if any(uvvertex in phantoms for uvvertex in uvface.vertices):
                    uvface.vertices = [phantoms.get(uvvertex, uvvertex) for uvvertex in uvface.vertices]
                    uvface.uvvertex_by_id = {
                        index: phantoms.get(uvvertex, uvvertex)
                        for index, uvvertex in uvface.uvvertex_by_id.items()}
        self.faces.extend(other.faces)

        self.boundary = [
            uvedge for uvedge in chain(self.boundary, other.boundary)
            if uvedge not in merged_uvedges]

        for uvedge, partner in merged_uvedge_pairs:
            # make sure that main faces are the ones actually merged (this changes nothing in most cases)
            uvedge.edge.main_faces[:] = uvedge.uvface.face, partner.uvface.face

        # everything seems to be OK
        return True

    def add_marker(self, marker):
        self.fake_vertices.extend(marker.bounds)
        self.markers.append(marker)

    def generate_label(self, label=None, abbreviation=None):
        """Assign a name to this island automatically"""
        abbr = abbreviation or self.abbreviation or str(self.number)
        # TODO: dots should be added in the last instant when outputting any text
        if is_upsidedown_wrong(abbr):
            abbr += "."
        self.label = label or self.label or "Island {}".format(self.number)
        self.abbreviation = abbr

    def save_uv(self, tex, cage_size):
        """Save UV Coordinates of all UVFaces to a given UV texture
        tex: UV Texture layer to use (BPy MeshUVLoopLayer struct)
        page_size: size of the page in pixels (vector)"""
        texface = tex.data
        for uvface in self.faces:
            for i, uvvertex in enumerate(uvface.vertices):
                uv = uvvertex.co + self.pos
                texface[uvface.face.loop_start + i].uv[0] = uv.x / cage_size.x
                texface[uvface.face.loop_start + i].uv[1] = uv.y / cage_size.y

    def save_uv_separate(self, tex):
        """Save UV Coordinates of all UVFaces to a given UV texture, spanning from 0 to 1
        tex: UV Texture layer to use (BPy MeshUVLoopLayer struct)
        page_size: size of the page in pixels (vector)"""
        texface = tex.data
        scale_x, scale_y = 1 / self.bounding_box.x, 1 / self.bounding_box.y
        for uvface in self.faces:
            for i, uvvertex in enumerate(uvface.vertices):
                texface[uvface.face.loop_start + i].uv[0] = uvvertex.co.x * scale_x
                texface[uvface.face.loop_start + i].uv[1] = uvvertex.co.y * scale_y


class Page:
    """Container for several Islands"""
    __slots__ = ('islands', 'name', 'image_path')

    def __init__(self, num=1):
        self.islands = list()
        self.name = "page{}".format(num)
        self.image_path = None


class UVVertex:
    """Vertex in 2D"""
    __slots__ = ('co', 'vertex', 'tup')

    def __init__(self, vector, vertex=None):
        self.co = vector.xy
        self.vertex = vertex
        self.tup = tuple(self.co)

    def __repr__(self):
        if self.vertex:
            return "UV {} [{:.3f}, {:.3f}]".format(self.vertex.index, self.co.x, self.co.y)
        else:
            return "UV * [{:.3f}, {:.3f}]".format(self.co.x, self.co.y)


class UVEdge:
    """Edge in 2D"""
    # Every UVEdge is attached to only one UVFace
    # UVEdges are doubled as needed because they both have to point clockwise around their faces
    __slots__ = ('va', 'vb', 'island', 'uvface', 'edge',
        'min', 'max', 'bottom', 'top',
        'neighbor_left', 'neighbor_right', 'sticker')

    def __init__(self, vertex1: UVVertex, vertex2: UVVertex, island: Island, uvface, edge):
        self.va = vertex1
        self.vb = vertex2
        self.update()
        self.island = island
        self.uvface = uvface
        self.sticker = None
        self.edge = edge

    def update(self):
        """Update data if UVVertices have moved"""
        self.min, self.max = (self.va, self.vb) if (self.va.tup < self.vb.tup) else (self.vb, self.va)
        y1, y2 = self.va.co.y, self.vb.co.y
        self.bottom, self.top = (y1, y2) if y1 < y2 else (y2, y1)

    def is_uvface_upwards(self):
        return (self.va.tup < self.vb.tup) ^ self.uvface.flipped

    def __repr__(self):
        return "({0.va} - {0.vb})".format(self)


class PhantomUVEdge:
    """Temporary 2D Segment for calculations"""
    __slots__ = ('va', 'vb', 'min', 'max', 'bottom', 'top')

    def __init__(self, vertex1: UVVertex, vertex2: UVVertex, flip):
        self.va, self.vb = (vertex2, vertex1) if flip else (vertex1, vertex2)
        self.min, self.max = (self.va, self.vb) if (self.va.tup < self.vb.tup) else (self.vb, self.va)
        y1, y2 = self.va.co.y, self.vb.co.y
        self.bottom, self.top = (y1, y2) if y1 < y2 else (y2, y1)

    def is_uvface_upwards(self):
        return self.va.tup < self.vb.tup

    def __repr__(self):
        return "[{0.va} - {0.vb}]".format(self)


class UVFace:
    """Face in 2D"""
    __slots__ = ('vertices', 'edges', 'face', 'island', 'flipped', 'uvvertex_by_id')

    def __init__(self, face: Face, island: Island):
        """Creace an UVFace from a Face and a fixed edge.
        face: Face to take coordinates from
        island: Island to register itself in
        fixed_edge: Edge to connect to (that already has UV coordinates)"""
        self.vertices = list()
        self.face = face
        face.uvface = self
        self.island = island
        self.flipped = False  # a flipped UVFace has edges clockwise

        rot = z_up_matrix(face.normal)
        self.uvvertex_by_id = dict()  # link vertex id -> UVVertex
        for vertex in face.vertices:
            uvvertex = UVVertex(rot * vertex.co, vertex)
            self.vertices.append(uvvertex)
            self.uvvertex_by_id[vertex.index] = uvvertex
        self.edges = list()
        edge_by_verts = dict()
        for edge in face.edges:
            edge_by_verts[(edge.va.index, edge.vb.index)] = edge
            edge_by_verts[(edge.vb.index, edge.va.index)] = edge
        for va, vb in pairs(self.vertices):
            edge = edge_by_verts[(va.vertex.index, vb.vertex.index)]
            uvedge = UVEdge(va, vb, island, self, edge)
            self.edges.append(uvedge)
            edge.uvedges.append(uvedge)  # FIXME: editing foreign attribute


class Arrow:
    """Mark in the document: an arrow denoting the number of the edge it points to"""
    __slots__ = ('bounds', 'center', 'rot', 'text', 'size')

    def __init__(self, uvedge, size, index):
        self.text = str(index)
        edge = (uvedge.vb.co - uvedge.va.co) if not uvedge.uvface.flipped else (uvedge.va.co - uvedge.vb.co)
        self.center = (uvedge.va.co + uvedge.vb.co) / 2
        self.size = size
        tangent = edge.normalized()
        cos, sin = tangent
        self.rot = M.Matrix(((cos, -sin), (sin, cos)))
        normal = M.Vector((sin, -cos))
        self.bounds = [self.center, self.center + (1.2*normal + tangent)*size, self.center + (1.2*normal - tangent)*size]


class Sticker:
    """Mark in the document: sticker tab"""
    __slots__ = ('bounds', 'center', 'rot', 'text', 'width', 'vertices')

    def __init__(self, uvedge, default_width=0.005, index=None, target_island=None):
        """Sticker is directly attached to the given UVEdge"""
        first_vertex, second_vertex = (uvedge.va, uvedge.vb) if not uvedge.uvface.flipped else (uvedge.vb, uvedge.va)
        edge = first_vertex.co - second_vertex.co
        sticker_width = min(default_width, edge.length / 2)
        other = uvedge.edge.other_uvedge(uvedge)  # This is the other uvedge - the sticking target

        other_first, other_second = (other.va, other.vb) if not other.uvface.flipped else (other.vb, other.va)
        other_edge = other_second.co - other_first.co

        # angle a is at vertex uvedge.va, b is at uvedge.vb
        cos_a = cos_b = 0.5
        sin_a = sin_b = 0.75**0.5
        # len_a is length of the side adjacent to vertex a, len_b likewise
        len_a = len_b = sticker_width / sin_a

        # fix overlaps with the most often neighbour - its sticking target
        if first_vertex == other_second:
            cos_a = max(cos_a, (edge*other_edge) / (edge.length**2))  # angles between pi/3 and 0
        elif second_vertex == other_first:
            cos_b = max(cos_b, (edge*other_edge) / (edge.length**2))  # angles between pi/3 and 0

        # Fix tabs for sticking targets with small angles
        # Index of other uvedge in its face (not in its island)
        other_idx = other.uvface.edges.index(other)
        # Left and right neighbors in the face
        other_face_neighbor_left = other.uvface.edges[(other_idx+1) % len(other.uvface.edges)]
        other_face_neighbor_right = other.uvface.edges[(other_idx-1) % len(other.uvface.edges)]
        other_edge_neighbor_a = other_face_neighbor_left.vb.co - other.vb.co
        other_edge_neighbor_b = other_face_neighbor_right.va.co - other.va.co
        # Adjacent angles in the face
        cos_a = max(cos_a, (-other_edge*other_edge_neighbor_a) / (other_edge.length*other_edge_neighbor_a.length))
        cos_b = max(cos_b, (other_edge*other_edge_neighbor_b) / (other_edge.length*other_edge_neighbor_b.length))

        # Calculate the lengths of the glue tab edges using the possibly smaller angles
        sin_a = abs(1 - cos_a**2)**0.5
        len_b = min(len_a, (edge.length * sin_a) / (sin_a * cos_b + sin_b * cos_a))
        len_a = 0 if sin_a == 0 else min(sticker_width / sin_a, (edge.length - len_b*cos_b) / cos_a)

        sin_b = abs(1 - cos_b**2)**0.5
        len_a = min(len_a, (edge.length * sin_b) / (sin_a * cos_b + sin_b * cos_a))
        len_b = 0 if sin_b == 0 else min(sticker_width / sin_b, (edge.length - len_a * cos_a) / cos_b)

        v3 = UVVertex(second_vertex.co + M.Matrix(((cos_b, -sin_b), (sin_b, cos_b))) * edge * len_b / edge.length)
        v4 = UVVertex(first_vertex.co + M.Matrix(((-cos_a, -sin_a), (sin_a, -cos_a))) * edge * len_a / edge.length)
        if v3.co != v4.co:
            self.vertices = [second_vertex, v3, v4, first_vertex]
        else:
            self.vertices = [second_vertex, v3, first_vertex]

        sin, cos = edge.y / edge.length, edge.x / edge.length
        self.rot = M.Matrix(((cos, -sin), (sin, cos)))
        self.width = sticker_width * 0.9
        if index and target_island is not uvedge.island:
            self.text = "{}:{}".format(target_island.abbreviation, index)
        else:
            self.text = index
        self.center = (uvedge.va.co + uvedge.vb.co) / 2 + self.rot*M.Vector((0, self.width*0.2))
        self.bounds = [v3.co, v4.co, self.center] if v3.co != v4.co else [v3.co, self.center]


class NumberAlone:
    """Mark in the document: numbering inside the island denoting edges to be sticked"""
    __slots__ = ('bounds', 'center', 'rot', 'text', 'size')

    def __init__(self, uvedge, index, default_size=0.005):
        """Sticker is directly attached to the given UVEdge"""
        edge = (uvedge.va.co - uvedge.vb.co) if not uvedge.uvface.flipped else (uvedge.vb.co - uvedge.va.co)

        self.size = default_size
        sin, cos = edge.y / edge.length, edge.x / edge.length
        self.rot = M.Matrix(((cos, -sin), (sin, cos)))
        self.text = index
        self.center = (uvedge.va.co + uvedge.vb.co) / 2 - self.rot*M.Vector((0, self.size*1.2))
        self.bounds = [self.center]


class SVG:
    """Simple SVG exporter"""

    def __init__(self, page_size: M.Vector, style, margin, pure_net=True, angle_epsilon=0.01):
        """Initialize document settings.
        page_size: document dimensions in meters
        pure_net: if True, do not use image"""
        self.page_size = page_size
        self.pure_net = pure_net
        self.style = style
        self.margin = margin
        self.text_size = 12
        self.angle_epsilon = angle_epsilon

    @classmethod
    def encode_image(cls, bpy_image):
        import tempfile
        import base64
        with tempfile.TemporaryDirectory() as directory:
            filename = directory + "/i.png"
            bpy_image.filepath_raw = filename
            bpy_image.save()
            return base64.encodebytes(open(filename, "rb").read()).decode('ascii')

    def format_vertex(self, vector, pos=M.Vector((0, 0))):
        """Return a string with both coordinates of the given vertex."""
        x, y = vector + pos
        return "{:.6f} {:.6f}".format((x + self.margin) * 1000, (self.page_size.y - y - self.margin) * 1000)

    def write(self, mesh, filename):
        """Write data to a file given by its name."""
        line_through = " L ".join  # used for formatting of SVG path data
        rows = "\n".join

        dl = ["{:.2f}".format(length * self.style.line_width * 1000) for length in (2, 5, 10)]
        format_style = {
            'SOLID': "none", 'DOT': "{0},{1}".format(*dl), 'DASH': "{1},{2}".format(*dl),
            'LONGDASH': "{2},{1}".format(*dl), 'DASHDOT': "{2},{1},{0},{1}".format(*dl)}

        def format_color(vec):
            return "#{:02x}{:02x}{:02x}".format(round(vec[0] * 255), round(vec[1] * 255), round(vec[2] * 255))

        def format_matrix(matrix):
            return " ".join("{:.6f}".format(cell) for column in matrix for cell in column)

        def path_convert(string, relto=os_path.dirname(filename)):
            assert(os_path)  # check the module was imported
            string = os_path.relpath(string, relto)
            if os_path.sep != '/':
                string = string.replace(os_path.sep, '/')
            return string

        styleargs = {
            name: format_color(getattr(self.style, name)) for name in (
                "outer_color", "outbg_color", "convex_color", "concave_color", "freestyle_color",
                "inbg_color", "sticker_fill", "text_color")}
        styleargs.update({
            name: format_style[getattr(self.style, name)] for name in
            ("outer_style", "convex_style", "concave_style", "freestyle_style")})
        styleargs.update({
            name: getattr(self.style, attr)[3] for name, attr in (
                ("outer_alpha", "outer_color"), ("outbg_alpha", "outbg_color"),
                ("convex_alpha", "convex_color"), ("concave_alpha", "concave_color"),
                ("freestyle_alpha", "freestyle_color"),
                ("inbg_alpha", "inbg_color"), ("sticker_alpha", "sticker_fill"),
                ("text_alpha", "text_color"))})
        styleargs.update({
            name: getattr(self.style, name) * self.style.line_width * 1000 for name in
            ("outer_width", "convex_width", "concave_width", "freestyle_width", "outbg_width", "inbg_width")})
        for num, page in enumerate(mesh.pages):
            page_filename = "{}_{}.svg".format(filename[:filename.rfind(".svg")], page.name) if len(mesh.pages) > 1 else filename
            with open(page_filename, 'w') as f:
                print(self.svg_base.format(width=self.page_size.x*1000, height=self.page_size.y*1000), file=f)
                print(self.css_base.format(**styleargs), file=f)
                if page.image_path:
                    print(
                        self.image_linked_tag.format(
                            pos="{0:.6f} {0:.6f}".format(self.margin*1000),
                            width=(self.page_size.x - 2 * self.margin)*1000,
                            height=(self.page_size.y - 2 * self.margin)*1000,
                            path=path_convert(page.image_path)),
                        file=f)
                if len(page.islands) > 1:
                    print("<g>", file=f)

                for island in page.islands:
                    print("<g>", file=f)
                    if island.image_path:
                        print(
                            self.image_linked_tag.format(
                                pos=self.format_vertex(island.pos + M.Vector((0, island.bounding_box.y))),
                                width=island.bounding_box.x*1000,
                                height=island.bounding_box.y*1000,
                                path=path_convert(island.image_path)),
                            file=f)
                    elif island.embedded_image:
                        print(
                            self.image_embedded_tag.format(
                                pos=self.format_vertex(island.pos + M.Vector((0, island.bounding_box.y))),
                                width=island.bounding_box.x*1000,
                                height=island.bounding_box.y*1000,
                                path=island.image_path),
                            island.embedded_image, "'/>",
                            file=f, sep="")
                    if island.title:
                        print(
                            self.text_tag.format(
                                size=1000 * self.text_size,
                                x=1000 * (island.bounding_box.x*0.5 + island.pos.x + self.margin),
                                y=1000 * (self.page_size.y - island.pos.y - self.margin - 0.2 * self.text_size),
                                label=island.title),
                            file=f)

                    data_markers, data_stickerfill, data_outer, data_convex, data_concave, data_freestyle = (list() for i in range(6))
                    for marker in island.markers:
                        if isinstance(marker, Sticker):
                            data_stickerfill.append("M {} Z".format(
                                line_through(self.format_vertex(vertex.co, island.pos) for vertex in marker.vertices)))
                            if marker.text:
                                data_markers.append(self.text_transformed_tag.format(
                                    label=marker.text,
                                    pos=self.format_vertex(marker.center, island.pos),
                                    mat=format_matrix(marker.rot),
                                    size=marker.width * 1000))
                        elif isinstance(marker, Arrow):
                            size = marker.size * 1000
                            position = marker.center + marker.rot*marker.size*M.Vector((0, -0.9))
                            data_markers.append(self.arrow_marker_tag.format(
                                index=marker.text,
                                arrow_pos=self.format_vertex(marker.center, island.pos),
                                scale=size,
                                pos=self.format_vertex(position, island.pos - marker.size*M.Vector((0, 0.4))),
                                mat=format_matrix(size * marker.rot)))
                        elif isinstance(marker, NumberAlone):
                            data_markers.append(self.text_transformed_tag.format(
                                label=marker.text,
                                pos=self.format_vertex(marker.center, island.pos),
                                mat=format_matrix(marker.rot),
                                size=marker.size * 1000))
                    if data_stickerfill and self.style.sticker_fill[3] > 0:
                        print("<path class='sticker' d='", rows(data_stickerfill), "'/>", file=f)

                    outer_edges = set(island.boundary)
                    while outer_edges:
                        data_loop = list()
                        uvedge = outer_edges.pop()
                        while 1:
                            if uvedge.sticker:
                                data_loop.extend(self.format_vertex(vertex.co, island.pos) for vertex in uvedge.sticker.vertices[1:])
                            else:
                                vertex = uvedge.vb if uvedge.uvface.flipped else uvedge.va
                                data_loop.append(self.format_vertex(vertex.co, island.pos))
                            uvedge = uvedge.neighbor_right
                            try:
                                outer_edges.remove(uvedge)
                            except KeyError:
                                break
                        data_outer.append("M {} Z".format(line_through(data_loop)))

                    for uvedge in island.edges:
                        edge = uvedge.edge
                        if edge.is_cut(uvedge.uvface.face) and not uvedge.sticker:
                            continue
                        data_uvedge = "M {}".format(
                            line_through(self.format_vertex(vertex.co, island.pos) for vertex in (uvedge.va, uvedge.vb)))
                        if edge.freestyle:
                            data_freestyle.append(data_uvedge)
                        # each uvedge is in two opposite-oriented variants; we want to add each only once
                        if uvedge.sticker or uvedge.uvface.flipped != (uvedge.va.vertex.index > uvedge.vb.vertex.index):
                            if edge.angle > self.angle_epsilon:
                                data_convex.append(data_uvedge)
                            elif edge.angle < -self.angle_epsilon:
                                data_concave.append(data_uvedge)
                    if island.is_inside_out:
                        data_convex, data_concave = data_concave, data_convex

                    if data_freestyle:
                        print("<path class='freestyle' d='", rows(data_freestyle), "'/>", file=f)
                    if (data_convex or data_concave) and not self.pure_net and self.style.use_inbg:
                        print("<path class='inner_background' d='", rows(data_convex + data_concave), "'/>", file=f)
                    if data_convex:
                        print("<path class='convex' d='", rows(data_convex), "'/>", file=f)
                    if data_concave:
                        print("<path class='concave' d='", rows(data_concave), "'/>", file=f)
                    if data_outer:
                        if not self.pure_net and self.style.use_outbg:
                            print("<path class='outer_background' d='", rows(data_outer), "'/>", file=f)
                        print("<path class='outer' d='", rows(data_outer), "'/>", file=f)
                    if data_markers:
                        print(rows(data_markers), file=f)
                    print("</g>", file=f)

                if len(page.islands) > 1:
                    print("</g>", file=f)
                print("</svg>", file=f)

    image_linked_tag = "<image transform='translate({pos})' width='{width:.6f}' height='{height:.6f}' xlink:href='{path}'/>"
    image_embedded_tag = "<image transform='translate({pos})' width='{width:.6f}' height='{height:.6f}' xlink:href='data:image/png;base64,"
    text_tag = "<text transform='translate({x} {y})' style='font-size:{size:.2f}'><tspan>{label}</tspan></text>"
    text_transformed_tag = "<text transform='matrix({mat} {pos})' style='font-size:{size:.2f}'><tspan>{label}</tspan></text>"
    arrow_marker_tag = "<g><path transform='matrix({mat} {arrow_pos})' class='arrow' d='M 0 0 L 1 1 L 0 0.25 L -1 1 Z'/>" \
        "<text transform='translate({pos})' style='font-size:{scale:.2f}'><tspan>{index}</tspan></text></g>"

    svg_base = """<?xml version='1.0' encoding='UTF-8' standalone='no'?>
    <svg xmlns='http://www.w3.org/2000/svg' xmlns:xlink='http://www.w3.org/1999/xlink' version='1.1'
    width='{width:.2f}mm' height='{height:.2f}mm' viewBox='0 0 {width:.2f} {height:.2f}'>"""

    css_base = """<style type="text/css">
    path {{
        fill: none;
        stroke-linecap: butt;
        stroke-linejoin: bevel;
        stroke-dasharray: none;
    }}
    path.outer {{
        stroke: {outer_color};
        stroke-dasharray: {outer_style};
        stroke-dashoffset: 0;
        stroke-width: {outer_width:.2};
        stroke-opacity: {outer_alpha:.2};
    }}
    path.convex {{
        stroke: {convex_color};
        stroke-dasharray: {convex_style};
        stroke-dashoffset:0;
        stroke-width:{convex_width:.2};
        stroke-opacity: {convex_alpha:.2}
    }}
    path.concave {{
        stroke: {concave_color};
        stroke-dasharray: {concave_style};
        stroke-dashoffset: 0;
        stroke-width: {concave_width:.2};
        stroke-opacity: {concave_alpha:.2}
    }}
    path.freestyle {{
        stroke: {freestyle_color};
        stroke-dasharray: {freestyle_style};
        stroke-dashoffset: 0;
        stroke-width: {freestyle_width:.2};
        stroke-opacity: {freestyle_alpha:.2}
    }}
    path.outer_background {{
        stroke: {outbg_color};
        stroke-opacity: {outbg_alpha};
        stroke-width: {outbg_width:.2}
    }}
    path.inner_background {{
        stroke: {inbg_color};
        stroke-opacity: {inbg_alpha};
        stroke-width: {inbg_width:.2}
    }}
    path.sticker {{
        fill: {sticker_fill};
        stroke: none;
        fill-opacity: {sticker_alpha:.2};
    }}
    path.arrow {{
        fill: #000;
    }}
    text {{
        font-style: normal;
        fill: {text_color};
        fill-opacity: {text_alpha:.2};
        stroke: none;
    }}
    text, tspan {{
        text-anchor:middle;
    }}
    </style>"""


class PDF:
    """Simple PDF exporter"""

    mm_to_pt = 72 / 25.4
    character_width_packed = {
        191: "'", 222: 'ijl\x82\x91\x92', 278: '|¦\x00\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c\r\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f !,./:;I[\\]ft\xa0·ÌÍÎÏìíîï',
        333: '()-`r\x84\x88\x8b\x93\x94\x98\x9b¡¨\xad¯²³´¸¹{}', 350: '\x7f\x81\x8d\x8f\x90\x95\x9d', 365: '"ºª*°', 469: '^', 500: 'Jcksvxyz\x9a\x9eçýÿ', 584: '¶+<=>~¬±×÷', 611: 'FTZ\x8e¿ßø',
        667: '&ABEKPSVXY\x8a\x9fÀÁÂÃÄÅÈÉÊËÝÞ', 722: 'CDHNRUwÇÐÑÙÚÛÜ', 737: '©®', 778: 'GOQÒÓÔÕÖØ', 833: 'Mm¼½¾', 889: '%æ', 944: 'W\x9c', 1000: '\x85\x89\x8c\x97\x99Æ', 1015: '@', }
    character_width = {c: value for (value, chars) in character_width_packed.items() for c in chars}

    def __init__(self, page_size: M.Vector, style, margin, pure_net=True, angle_epsilon=0.01):
        self.page_size = page_size
        self.style = style
        self.margin = M.Vector((margin, margin))
        self.pure_net = pure_net
        self.angle_epsilon = angle_epsilon

    def text_width(self, text, scale=None):
        return (scale or self.text_size) * sum(self.character_width.get(c, 556) for c in text) / 1000

    @classmethod
    def encode_image(cls, bpy_image):
        data = bytes(int(255 * px) for (i, px) in enumerate(bpy_image.pixels) if i % 4 != 3)
        image = {
            "Type": "XObject", "Subtype": "Image", "Width": bpy_image.size[0], "Height": bpy_image.size[1],
            "ColorSpace": "DeviceRGB", "BitsPerComponent": 8, "Interpolate": True,
            "Filter": ["ASCII85Decode", "FlateDecode"], "stream": data}
        return image

    def write(self, mesh, filename):
        def format_dict(obj, refs=tuple()):
            return "<< " + "".join("/{} {}\n".format(key, format_value(value, refs)) for (key, value) in obj.items()) + ">>"

        def line_through(seq):
            return "".join("{0.x:.6f} {0.y:.6f} {1} ".format(1000*v.co, c) for (v, c) in zip(seq, chain("m", repeat("l"))))

        def format_value(value, refs=tuple()):
            if value in refs:
                return "{} 0 R".format(refs.index(value) + 1)
            elif type(value) is dict:
                return format_dict(value, refs)
            elif type(value) in (list, tuple):
                return "[ " + " ".join(format_value(item, refs) for item in value) + " ]"
            elif type(value) is int:
                return str(value)
            elif type(value) is float:
                return "{:.6f}".format(value)
            elif type(value) is bool:
                return "true" if value else "false"
            else:
                return "/{}".format(value)  # this script can output only PDF names, no strings

        def write_object(index, obj, refs, f, stream=None):
            byte_count = f.write("{} 0 obj\n".format(index))
            if type(obj) is not dict:
                stream, obj = obj, dict()
            elif "stream" in obj:
                stream = obj.pop("stream")
            if stream:
                if True or type(stream) is bytes:
                    obj["Filter"] = ["ASCII85Decode", "FlateDecode"]
                    stream = encode(stream)
                obj["Length"] = len(stream)
            byte_count += f.write(format_dict(obj, refs))
            if stream:
                byte_count += f.write("\nstream\n")
                byte_count += f.write(stream)
                byte_count += f.write("\nendstream")
            return byte_count + f.write("\nendobj\n")

        def encode(data):
            from base64 import a85encode
            from zlib import compress
            if hasattr(data, "encode"):
                data = data.encode()
            return a85encode(compress(data), adobe=True, wrapcol=250)[2:].decode()

        page_size_pt = 1000 * self.mm_to_pt * self.page_size
        root = {"Type": "Pages", "MediaBox": [0, 0, page_size_pt.x, page_size_pt.y], "Kids": list()}
        catalog = {"Type": "Catalog", "Pages": root}
        font = {
            "Type": "Font", "Subtype": "Type1", "Name": "F1",
            "BaseFont": "Helvetica", "Encoding": "MacRomanEncoding"}

        dl = [length * self.style.line_width * 1000 for length in (1, 4, 9)]
        format_style = {
            'SOLID': list(), 'DOT': [dl[0], dl[1]], 'DASH': [dl[1], dl[2]],
            'LONGDASH': [dl[2], dl[1]], 'DASHDOT': [dl[2], dl[1], dl[0], dl[1]]}
        styles = {
            "Gtext": {"ca": self.style.text_color[3], "Font": [font, 1000 * self.text_size]},
            "Gsticker": {"ca": self.style.sticker_fill[3]}}
        for name in ("outer", "convex", "concave", "freestyle"):
            gs = {
                "LW": self.style.line_width * 1000 * getattr(self.style, name + "_width"),
                "CA": getattr(self.style, name + "_color")[3],
                "D": [format_style[getattr(self.style, name + "_style")], 0]}
            styles["G" + name] = gs
        for name in ("outbg", "inbg"):
            gs = {
                "LW": self.style.line_width * 1000 * getattr(self.style, name + "_width"),
                "CA": getattr(self.style, name + "_color")[3],
                "D": [format_style['SOLID'], 0]}
            styles["G" + name] = gs

        objects = [root, catalog, font]
        objects.extend(styles.values())

        for page in mesh.pages:
            commands = ["{0:.6f} 0 0 {0:.6f} 0 0 cm".format(self.mm_to_pt)]
            resources = {"Font": {"F1": font}, "ExtGState": styles, "XObject": dict()}
            for island in page.islands:
                commands.append("q 1 0 0 1 {0.x:.6f} {0.y:.6f} cm".format(1000*(self.margin + island.pos)))
                if island.embedded_image:
                    identifier = "Im{}".format(len(resources["XObject"]) + 1)
                    commands.append(self.command_image.format(1000 * island.bounding_box, identifier))
                    objects.append(island.embedded_image)
                    resources["XObject"][identifier] = island.embedded_image

                if island.title:
                    commands.append(self.command_label.format(
                        size=1000*self.text_size,
                        x=500 * (island.bounding_box.x - self.text_width(island.title)),
                        y=1000 * 0.2 * self.text_size,
                        label=island.title))

                data_markers, data_stickerfill, data_outer, data_convex, data_concave, data_freestyle = (list() for i in range(6))
                for marker in island.markers:
                    if isinstance(marker, Sticker):
                        data_stickerfill.append(line_through(marker.vertices) + "f")
                        if marker.text:
                            data_markers.append(self.command_sticker.format(
                                label=marker.text,
                                pos=1000*marker.center,
                                mat=marker.rot,
                                align=-500 * self.text_width(marker.text, marker.width),
                                size=1000*marker.width))
                    elif isinstance(marker, Arrow):
                        size = 1000 * marker.size
                        position = 1000 * (marker.center + marker.rot*marker.size*M.Vector((0, -0.9)))
                        data_markers.append(self.command_arrow.format(
                            index=marker.text,
                            arrow_pos=1000 * marker.center,
                            pos=position - 1000 * M.Vector((0.5 * self.text_width(marker.text), 0.4 * self.text_size)),
                            mat=size * marker.rot,
                            size=size))
                    elif isinstance(marker, NumberAlone):
                        data_markers.append(self.command_number.format(
                            label=marker.text,
                            pos=1000*marker.center,
                            mat=marker.rot,
                            size=1000*marker.size))

                outer_edges = set(island.boundary)
                while outer_edges:
                    data_loop = list()
                    uvedge = outer_edges.pop()
                    while 1:
                        if uvedge.sticker:
                            data_loop.extend(uvedge.sticker.vertices[1:])
                        else:
                            vertex = uvedge.vb if uvedge.uvface.flipped else uvedge.va
                            data_loop.append(vertex)
                        uvedge = uvedge.neighbor_right
                        try:
                            outer_edges.remove(uvedge)
                        except KeyError:
                            break
                    data_outer.append(line_through(data_loop) + "s")

                for uvedge in island.edges:
                    edge = uvedge.edge
                    if edge.is_cut(uvedge.uvface.face) and not uvedge.sticker:
                        continue
                    data_uvedge = line_through((uvedge.va, uvedge.vb)) + "S"
                    if edge.freestyle:
                        data_freestyle.append(data_uvedge)
                    # each uvedge is in two opposite-oriented variants; we want to add each only once
                    if uvedge.sticker or uvedge.uvface.flipped != (uvedge.va.vertex.index > uvedge.vb.vertex.index):
                        if edge.angle > self.angle_epsilon:
                            data_convex.append(data_uvedge)
                        elif edge.angle < -self.angle_epsilon:
                            data_concave.append(data_uvedge)
                if island.is_inside_out:
                    data_convex, data_concave = data_concave, data_convex

                if data_stickerfill and self.style.sticker_fill[3] > 0:
                    commands.append("/Gsticker gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} rg".format(self.style.sticker_fill))
                    commands.extend(data_stickerfill)
                if data_freestyle:
                    commands.append("/Gfreestyle gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} RG".format(self.style.freestyle_color))
                    commands.extend(data_freestyle)
                if (data_convex or data_concave) and not self.pure_net and self.style.use_inbg:
                    commands.append("/Ginbg gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} RG".format(self.style.inbg_color))
                    commands.extend(chain(data_convex, data_concave))
                if data_convex:
                    commands.append("/Gconvex gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} RG".format(self.style.convex_color))
                    commands.extend(data_convex)
                if data_concave:
                    commands.append("/Gconcave gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} RG".format(self.style.concave_color))
                    commands.extend(data_concave)
                if data_outer:
                    if not self.pure_net and self.style.use_outbg:
                        commands.append("/Goutbg gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} RG".format(self.style.outbg_color))
                        commands.extend(data_outer)
                    commands.append("/Gouter gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} RG".format(self.style.outer_color))
                    commands.extend(data_outer)
                commands.append("/Gtext gs {0[0]:.3f} {0[1]:.3f} {0[2]:.3f} rg".format(self.style.text_color))
                commands.extend(data_markers)
                commands.append("Q")
            content = "\n".join(commands)
            page = {"Type": "Page", "Parent": root, "Contents": content, "Resources": resources}
            root["Kids"].append(page)
            objects.extend((page, content))

        root["Count"] = len(root["Kids"])
        with open(filename, "w+") as f:
            xref_table = list()
            position = f.write("%PDF-1.4\n")
            for index, obj in enumerate(objects, 1):
                xref_table.append(position)
                position += write_object(index, obj, objects, f)
            xref_pos = position
            f.write("xref_table\n0 {}\n".format(len(xref_table) + 1))
            f.write("{:010} {:05} f\n".format(0, 65536))
            for position in xref_table:
                f.write("{:010} {:05} n\n".format(position, 0))
            f.write("trailer\n")
            f.write(format_dict({"Size": len(xref_table), "Root": catalog}, objects))
            f.write("\nstartxref\n{}\n%%EOF\n".format(xref_pos))

    command_label = "/Gtext gs BT {x:.6f} {y:.6f} Td ({label}) Tj ET"
    command_image = "q {0.x:.6f} 0 0 {0.y:.6f} 0 0 cm 1 0 0 -1 0 1 cm /{1} Do Q"
    command_sticker = "q {mat[0][0]:.6f} {mat[1][0]:.6f} {mat[0][1]:.6f} {mat[1][1]:.6f} {pos.x:.6f} {pos.y:.6f} cm BT {align:.6f} 0 Td /F1 {size:.6f} Tf ({label}) Tj ET Q"
    command_arrow = "q BT {pos.x:.6f} {pos.y:.6f} Td /F1 {size:.6f} Tf ({index}) Tj ET {mat[0][0]:.6f} {mat[1][0]:.6f} {mat[0][1]:.6f} {mat[1][1]:.6f} {arrow_pos.x:.6f} {arrow_pos.y:.6f} cm 0 0 m 1 -1 l 0 -0.25 l -1 -1 l f Q"
    command_number = "q {mat[0][0]:.6f} {mat[1][0]:.6f} {mat[0][1]:.6f} {mat[1][1]:.6f} {pos.x:.6f} {pos.y:.6f} cm BT /F1 {size:.6f} Tf ({label}) Tj ET Q"


class Unfold(bpy.types.Operator):
    """Blender Operator: unfold the selected object."""

    bl_idname = "mesh.unfold"
    bl_label = "Unfold"
    bl_description = "Mark seams so that the mesh can be exported as a paper model"
    bl_options = {'REGISTER', 'UNDO'}
    edit: bpy.props.BoolProperty(default=False, options={'HIDDEN'})
    priority_effect_convex: bpy.props.FloatProperty(
        name="Priority Convex", description="Priority effect for edges in convex angles",
        default=default_priority_effect['CONVEX'], soft_min=-1, soft_max=10, subtype='FACTOR')
    priority_effect_concave: bpy.props.FloatProperty(
        name="Priority Concave", description="Priority effect for edges in concave angles",
        default=default_priority_effect['CONCAVE'], soft_min=-1, soft_max=10, subtype='FACTOR')
    priority_effect_length: bpy.props.FloatProperty(
        name="Priority Length", description="Priority effect of edge length",
        default=default_priority_effect['LENGTH'], soft_min=-10, soft_max=1, subtype='FACTOR')
    do_create_uvmap: bpy.props.BoolProperty(
        name="Create UVMap", description="Create a new UV Map showing the islands and page layout", default=False)
    object = None

    @classmethod
    def poll(cls, context):
        return context.active_object and context.active_object.type == "MESH"

    def draw(self, context):
        layout = self.layout
        col = layout.column()
        col.active = not self.object or len(self.object.data.uv_textures) < 8
        col.prop(self.properties, "do_create_uvmap")
        layout.label(text="Edge Cutting Factors:")
        col = layout.column(align=True)
        col.label(text="Face Angle:")
        col.prop(self.properties, "priority_effect_convex", text="Convex")
        col.prop(self.properties, "priority_effect_concave", text="Concave")
        layout.prop(self.properties, "priority_effect_length", text="Edge Length")

    def execute(self, context):
        sce = bpy.context.scene
        settings = sce.paper_model
        recall_mode = context.object.mode
        bpy.ops.object.mode_set(mode='OBJECT')
        recall_display_islands, sce.paper_model.display_islands = sce.paper_model.display_islands, False

        self.object = context.active_object
        mesh = self.object.data

        cage_size = M.Vector((settings.output_size_x, settings.output_size_y)) if settings.limit_by_page else None
        priority_effect = {
            'CONVEX': self.priority_effect_convex,
            'CONCAVE': self.priority_effect_concave,
            'LENGTH': self.priority_effect_length}
        try:
            unfolder = Unfolder(self.object)
            unfolder.prepare(
                cage_size, self.do_create_uvmap, mark_seams=True,
                priority_effect=priority_effect, scale=sce.unit_settings.scale_length/settings.scale)
        except UnfoldError as error:
            self.report(type={'ERROR_INVALID_INPUT'}, message=error.args[0])
            bpy.ops.object.mode_set(mode=recall_mode)
            sce.paper_model.display_islands = recall_display_islands
            return {'CANCELLED'}
        if mesh.paper_island_list:
            unfolder.copy_island_names(mesh.paper_island_list)

        island_list = mesh.paper_island_list
        attributes = {item.label: (item.abbreviation, item.auto_label, item.auto_abbrev) for item in island_list}
        island_list.clear()  # remove previously defined islands
        for island in unfolder.mesh.islands:
            # add islands to UI list and set default descriptions
            list_item = island_list.add()
            # add faces' IDs to the island
            for uvface in island.faces:
                lface = list_item.faces.add()
                lface.id = uvface.face.index

            list_item["label"] = island.label
            list_item["abbreviation"], list_item["auto_label"], list_item["auto_abbrev"] = attributes.get(
                island.label,
                (island.abbreviation, True, True))
            island_item_changed(list_item, context)

        mesh.paper_island_index = -1
        mesh.show_edge_seams = True

        bpy.ops.object.mode_set(mode=recall_mode)
        sce.paper_model.display_islands = recall_display_islands
        return {'FINISHED'}


class ClearAllSeams(bpy.types.Operator):
    """Blender Operator: clear all seams of the active Mesh and all its unfold data"""

    bl_idname = "mesh.clear_all_seams"
    bl_label = "Clear All Seams"
    bl_description = "Clear all the seams and unfolded islands of the active object"

    @classmethod
    def poll(cls, context):
        return context.active_object and context.active_object.type == 'MESH'