"""
This file describes the shapes of the wing shells. The joints are defined in
`__init__.py`.
"""
import math
from enum import Enum
from dataclasses import dataclass, field
from typing import Mapping, Tuple, Optional
import cadquery as Cq
from nhf import Material, Role
from nhf.build import Model, TargetKind, target, assembly, submodel
from nhf.parts.box import box_with_centre_holes, MountingBox, Hole
from nhf.parts.joints import HirthJoint
from nhf.touhou.houjuu_nue.joints import ShoulderJoint, ElbowJoint, DiskJoint
import nhf.utils

@dataclass(kw_only=True)
class WingProfile(Model):

    name: str = "wing"

    base_joint: HirthJoint = field(default_factory=lambda: HirthJoint(
        radius=25.0,
        radius_inner=20.0,
        tooth_height=7.0,
        base_height=5,
        n_tooth=24,
    ))
    base_width: float = 80.0
    hs_joint_corner_dx: float = 17.0
    hs_joint_corner_dz: float = 24.0
    hs_joint_corner_hole_diam: float = 6.0
    hs_joint_axis_diam: float = 12.0
    base_plate_width: float = 50.0

    panel_thickness: float = 25.4 / 16
    spacer_thickness: float = 25.4 / 8

    shoulder_joint: ShoulderJoint = field(default_factory=lambda: ShoulderJoint(
    ))
    shoulder_width: float = 30.0
    shoulder_tip_x: float = -200.0
    shoulder_tip_y: float = 160.0
    shoulder_mid_x: float = -105.0
    shoulder_mid_y: float = 75.0

    s1_thickness: float = 25.0

    elbow_joint: ElbowJoint = field(default_factory=lambda: ElbowJoint(
        disk_joint=DiskJoint(
            movement_angle=55,
        ),
        flip=False,
    ))

    s2_thickness: float = 25.0

    wrist_joint: ElbowJoint = field(default_factory=lambda: ElbowJoint(
        disk_joint=DiskJoint(
            movement_angle=45,
        ),
        flip=True,
    ))

    s3_thickness: float = 25.0

    mat_panel: Material = Material.ACRYLIC_TRANSLUSCENT
    mat_bracket: Material = Material.ACRYLIC_TRANSPARENT
    mat_hs_joint: Material = Material.PLASTIC_PLA
    role_panel: Role = Role.STRUCTURE

    # Subclass must populate
    elbow_x: float
    elbow_y: float
    elbow_angle: float
    elbow_height: float
    wrist_x: float
    wrist_y: float
    wrist_angle: float
    wrist_height: float

    flip: bool = False

    def __post_init__(self):
        super().__init__(name=self.name)

        self.elbow_theta = math.radians(self.elbow_angle)
        self.elbow_c = math.cos(self.elbow_theta)
        self.elbow_s = math.sin(self.elbow_theta)
        self.elbow_top_x, self.elbow_top_y = self.elbow_to_abs(0, self.elbow_height)
        self.wrist_theta = math.radians(self.wrist_angle)
        self.wrist_c = math.cos(self.wrist_theta)
        self.wrist_s = math.sin(self.wrist_theta)
        self.wrist_top_x, self.wrist_top_y = self.wrist_to_abs(0, self.wrist_height)

    @submodel(name="shoulder-joint")
    def submodel_shoulder_joint(self) -> Model:
        return self.shoulder_joint
    @submodel(name="elbow-joint")
    def submodel_elbow_joint(self) -> Model:
        return self.elbow_joint
    @submodel(name="wrist-joint")
    def submodel_wrist_joint(self) -> Model:
        return self.wrist_joint

    @property
    def root_height(self) -> float:
        return self.shoulder_joint.height

    @property
    def shoulder_height(self) -> float:
        return self.shoulder_joint.height

    @target(name="base-hs-joint")
    def base_hs_joint(self) -> Cq.Workplane:
        """
        Parent part of the Houjuu-Scarlett joint, which is composed of a Hirth
        coupling, a cylindrical base, and a mounting base.
        """
        hirth = self.base_joint.generate(is_mated=True)
        dy = self.hs_joint_corner_dx
        dx = self.hs_joint_corner_dz
        conn = [
            (-dx, -dy),
            (dx, -dy),
            (dx, dy),
            (-dx, dy),
        ]
        result = (
            Cq.Workplane('XY')
            .box(
                self.root_height,
                self.base_plate_width,
                self.base_joint.base_height,
                centered=(True, True, False))
            #.translate((0, 0, -self.base_joint.base_height))
            #.edges("|Z")
            #.fillet(self.hs_joint_corner_fillet)
            .faces(">Z")
            .workplane()
            .pushPoints(conn)
            .hole(self.hs_joint_corner_hole_diam)
        )
        # Creates a plane parallel to the holes but shifted to the base
        plane = result.faces(">Z").workplane(offset=-self.base_joint.base_height)

        for i, (px, py) in enumerate(conn):
            plane.moveTo(px, py).tagPlane(f"conn{i}")
        result = (
            result
            .faces(">Z")
            .workplane()
            .union(hirth, tol=0.1)
            .clean()
        )
        result = (
            result.faces("<Z")
            .workplane()
            .hole(self.hs_joint_axis_diam)
        )
        return result

    @target(name="profile-s0", kind=TargetKind.DXF)
    def profile_s0(self) -> Cq.Sketch:
        tip_x = self.shoulder_tip_x
        tip_y = self.shoulder_tip_y
        mid_x = self.shoulder_mid_x
        mid_y = self.shoulder_mid_y
        sketch = (
            Cq.Sketch()
            .segment((-self.base_width, 0), (0, 0))
            .spline([
                (0, 0),
                (-30.0, 80.0),
                (tip_x, tip_y)
            ])
            .segment(
                (tip_x, tip_y),
                (tip_x, tip_y - self.shoulder_width),
            )
            .segment(
                (tip_x, tip_y - self.shoulder_width),
                (mid_x, mid_y),
            )
            .segment(
                (mid_x, mid_y),
                (-self.base_width, 0),
            )
            .assemble()
        )
        return sketch

    def outer_shell_s0(self) -> Cq.Workplane:
        tip_x = self.shoulder_tip_x
        tip_y = self.shoulder_tip_y
        t = self.panel_thickness
        edge = Cq.Edge.makeSpline([
            Cq.Vector(x, y, 0)
            for x,y in [
                (0, 0),
                (-30.0, 80.0),
                (tip_x, tip_y)
            ]
        ])
        result = (
            Cq.Workplane('XZ')
            .rect(t, self.root_height + t*2, centered=(False, False))
            .sweep(edge)
        )
        plane = result.copyWorkplane(Cq.Workplane('XZ'))
        plane.moveTo(0, 0).tagPlane("bot")
        plane.moveTo(0, self.root_height + t*2).tagPlane("top")
        return result

    @submodel(name="spacer-s0-shoulder")
    def spacer_s0_shoulder(self) -> MountingBox:
        """
        Should be cut
        """
        holes = [
            hole
            for i, x in enumerate(self.shoulder_joint.parent_conn_hole_pos)
            for hole in [
                Hole(x=x, tag=f"conn_top{i}"),
                Hole(x=-x, tag=f"conn_bot{i}"),
            ]
        ]
        return MountingBox(
            length=self.shoulder_joint.height,
            width=self.shoulder_width,
            thickness=self.spacer_thickness,
            holes=holes,
            hole_diam=self.shoulder_joint.parent_conn_hole_diam,
            centred=(True, True),
            flip_y=self.flip,
        )
    @submodel(name="spacer-s0-shoulder")
    def spacer_s0_base(self) -> MountingBox:
        """
        Should be cut
        """
        assert self.base_plate_width < self.base_width
        assert self.hs_joint_corner_dx * 2 < self.base_width
        assert self.hs_joint_corner_dz * 2 < self.root_height
        dy = self.hs_joint_corner_dx
        dx = self.hs_joint_corner_dz
        holes = [
            Hole(x=-dx, y=-dy),
            Hole(x=dx, y=-dy),
            Hole(x=dx, y=dy),
            Hole(x=-dx, y=dy),
        ]
        return MountingBox(
            length=self.root_height,
            width=self.base_plate_width,
            thickness=self.spacer_thickness,
            holes=holes,
            hole_diam=self.hs_joint_corner_hole_diam,
            centred=(True, True),
            flip_y=self.flip,
        )

    def surface_s0(self, top: bool = False) -> Cq.Workplane:
        base_dx = -(self.base_width - self.base_plate_width) / 2
        base_dy = self.base_joint.joint_height
        tags = [
            ("shoulder", (self.shoulder_tip_x, self.shoulder_tip_y - self.shoulder_width), 0),
            ("base", (base_dx,  base_dy), 90),
        ]
        result = nhf.utils.extrude_with_markers(
            self.profile_s0(),
            self.panel_thickness,
            tags,
            reverse=not top,
        )
        h = self.panel_thickness if top else 0
        result.copyWorkplane(Cq.Workplane('XZ')).moveTo(0, h).tagPlane("corner")
        return result

    @assembly()
    def assembly_s0(self) -> Cq.Assembly:
        result = (
            Cq.Assembly()
            .addS(self.surface_s0(top=True), name="bot",
                  material=self.mat_panel, role=self.role_panel)
            .addS(self.surface_s0(top=False), name="top",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("bot@faces@>Z", "top@faces@<Z", "Point",
                       param=self.shoulder_joint.height)
            .addS(self.outer_shell_s0(), name="outer_shell",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("bot?corner", "outer_shell?bot", "Plane", param=0)
            .constrain("top?corner", "outer_shell?top", "Plane", param=0)
        )
        for o, tag in [
                (self.spacer_s0_shoulder().generate(), "shoulder"),
                (self.spacer_s0_base().generate(), "base")
        ]:
            top_tag, bot_tag = "top", "bot"
            if self.flip:
                top_tag, bot_tag = bot_tag, top_tag
            (
                result
                .addS(o, name=tag,
                      role=Role.STRUCTURE | Role.CONNECTION,
                      material=self.mat_bracket)
                .constrain(f"{tag}?{bot_tag}", f"bot?{tag}", "Plane")
                .constrain(f"{tag}?{top_tag}", f"top?{tag}", "Plane")
                .constrain(f"{tag}?dir", f"top?{tag}_dir", "Axis")
            )
        hs_joint = self.base_hs_joint()
        (
            result
            .addS(hs_joint, name="hs", role=Role.CHILD, material=self.mat_hs_joint)
            .constrain("hs?conn0", "base?conn0", "Plane", param=0)
            .constrain("hs?conn1", "base?conn1", "Plane", param=0)
            .constrain("hs?conn2", "base?conn2", "Plane", param=0)
        )
        return result.solve()


    ### s1, s2, s3 ###
    def profile(self) -> Cq.Sketch:
        """
        Generates profile from shoulder and above
        """

    def _assembly_insert_spacer(
            self,
            a: Cq.Assembly,
            spacer: Cq.Workplane,
            point_tag: str,
            front_tag: str = "front",
            back_tag: str = "back",
            flipped: bool = False,
            ):
        """
        For a child joint facing up, front panel should be on the right, back
        panel on the left
        """
        site_front, site_back = "right", "left"
        if flipped:
            site_front, site_back = site_back, site_front
        angle = 0
        (
            a
            .addS(
                spacer,
                name=point_tag,
                material=self.mat_bracket,
                role=self.role_panel)
            .constrain(f"{front_tag}?{point_tag}",
                       f"{point_tag}?{site_front}", "Plane")
            .constrain(f"{back_tag}?{point_tag}",
                       f"{point_tag}?{site_back}", "Plane")
            .constrain(f"{point_tag}?dir", f"{front_tag}?{point_tag}_dir",
                       "Axis", param=angle)
        )

    def elbow_to_abs(self, x: float, y: float) -> Tuple[float, float]:
        elbow_x = self.elbow_x + x * self.elbow_c - y * self.elbow_s
        elbow_y = self.elbow_y + x * self.elbow_s + y * self.elbow_c
        return elbow_x, elbow_y
    def wrist_to_abs(self, x: float, y: float) -> Tuple[float, float]:
        wrist_x = self.wrist_x + x * self.wrist_c - y * self.wrist_s
        wrist_y = self.wrist_y + x * self.wrist_s + y * self.wrist_c
        return wrist_x, wrist_y



    def _mask_elbow(self) -> list[Tuple[float, float]]:
        """
        Polygon shape to mask out parts above the elbow
        """
        l = 200
        return [
            (0, -l),
            (self.elbow_x, -l),
            (self.elbow_x, self.elbow_y),
            (self.elbow_top_x, self.elbow_top_y),
            (self.elbow_top_x, l),
            (0, l)
        ]

    def _mask_wrist(self) -> list[Tuple[float, float]]:
        l = 200
        return [
            (0, -l),
            (self.wrist_x, -l),
            (self.wrist_x, self.wrist_y),
            (self.wrist_top_x, self.wrist_top_y),
            (self.wrist_top_x, l),
            (0, l),
        ]


    @target(name="profile-s1", kind=TargetKind.DXF)
    def profile_s1(self) -> Cq.Sketch:
        profile = (
            self.profile()
            .reset()
            .polygon(self._mask_elbow(), mode='i')
        )
        return profile
    def surface_s1(self,
                   shoulder_mount_inset: float = 0,
                   elbow_mount_inset: float = 0,
                   front: bool = True) -> Cq.Workplane:
        shoulder_h = self.shoulder_joint.child_height
        h = (self.shoulder_joint.height - shoulder_h) / 2
        tags_shoulder = [
            ("shoulder_bot", (shoulder_mount_inset, h), 90),
            ("shoulder_top", (shoulder_mount_inset, h + shoulder_h), 270),
        ]
        elbow_h = self.elbow_joint.parent_beam.total_height
        h = (self.elbow_height - elbow_h) / 2
        tags_elbow = [
            ("elbow_bot",
             self.elbow_to_abs(-elbow_mount_inset, h),
             self.elbow_angle + 90),
            ("elbow_top",
             self.elbow_to_abs(-elbow_mount_inset, h + elbow_h),
             self.elbow_angle + 270),
        ]
        profile = self.profile_s1()
        tags = tags_shoulder + tags_elbow
        return nhf.utils.extrude_with_markers(profile, self.panel_thickness, tags, reverse=front)
    @submodel(name="spacer-s1-shoulder")
    def spacer_s1_shoulder(self) -> MountingBox:
        holes = [
            Hole(x)
            for x in self.shoulder_joint.child_conn_hole_pos
        ]
        return MountingBox(
            length=50.0, # FIXME: magic
            width=self.s1_thickness,
            thickness=self.spacer_thickness,
            holes=holes,
            hole_diam=self.shoulder_joint.child_conn_hole_diam,
        )
    @submodel(name="spacer-s1-elbow")
    def spacer_s1_elbow(self) -> MountingBox:
        holes = [
            Hole(x)
            for x in self.elbow_joint.parent_hole_pos()
        ]
        return MountingBox(
            length=70.0, # FIXME: magic
            width=self.s1_thickness,
            thickness=self.spacer_thickness,
            holes=holes,
            hole_diam=self.elbow_joint.hole_diam,
        )
    @assembly()
    def assembly_s1(self) -> Cq.Assembly:
        result = (
            Cq.Assembly()
            .addS(self.surface_s1(front=True), name="front",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("front", "Fixed")
            .addS(self.surface_s1(front=False), name="back",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("front@faces@>Z", "back@faces@<Z", "Point",
                       param=self.s1_thickness)
        )
        for t in ["shoulder_bot", "shoulder_top", "elbow_bot", "elbow_top"]:
            is_top = t.endswith("_top")
            is_parent = t.startswith("shoulder")
            o = self.spacer_s1_shoulder().generate() if is_parent else self.spacer_s1_elbow().generate()
            self._assembly_insert_spacer(
                result,
                o,
                point_tag=t,
                flipped=is_top != is_parent,
            )
        return result.solve()

    @target(name="profile-s2", kind=TargetKind.DXF)
    def profile_s2(self) -> Cq.Sketch:
        profile = (
            self.profile()
            .reset()
            .polygon(self._mask_elbow(), mode='s')
            .reset()
            .polygon(self._mask_wrist(), mode='i')
        )
        return profile
    def surface_s2(self,
                   thickness: float = 25.4/16,
                   elbow_mount_inset: float = 0,
                   wrist_mount_inset: float = 0,
                   front: bool = True) -> Cq.Workplane:
        elbow_h = self.elbow_joint.child_beam.total_height
        h = (self.elbow_height - elbow_h) / 2
        tags_elbow = [
            ("elbow_bot",
             self.elbow_to_abs(elbow_mount_inset, h),
             self.elbow_angle + 90),
            ("elbow_top",
             self.elbow_to_abs(elbow_mount_inset, h + elbow_h),
             self.elbow_angle - 90),
        ]
        wrist_h = self.wrist_joint.parent_beam.total_height
        h = (self.wrist_height - wrist_h) / 2
        tags_wrist = [
            ("wrist_bot",
             self.wrist_to_abs(-wrist_mount_inset, h),
             self.wrist_angle + 90),
            ("wrist_top",
             self.wrist_to_abs(-wrist_mount_inset, h + wrist_h),
             self.wrist_angle - 90),
        ]
        profile = self.profile_s2()
        tags = tags_elbow + tags_wrist
        return nhf.utils.extrude_with_markers(profile, thickness, tags, reverse=front)
    @submodel(name="spacer-s2-elbow")
    def spacer_s2_elbow(self) -> MountingBox:
        holes = [
            Hole(x)
            for x in self.elbow_joint.child_hole_pos()
        ]
        return MountingBox(
            length=50.0, # FIXME: magic
            width=self.s2_thickness,
            thickness=self.spacer_thickness,
            holes=holes,
            hole_diam=self.elbow_joint.hole_diam,
        )
    @submodel(name="spacer-s2-wrist")
    def spacer_s2_wrist(self) -> MountingBox:
        holes = [
            Hole(x)
            for x in self.wrist_joint.parent_hole_pos()
        ]
        return MountingBox(
            length=70.0, # FIXME: magic
            width=self.s1_thickness,
            thickness=self.spacer_thickness,
            holes=holes,
            hole_diam=self.wrist_joint.hole_diam,
        )
    @assembly()
    def assembly_s2(self) -> Cq.Assembly:
        result = (
            Cq.Assembly()
            .addS(self.surface_s2(front=True), name="front",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("front", "Fixed")
            .addS(self.surface_s2(front=False), name="back",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("front@faces@>Z", "back@faces@<Z", "Point",
                       param=self.s1_thickness)
        )
        for t in ["elbow_bot", "elbow_top", "wrist_bot", "wrist_top"]:
            is_top = t.endswith("_top")
            is_parent = t.startswith("elbow")
            o = self.spacer_s2_elbow() if is_parent else self.spacer_s2_wrist()
            self._assembly_insert_spacer(
                result,
                o.generate(),
                point_tag=t,
                flipped=is_top != is_parent,
            )
        return result.solve()

    @target(name="profile-s3", kind=TargetKind.DXF)
    def profile_s3(self) -> Cq.Sketch:
        profile = (
            self.profile()
            .reset()
            .polygon(self._mask_wrist(), mode='s')
        )
        return profile
    def surface_s3(self,
                   front: bool = True) -> Cq.Workplane:
        wrist_mount_inset = 0
        wrist_h = self.wrist_joint.child_beam.total_height
        h = (self.wrist_height - wrist_h) / 2
        tags = [
            ("wrist_bot",
             self.wrist_to_abs(wrist_mount_inset, h),
             self.wrist_angle + 90),
            ("wrist_top",
             self.wrist_to_abs(wrist_mount_inset, h + wrist_h),
             self.wrist_angle - 90),
        ]
        profile = self.profile_s3()
        return nhf.utils.extrude_with_markers(profile, self.panel_thickness, tags, reverse=front)
    @submodel(name="spacer-s3-wrist")
    def spacer_s3_wrist(self) -> MountingBox:
        holes = [
            Hole(x)
            for x in self.wrist_joint.child_hole_pos()
        ]
        return MountingBox(
            length=70.0, # FIXME: magic
            width=self.s1_thickness,
            thickness=self.spacer_thickness,
            holes=holes,
            hole_diam=self.wrist_joint.hole_diam
        )
    @assembly()
    def assembly_s3(self) -> Cq.Assembly:
        result = (
            Cq.Assembly()
            .addS(self.surface_s3(front=True), name="front",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("front", "Fixed")
            .addS(self.surface_s3(front=False), name="back",
                  material=self.mat_panel, role=self.role_panel)
            .constrain("front@faces@>Z", "back@faces@<Z", "Point",
                       param=self.s1_thickness)
        )
        for t in ["wrist_bot", "wrist_top"]:
            is_top = t.endswith("_top")
            is_parent = True
            o = self.spacer_s3_wrist()
            self._assembly_insert_spacer(
                result,
                o.generate(),
                point_tag=t,
                flipped=is_top != is_parent,
            )
        return result.solve()

    @assembly()
    def assembly(self,
                 parts: Optional[list[str]] = None,
                 angle_elbow_wrist: float = 0.0,
                 ) -> Cq.Assembly():
        assert not self.elbow_joint.flip
        assert self.wrist_joint.flip
        if parts is None:
            parts = ["s0", "shoulder", "s1", "elbow", "s2", "wrist", "s3"]
        result = (
            Cq.Assembly()
        )
        if "s0" in parts:
            result.add(self.assembly_s0(), name="s0")
        if "shoulder" in parts:
            result.add(self.shoulder_joint.assembly(), name="shoulder")
        if "s0" in parts and "shoulder" in parts:
            (
                result
                .constrain("s0/shoulder?conn_top0", "shoulder/parent_top/lip?conn0", "Plane")
                #.constrain("s0/shoulder?conn_top1", "shoulder/parent_top/lip?conn1", "Plane")
                .constrain("s0/shoulder?conn_bot0", "shoulder/parent_bot/lip?conn0", "Plane")
                #.constrain("s0/shoulder?conn_bot1", "shoulder/parent_bot/lip?conn1", "Plane")
            )
        if "s1" in parts:
            result.add(self.assembly_s1(), name="s1")
        if "s1" in parts and "shoulder" in parts:
            (
                result
                .constrain("s1/shoulder_top?conn0", "shoulder/child/lip_top?conn0", "Plane")
                .constrain("s1/shoulder_top?conn1", "shoulder/child/lip_top?conn1", "Plane")
                .constrain("s1/shoulder_bot?conn0", "shoulder/child/lip_bot?conn0", "Plane")
                .constrain("s1/shoulder_bot?conn1", "shoulder/child/lip_bot?conn1", "Plane")
            )
        if "elbow" in parts:
            result.add(self.elbow_joint.assembly(angle=angle_elbow_wrist), name="elbow")
        if "s1" in parts and "elbow" in parts:
            (
                result
                .constrain("s1/elbow_top?conn0", "elbow/parent_upper/top?conn0", "Plane")
                .constrain("s1/elbow_top?conn1", "elbow/parent_upper/top?conn1", "Plane")
                .constrain("s1/elbow_bot?conn0", "elbow/parent_upper/bot?conn0", "Plane")
                .constrain("s1/elbow_bot?conn1", "elbow/parent_upper/bot?conn1", "Plane")
            )
        if "s2" in parts:
            result.add(self.assembly_s2(), name="s2")
        if "s2" in parts and "elbow" in parts:
            (
                result
                .constrain("s2/elbow_top?conn0", "elbow/child/top?conn0", "Plane")
                .constrain("s2/elbow_top?conn1", "elbow/child/top?conn1", "Plane")
                .constrain("s2/elbow_bot?conn0", "elbow/child/bot?conn0", "Plane")
                .constrain("s2/elbow_bot?conn1", "elbow/child/bot?conn1", "Plane")
            )
        if "wrist" in parts:
            result.add(self.wrist_joint.assembly(angle=angle_elbow_wrist), name="wrist")
        if "s2" in parts and "wrist" in parts:
            # Mounted backwards to bend in other direction
            (
                result
                .constrain("s2/wrist_top?conn0", "wrist/parent_upper/top?conn0", "Plane")
                .constrain("s2/wrist_top?conn1", "wrist/parent_upper/top?conn1", "Plane")
                .constrain("s2/wrist_bot?conn0", "wrist/parent_upper/bot?conn0", "Plane")
                .constrain("s2/wrist_bot?conn1", "wrist/parent_upper/bot?conn1", "Plane")
            )
        if "s3" in parts:
            result.add(self.assembly_s3(), name="s3")
        if "s3" in parts and "wrist" in parts:
            (
                result
                .constrain("s3/wrist_top?conn0", "wrist/child/top?conn0", "Plane")
                .constrain("s3/wrist_top?conn1", "wrist/child/top?conn1", "Plane")
                .constrain("s3/wrist_bot?conn0", "wrist/child/bot?conn0", "Plane")
                .constrain("s3/wrist_bot?conn1", "wrist/child/bot?conn1", "Plane")
            )
        if len(parts) > 1:
            result.solve()

        return result



@dataclass(kw_only=True)
class WingR(WingProfile):
    """
    Right side wings
    """

    elbow_height: float = 111.0
    elbow_x: float = 363.0
    elbow_y: float = 44.0
    # Tilt of elbow w.r.t. shoulder
    elbow_angle: float = 30.0

    wrist_height: float = 60.0
    # Bottom point of the wrist
    wrist_x: float = 403.0
    wrist_y: float = 253.0

    # Tile of wrist w.r.t. shoulder
    wrist_angle: float = 40
    # Extends from the wrist to the tip of the arrow
    arrow_height: float = 300
    arrow_angle: float = 8

    # Relative (in wrist coordinate) centre of the ring
    ring_x: float = 45
    ring_y: float = 25
    ring_radius_inner: float = 22

    def __post_init__(self):
        super().__post_init__()
        self.arrow_theta = math.radians(self.arrow_angle)
        self.arrow_x, self.arrow_y = self.wrist_to_abs(0, -self.arrow_height)
        self.arrow_tip_x = self.arrow_x + (self.arrow_height + self.wrist_height) \
            * math.sin(self.arrow_theta - self.wrist_theta)
        self.arrow_tip_y = self.arrow_y + (self.arrow_height + self.wrist_height) \
            * math.cos(self.arrow_theta - self.wrist_theta)
        # [[c, s], [-s, c]] * [ring_x, ring_y]
        self.ring_abs_x = self.wrist_top_x + self.wrist_c * self.ring_x - self.wrist_s * self.ring_y
        self.ring_abs_y = self.wrist_top_y + self.wrist_s * self.ring_x + self.wrist_c * self.ring_y
        assert self.ring_radius > self.ring_radius_inner

    @property
    def ring_radius(self) -> float:
        dx = self.ring_x
        dy = self.ring_y
        return (dx * dx + dy * dy) ** 0.5

    def profile(self) -> Cq.Sketch:
        """
        Net profile of the wing starting from the wing root with no divisions
        """
        result = (
            Cq.Sketch()
            .segment(
                (0, 0),
                (0, self.shoulder_joint.height),
                tag="shoulder")
            .spline([
                (0, self.shoulder_joint.height),
                (self.elbow_top_x, self.elbow_top_y),
                (self.wrist_top_x, self.wrist_top_y),
            ],
                tag="s1_top")
            #.segment(
            #    (self.wrist_x, self.wrist_y),
            #    (wrist_top_x, wrist_top_y),
            #    tag="wrist")
            .spline([
                (0, 0),
                (self.elbow_x, self.elbow_y),
                (self.wrist_x, self.wrist_y),
            ],
                tag="s1_bot")
        )
        result = (
            result
            .segment(
                (self.wrist_x, self.wrist_y),
                (self.arrow_x, self.arrow_y)
            )
            .segment(
                (self.arrow_x, self.arrow_y),
                (self.arrow_tip_x, self.arrow_tip_y)
            )
            .segment(
                (self.arrow_tip_x, self.arrow_tip_y),
                (self.wrist_top_x, self.wrist_top_y)
            )
        )
        # Carve out the ring
        result = result.assemble()
        result = (
            result
            .push([(self.ring_abs_x, self.ring_abs_y)])
            .circle(self.ring_radius, mode='a')
            .circle(self.ring_radius_inner, mode='s')
            .clean()
        )
        return result

@dataclass(kw_only=True)
class WingL(WingProfile):

    elbow_x: float = 230.0
    elbow_y: float = 110.0
    elbow_angle: float = -10.0
    elbow_height: float = 80.0

    wrist_x: float = 480.0
    wrist_y: float = 0.0
    wrist_angle: float = -45
    wrist_height: float = 43.0

    shoulder_bezier_ext: float = 80.0
    elbow_bezier_ext: float = 100.0
    wrist_bezier_ext: float = 30.0

    arrow_length: float = 135.0
    arrow_height: float = 120.0

    flip: bool = True

    def __post_init__(self):
        super().__post_init__()
        assert self.wrist_height <= self.shoulder_joint.height

    def arrow_to_abs(self, x, y) -> Tuple[float, float]:
        return self.wrist_to_abs(x * self.arrow_length, y * self.arrow_height / 2 + self.wrist_height / 2)

    def profile(self) -> Cq.Sketch:
        result = (
            Cq.Sketch()
            .segment(
                (0,0),
                (0, self.shoulder_height)
            )
            #.spline([
            #    (0, 0),
            #    self.elbow_to_abs(0, 0),
            #    self.wrist_to_abs(0, 0),
            #])
            #.spline([
            #    (0, self.shoulder_height),
            #    self.elbow_to_abs(0, self.elbow_height),
            #    self.wrist_to_abs(0, self.wrist_height),
            #])
            .bezier([
                (0, 0),
                (self.shoulder_bezier_ext, 0),
                self.elbow_to_abs(-self.elbow_bezier_ext, 0),
                self.elbow_to_abs(0, 0),
            ])
            .bezier([
                (0, self.shoulder_joint.height),
                (self.shoulder_bezier_ext, self.shoulder_joint.height),
                self.elbow_to_abs(-self.elbow_bezier_ext, self.elbow_height),
                self.elbow_to_abs(0, self.elbow_height),
            ])
            .bezier([
                self.elbow_to_abs(0, 0),
                self.elbow_to_abs(self.elbow_bezier_ext, 0),
                self.wrist_to_abs(-self.wrist_bezier_ext, 0),
                self.wrist_to_abs(0, 0),
            ])
            .bezier([
                self.elbow_to_abs(0, self.elbow_height),
                self.elbow_to_abs(self.elbow_bezier_ext, self.elbow_height),
                self.wrist_to_abs(-self.wrist_bezier_ext, self.wrist_height),
                self.wrist_to_abs(0, self.wrist_height),
            ])
        )
        # arrow base positions
        base_u, base_v = 0.3, 0.3
        result = (
            result
            .bezier([
                self.wrist_to_abs(0, self.wrist_height),
                self.wrist_to_abs(self.wrist_bezier_ext, self.wrist_height),
                self.arrow_to_abs(base_u, base_v),
            ])
            .bezier([
                self.wrist_to_abs(0, 0),
                self.wrist_to_abs(self.wrist_bezier_ext, 0),
                self.arrow_to_abs(base_u, -base_v),
            ])
        )
        # Create the arrow
        arrow_beziers = [
            [
                (0, 1),
                (0.3, 1),
                (0.8, .2),
                (1, 0),
            ],
            [
                (0, 1),
                (0.1, 0.8),
                (base_u, base_v),
            ]
        ]
        arrow_beziers = [
            l2
            for l in arrow_beziers
            for l2 in [l, [(x, -y) for x,y in l]]
        ]
        for line in arrow_beziers:
            result = result.bezier([self.arrow_to_abs(x, y) for x,y in line])
        return result.assemble()