RoboTwin / robosuite /models /objects /generated_objects.py
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from copy import deepcopy
import numpy as np
from robosuite.models.objects import MujocoGeneratedObject, MujocoObject
from robosuite.utils.mjcf_utils import (
OBJECT_COLLISION_COLOR,
CustomMaterial,
add_prefix,
array_to_string,
find_elements,
new_body,
new_geom,
new_joint,
new_site,
)
class CompositeBodyObject(MujocoGeneratedObject):
"""
An object constructed out of multiple bodies to make more complex shapes.
Args:
name (str): Name of overall object
objects (MujocoObject or list of MujocoObjects): object(s) to combine to form the composite body object.
Note that these objects will be added sequentially, so if an object is required to be nested relative to
another object, that nested object should be listed after the parent object. Note that all top-level joints
for any inputted objects are automatically stripped
object_locations (list): list of body locations in the composite. Each
location should be a list or tuple of 3 elements and all
locations are taken relative to that object's parent body. Giving None for a location results in (0,0,0)
for that object.
object_quats (None or list): list of (w, x, y, z) quaternions for each body. None results in (1,0,0,0) for
that object.
object_parents (None or list): Parent bodies to append each object to. Note that specifying "None" will
automatically append all objects to the root body ("root")
joints (None or list): Joints to use for the top-level composite body object. If None, no joints will be used
for this top-level object. If "default", a single free joint will be added to the top-level body of this
object. Otherwise, should be a list of dictionaries, where each dictionary should specify the specific
joint attributes necessary. See http://www.mujoco.org/book/XMLreference.html#joint for reference.
body_joints (None or dict): If specified, maps body names to joint specifications to append to that
body. If None, no extra joints will be used. If mapped value is "default", a single free joint will be
added to the specified body. Otherwise, should be a list of dictionaries, where each dictionary should
specify the specific joint attributes necessary. See http://www.mujoco.org/book/XMLreference.html#joint
for reference.
sites (None or list): list of sites to add to top-level composite body object. If None, only the default
top-level object site will be used. Otherwise, should be a list of dictionaries, where each dictionary
should specify the appropriate attributes for the given site.
See http://www.mujoco.org/book/XMLreference.html#site for reference.
total_size (None or np.array): if provided, use this to describe the bounding box for this composite body
object. Can also be used to specify @object_locations relative to the lower left corner of the bounding
box defined by @total_size, instead of the center of this body, with @locations_relative_to_corner.
locations_relative_to_corner (bool): if True, must supply @total_size. All object locations will be
relative to the lower left corner of the bounding box.
"""
def __init__(
self,
name,
objects,
object_locations,
object_quats=None,
object_parents=None,
joints="default",
body_joints=None,
sites=None,
total_size=None,
locations_relative_to_corner=False,
):
# Always call superclass first
super().__init__()
self._name = name
# Set internal variable geometric properties which will be modified later
self._object_absolute_positions = {"root": np.zeros(3)} # maps body names to abs positions (rel to root)
self._top = 0
self._bottom = 0
self._horizontal = 0
# Standardize inputs
if isinstance(objects, MujocoObject):
self.objects = [objects]
elif type(objects) in {list, tuple}:
self.objects = list(objects)
else:
# Invalid objects received
raise ValueError("Invalid objects received, got type: {}".format(type(objects)))
n_objects = len(self.objects)
self.object_locations = np.array(object_locations)
self.object_quats = deepcopy(object_quats) if object_quats is not None else [None] * n_objects
self.object_parents = deepcopy(object_parents) if object_parents is not None else ["root"] * n_objects
# Set joints
if joints == "default":
self.joint_specs = [self.get_joint_attrib_template()] # default free joint
elif joints is None:
self.joint_specs = []
else:
self.joint_specs = joints
# Set body joints
if body_joints is None:
body_joints = {}
self.body_joint_specs = body_joints
# Make sure all joints are named appropriately
j_num = 0
for joint_spec in self.joint_specs:
if "name" not in joint_spec:
joint_spec["name"] = "joint{}".format(j_num)
j_num += 1
# Set sites
self.site_specs = deepcopy(sites) if sites is not None else []
# Add default site
site_element_attr = self.get_site_attrib_template()
site_element_attr["rgba"] = "1 0 0 0"
site_element_attr["name"] = "default_site"
self.site_specs.append(site_element_attr)
# Make sure all sites are named appropriately
s_num = 0
for site_spec in self.site_specs:
if "name" not in site_spec:
site_spec["name"] = "site{}".format(s_num)
s_num += 1
self.total_size = np.array(total_size) if total_size is not None else None
self.locations_relative_to_corner = locations_relative_to_corner
if self.locations_relative_to_corner:
assert self.total_size is not None
# Always run sanity check
self.sanity_check()
# Lastly, parse XML tree appropriately
self._obj = self._get_object_subtree()
# Extract the appropriate private attributes for this
self._get_object_properties()
def _get_object_subtree(self):
# Initialize top-level body
obj = new_body(name="root")
# Add all joints and sites
for joint_spec in self.joint_specs:
obj.append(new_joint(**joint_spec))
for site_spec in self.site_specs:
obj.append(new_site(**site_spec))
# Loop through all objects and associated args and append them appropriately
for o, o_parent, o_pos, o_quat in zip(
self.objects, self.object_parents, self.object_locations, self.object_quats
):
self._append_object(root=obj, obj=o, parent_name=o_parent, pos=o_pos, quat=o_quat)
# Loop through all joints and append them appropriately
for body_name, joint_specs in self.body_joint_specs.items():
self._append_joints(root=obj, body_name=body_name, joint_specs=joint_specs)
# Return final object
return obj
def _get_object_properties(self):
"""
Extends the superclass method to add prefixes to all assets
"""
super()._get_object_properties()
# Add prefix to all assets
add_prefix(root=self.asset, prefix=self.naming_prefix, exclude=self.exclude_from_prefixing)
def _append_object(self, root, obj, parent_name=None, pos=None, quat=None):
"""
Helper function to add pre-generated object @obj to the body with name @parent_name
Args:
root (ET.Element): Top-level element to iteratively search through for @parent_name to add @obj to
obj (MujocoObject): Object to append to the body specified by @parent_name
parent_name (None or str): Body name to search for in @root to append @obj to.
None defaults to "root" (top-level body)
pos (None or 3-array): (x,y,z) relative offset from parent body when appending @obj.
None defaults to (0,0,0)
quat (None or 4-array) (w,x,y,z) relative quaternion rotation from parent body when appending @obj.
None defaults to (1,0,0,0)
"""
# Set defaults if any are None
if parent_name is None:
parent_name = "root"
if pos is None:
pos = np.zeros(3)
if quat is None:
quat = np.array([1, 0, 0, 0])
# First, find parent body
parent = find_elements(root=root, tags="body", attribs={"name": parent_name}, return_first=True)
assert parent is not None, "Could not find parent body with name: {}".format(parent_name)
# Get the object xml element tree, remove its top-level joints, and modify its top-level pos / quat
child = obj.get_obj()
self._remove_joints(child)
if self.locations_relative_to_corner:
# use object location to convert to position coordinate (the origin is the
# center of the composite object)
cartesian_size = obj.get_bounding_box_half_size()
pos = [
(-self.total_size[0] + cartesian_size[0]) + pos[0],
(-self.total_size[1] + cartesian_size[1]) + pos[1],
(-self.total_size[2] + cartesian_size[2]) + pos[2],
]
child.set("pos", array_to_string(pos))
child.set("quat", array_to_string(quat))
# Add this object and its assets to this composite object
self.merge_assets(other=obj)
parent.append(child)
# Update geometric properties for this composite object
obj_abs_pos = self._object_absolute_positions[parent_name] + np.array(pos)
self._object_absolute_positions[obj.root_body] = obj_abs_pos
self._top = max(self._top, obj_abs_pos[2] + obj.top_offset[2])
self._bottom = min(self._bottom, obj_abs_pos[2] + obj.bottom_offset[2])
self._horizontal = max(self._horizontal, max(obj_abs_pos[:2]) + obj.horizontal_radius)
def _append_joints(self, root, body_name=None, joint_specs="default"):
"""
Appends all joints as specified by @joint_specs to @body.
Args:
root (ET.Element): Top-level element to iteratively search through for @body_name
body_name (None or str): Name of the body to append the joints to.
None defaults to "root" (top-level body)
joint_specs (str or list): List of joint specifications to add to the specified body, or
"default", which results in a single free joint
"""
# Standardize inputs
if body_name is None:
body_name = "root"
if joint_specs == "default":
joint_specs = [self.get_joint_attrib_template()]
for i, joint_spec in enumerate(joint_specs):
if "name" not in joint_spec:
joint_spec["name"] = f"{body_name}_joint{i}"
# Search for body and make sure it exists
body = find_elements(root=root, tags="body", attribs={"name": body_name}, return_first=True)
assert body is not None, "Could not find body with name: {}".format(body_name)
# Add joint(s) to this body
for joint_spec in joint_specs:
body.append(new_joint(**joint_spec))
@staticmethod
def _remove_joints(body):
"""
Helper function to strip all joints directly appended to the specified @body.
Args:
body (ET.Element): Body to strip joints from
"""
children_to_remove = []
for child in body:
if child.tag == "joint":
children_to_remove.append(child)
for child in children_to_remove:
body.remove(child)
@property
def bottom_offset(self):
return np.array([0.0, 0.0, self._bottom])
@property
def top_offset(self):
return np.array([0.0, 0.0, self._top])
@property
def horizontal_radius(self):
return self._horizontal
def get_bounding_box_half_size(self):
if self.total_size is not None:
return np.array(self.total_size)
return super().get_bounding_box_half_size()
class CompositeObject(MujocoGeneratedObject):
"""
An object constructed out of basic geoms to make more intricate shapes.
Note that by default, specifying None for a specific geom element will usually set a value to the mujoco defaults.
Args:
name (str): Name of overall object
total_size (list): (x, y, z) half-size in each dimension for the bounding box for
this Composite object
geom_types (list): list of geom types in the composite. Must correspond
to MuJoCo geom primitives, such as "box" or "capsule".
geom_locations (list): list of geom locations in the composite. Each
location should be a list or tuple of 3 elements and all
locations are relative to the lower left corner of the total box
(e.g. (0, 0, 0) corresponds to this corner).
geom_sizes (list): list of geom sizes ordered the same as @geom_locations
geom_quats (None or list): list of (w, x, y, z) quaternions for each geom.
geom_names (None or list): list of geom names ordered the same as @geom_locations. The
names will get appended with an underscore to the passed name in @get_collision
and @get_visual
geom_rgbas (None or list): list of geom colors ordered the same as @geom_locations. If
passed as an argument, @rgba is ignored.
geom_materials (None or list of CustomTexture): list of custom textures to use for this object material
geom_frictions (None or list): list of geom frictions to use for each geom.
rgba (None or list): (r, g, b, a) default values to use if geom-specific @geom_rgbas isn't specified for a given element
density (float or list of float): either single value to use for all geom densities or geom-specific values
solref (list or list of list): parameters used for the mujoco contact solver. Can be single set of values or
element-specific values. See http://www.mujoco.org/book/modeling.html#CSolver for details.
solimp (list or list of list): parameters used for the mujoco contact solver. Can be single set of values or
element-specific values. See http://www.mujoco.org/book/modeling.html#CSolver for details.
locations_relative_to_center (bool): If true, @geom_locations will be considered relative to the center of the
overall object bounding box defined by @total_size. Else, the corner of this bounding box is considered the
origin.
joints (None or list): Joints to use for this composite object. If None, no joints will be used
for this top-level object. If "default", a single free joint will be added to this object.
Otherwise, should be a list of dictionaries, where each dictionary should specify the specific
joint attributes necessary. See http://www.mujoco.org/book/XMLreference.html#joint for reference.
sites (None or list): list of sites to add to this composite object. If None, only the default
object site will be used. Otherwise, should be a list of dictionaries, where each dictionary
should specify the appropriate attributes for the given site.
See http://www.mujoco.org/book/XMLreference.html#site for reference.
obj_types (str or list of str): either single obj_type for all geoms or geom-specific type. Choices are
{"collision", "visual", "all"}
"""
def __init__(
self,
name,
total_size,
geom_types,
geom_sizes,
geom_locations,
geom_quats=None,
geom_names=None,
geom_rgbas=None,
geom_materials=None,
geom_frictions=None,
geom_condims=None,
rgba=None,
density=100.0,
solref=(0.02, 1.0),
solimp=(0.9, 0.95, 0.001),
locations_relative_to_center=False,
joints="default",
sites=None,
obj_types="all",
duplicate_collision_geoms=True,
):
# Always call superclass first
super().__init__(duplicate_collision_geoms=duplicate_collision_geoms)
self._name = name
# Set joints
if joints == "default":
self.joint_specs = [self.get_joint_attrib_template()] # default free joint
elif joints is None:
self.joint_specs = []
else:
self.joint_specs = joints
# Make sure all joints are named appropriately
j_num = 0
for joint_spec in self.joint_specs:
if "name" not in joint_spec:
joint_spec["name"] = "joint{}".format(j_num)
j_num += 1
# Set sites
self.site_specs = deepcopy(sites) if sites is not None else []
# Add default site
site_element_attr = self.get_site_attrib_template()
site_element_attr["rgba"] = "1 0 0 0"
site_element_attr["name"] = "default_site"
self.site_specs.append(site_element_attr)
# Make sure all sites are named appropriately
s_num = 0
for site_spec in self.site_specs:
if "name" not in site_spec:
site_spec["name"] = "site{}".format(s_num)
s_num += 1
n_geoms = len(geom_types)
self.total_size = np.array(total_size)
self.geom_types = np.array(geom_types)
self.geom_sizes = deepcopy(geom_sizes)
self.geom_locations = np.array(geom_locations)
self.geom_quats = deepcopy(geom_quats) if geom_quats is not None else [None] * n_geoms
self.geom_names = list(geom_names) if geom_names is not None else [None] * n_geoms
self.geom_rgbas = list(geom_rgbas) if geom_rgbas is not None else [None] * n_geoms
self.geom_materials = list(geom_materials) if geom_materials is not None else [None] * n_geoms
self.geom_frictions = list(geom_frictions) if geom_frictions is not None else [None] * n_geoms
self.geom_condims = list(geom_condims) if geom_condims is not None else [None] * n_geoms
self.density = [density] * n_geoms if density is None or type(density) in {float, int} else list(density)
self.solref = [solref] * n_geoms if solref is None or type(solref[0]) in {float, int} else list(solref)
self.solimp = [solimp] * n_geoms if obj_types is None or type(solimp[0]) in {float, int} else list(solimp)
self.rgba = rgba # override superclass setting of this variable
self.locations_relative_to_center = locations_relative_to_center
self.obj_types = [obj_types] * n_geoms if obj_types is None or type(obj_types) is str else list(obj_types)
# Always run sanity check
self.sanity_check()
# Lastly, parse XML tree appropriately
self._obj = self._get_object_subtree()
# Extract the appropriate private attributes for this
self._get_object_properties()
def get_bounding_box_half_size(self):
return np.array(self.total_size)
def in_box(self, position, object_position):
"""
Checks whether the object is contained within this CompositeObject.
Useful for when the CompositeObject has holes and the object should
be within one of the holes. Makes an approximation by treating the
object as a point, and the CompositeBoxObject as an axis-aligned grid.
Args:
position: 3D body position of CompositeObject
object_position: 3D position of object to test for insertion
"""
ub = position + self.total_size
lb = position - self.total_size
# fudge factor for the z-check, since after insertion the object falls to table
lb[2] -= 0.01
return np.all(object_position > lb) and np.all(object_position < ub)
def _get_object_subtree(self):
# Initialize top-level body
obj = new_body(name="root")
# Add all joints and sites
for joint_spec in self.joint_specs:
obj.append(new_joint(**joint_spec))
for site_spec in self.site_specs:
obj.append(new_site(**site_spec))
# Loop through all geoms and generate the composite object
for i, (
obj_type,
g_type,
g_size,
g_loc,
g_name,
g_rgba,
g_friction,
g_condim,
g_quat,
g_material,
g_density,
g_solref,
g_solimp,
) in enumerate(
zip(
self.obj_types,
self.geom_types,
self.geom_sizes,
self.geom_locations,
self.geom_names,
self.geom_rgbas,
self.geom_frictions,
self.geom_condims,
self.geom_quats,
self.geom_materials,
self.density,
self.solref,
self.solimp,
)
):
# geom type
geom_type = g_type
# get cartesian size from size spec
size = g_size
cartesian_size = self._size_to_cartesian_half_lengths(geom_type, size)
if self.locations_relative_to_center:
# no need to convert
pos = g_loc
else:
# use geom location to convert to position coordinate (the origin is the
# center of the composite object)
pos = [
(-self.total_size[0] + cartesian_size[0]) + g_loc[0],
(-self.total_size[1] + cartesian_size[1]) + g_loc[1],
(-self.total_size[2] + cartesian_size[2]) + g_loc[2],
]
# geom name
geom_name = g_name if g_name is not None else f"g{i}"
# geom rgba
geom_rgba = g_rgba if g_rgba is not None else self.rgba
# geom friction
geom_friction = (
array_to_string(g_friction)
if g_friction is not None
else array_to_string(np.array([1.0, 0.005, 0.0001]))
) # mujoco default
# Define base geom attributes
geom_attr = {
"size": size,
"pos": pos,
"name": geom_name,
"type": geom_type,
}
# Optionally define quat if specified
if g_quat is not None:
geom_attr["quat"] = array_to_string(g_quat)
# Add collision geom if necessary
if obj_type in {"collision", "all"}:
col_geom_attr = deepcopy(geom_attr)
col_geom_attr.update(self.get_collision_attrib_template())
if g_density is not None:
col_geom_attr["density"] = str(g_density)
col_geom_attr["friction"] = geom_friction
col_geom_attr["solref"] = array_to_string(g_solref)
col_geom_attr["solimp"] = array_to_string(g_solimp)
col_geom_attr["rgba"] = OBJECT_COLLISION_COLOR
if g_condim is not None:
col_geom_attr["condim"] = str(g_condim)
obj.append(new_geom(**col_geom_attr))
# Add visual geom if necessary
if obj_type in {"visual", "all"}:
vis_geom_attr = deepcopy(geom_attr)
vis_geom_attr.update(self.get_visual_attrib_template())
vis_geom_attr["name"] += "_vis"
if g_material is not None:
vis_geom_attr["material"] = g_material
vis_geom_attr["rgba"] = geom_rgba
obj.append(new_geom(**vis_geom_attr))
return obj
@staticmethod
def _size_to_cartesian_half_lengths(geom_type, geom_size):
"""
converts from geom size specification to x, y, and z half-length bounding box
"""
if geom_type in ["box", "ellipsoid"]:
return geom_size
if geom_type == "sphere":
# size is radius
return [geom_size[0], geom_size[0], geom_size[0]]
if geom_type == "capsule":
# size is radius, half-length of cylinder part
return [geom_size[0], geom_size[0], geom_size[0] + geom_size[1]]
if geom_type == "cylinder":
# size is radius, half-length
return [geom_size[0], geom_size[0], geom_size[1]]
raise Exception("unsupported geom type!")
@property
def bottom_offset(self):
return np.array([0.0, 0.0, -self.total_size[2]])
@property
def top_offset(self):
return np.array([0.0, 0.0, self.total_size[2]])
@property
def horizontal_radius(self):
return np.linalg.norm(self.total_size[:2], 2)
class PrimitiveObject(MujocoGeneratedObject):
"""
Base class for all programmatically generated mujoco object
i.e., every MujocoObject that does not have an corresponding xml file
Args:
name (str): (unique) name to identify this generated object
size (n-tuple of float): relevant size parameters for the object, should be of size 1 - 3
rgba (4-tuple of float): Color
density (float): Density
friction (3-tuple of float): (sliding friction, torsional friction, and rolling friction).
A single float can also be specified, in order to set the sliding friction (the other values) will
be set to the MuJoCo default. See http://www.mujoco.org/book/modeling.html#geom for details.
solref (2-tuple of float): MuJoCo solver parameters that handle contact.
See http://www.mujoco.org/book/XMLreference.html for more details.
solimp (3-tuple of float): MuJoCo solver parameters that handle contact.
See http://www.mujoco.org/book/XMLreference.html for more details.
material (CustomMaterial or `'default'` or None): if "default", add a template material and texture for this
object that is used to color the geom(s).
Otherwise, input is expected to be a CustomMaterial object
See http://www.mujoco.org/book/XMLreference.html#asset for specific details on attributes expected for
Mujoco texture / material tags, respectively
Note that specifying a custom texture in this way automatically overrides any rgba values set
joints (None or str or list of dict): Joints for this object. If None, no joint will be created. If "default",
a single (free) joint will be crated. Else, should be a list of dict, where each dictionary corresponds to
a joint that will be created for this object. The dictionary should specify the joint attributes
(type, pos, etc.) according to the MuJoCo xml specification.
obj_type (str): Geom elements to generate / extract for this object. Must be one of:
:`'collision'`: Only collision geoms are returned (this corresponds to group 0 geoms)
:`'visual'`: Only visual geoms are returned (this corresponds to group 1 geoms)
:`'all'`: All geoms are returned
duplicate_collision_geoms (bool): If set, will guarantee that each collision geom has a
visual geom copy
"""
def __init__(
self,
name,
size=None,
rgba=None,
density=None,
friction=None,
solref=None,
solimp=None,
material=None,
joints="default",
obj_type="all",
duplicate_collision_geoms=True,
):
# Always call superclass first
super().__init__(obj_type=obj_type, duplicate_collision_geoms=duplicate_collision_geoms)
# Set name
self._name = name
if size is None:
size = [0.05, 0.05, 0.05]
self.size = list(size)
if rgba is None:
rgba = [1, 0, 0, 1]
assert len(rgba) == 4, "rgba must be a length 4 array"
self.rgba = list(rgba)
if density is None:
density = 1000 # water
self.density = density
if friction is None:
friction = [1, 0.005, 0.0001] # MuJoCo default
elif isinstance(friction, float) or isinstance(friction, int):
friction = [friction, 0.005, 0.0001]
assert len(friction) == 3, "friction must be a length 3 array or a single number"
self.friction = list(friction)
if solref is None:
self.solref = [0.02, 1.0] # MuJoCo default
else:
self.solref = solref
if solimp is None:
self.solimp = [0.9, 0.95, 0.001] # MuJoCo default
else:
self.solimp = solimp
self.material = material
if material == "default":
# add in default texture and material for this object (for domain randomization)
default_tex = CustomMaterial(
texture=self.rgba,
tex_name="tex",
mat_name="mat",
)
self.append_material(default_tex)
elif material is not None:
# add in custom texture and material
self.append_material(material)
# joints for this object
if joints == "default":
self.joint_specs = [self.get_joint_attrib_template()] # default free joint
elif joints is None:
self.joint_specs = []
else:
self.joint_specs = joints
# Make sure all joints have names!
for i, joint_spec in enumerate(self.joint_specs):
if "name" not in joint_spec:
joint_spec["name"] = "joint{}".format(i)
# Always run sanity check
self.sanity_check()
# Lastly, parse XML tree appropriately
self._obj = self._get_object_subtree()
# Extract the appropriate private attributes for this
self._get_object_properties()
def _get_object_subtree_(self, ob_type="box"):
# Create element tree
obj = new_body(name="main")
# Get base element attributes
element_attr = {"name": "g0", "type": ob_type, "size": array_to_string(self.size)}
# Add collision geom if necessary
if self.obj_type in {"collision", "all"}:
col_element_attr = deepcopy(element_attr)
col_element_attr.update(self.get_collision_attrib_template())
col_element_attr["density"] = str(self.density)
col_element_attr["friction"] = array_to_string(self.friction)
col_element_attr["solref"] = array_to_string(self.solref)
col_element_attr["solimp"] = array_to_string(self.solimp)
obj.append(new_geom(**col_element_attr))
# Add visual geom if necessary
if self.obj_type in {"visual", "all"}:
vis_element_attr = deepcopy(element_attr)
vis_element_attr.update(self.get_visual_attrib_template())
vis_element_attr["name"] += "_vis"
if self.material == "default":
vis_element_attr["rgba"] = "0.5 0.5 0.5 1" # mujoco default
vis_element_attr["material"] = "mat"
elif self.material is not None:
vis_element_attr["material"] = self.material.mat_attrib["name"]
else:
vis_element_attr["rgba"] = array_to_string(self.rgba)
obj.append(new_geom(**vis_element_attr))
# add joint(s)
for joint_spec in self.joint_specs:
obj.append(new_joint(**joint_spec))
# add a site as well
site_element_attr = self.get_site_attrib_template()
site_element_attr["name"] = "default_site"
obj.append(new_site(**site_element_attr))
return obj
# Methods that still need to be defined by subclass
def _get_object_subtree(self):
raise NotImplementedError
def bottom_offset(self):
raise NotImplementedError
def top_offset(self):
raise NotImplementedError
def horizontal_radius(self):
raise NotImplementedError