Shape

class Shape(lines: List[Line], arcs: List[Arc], points: List[Point], *, maximal: bool = False, update_carrier_attrs: bool = False)

A Shape represents a collection of shape elements (see ShapeElement) that can be queried and modified. This is the primary unit of computation within Shape Machine.

Parameters:

lines – The Line instances in this shape.
arcs – The Arc instances in this shape.
points – The Point instances in this shape.
maximal – Whether this shape is maximal or not. If False, maximize_and_recalibrate() is called in __init__ to maximize the geometry of the shape.
update_carrier_attrs – If True, carrier attribute sets (attributes_set) will be recomputed.

Attributes

`all_attributes`
`all_concentric_carriers`	Returns `True` if all carriers in this shape are concentric.
`carriers`	A list of all `Carrier` instances underlying the geometry of this shape.
`center`	The center of this shape.
`convex_hull`
`elements_by_carrier_id`	A mapping of `id(carrier)` to all `ShapeElement` instances in this shape that have `carrier` as their `carrier` attribute.
`point_line_perpendicular_signature`	A special `ShapeSignature` made of registration points (`RegistrationPoint`) at each point carrier (`PointCarrier`) and their perpendicular projection onto each line carrier (`Line`).
`signature`	This shape's `ShapeSignature`.
`lines`	The `Line` instances in this shape.
`arcs`	The `Arc` instances in this shape.
`points`	The `Point` instances in this shape.

Methods

`centered_at_origin`	Returns `self - self.center`.
`difference`	Compute the boolean difference between this shape and another.
`equivalent_to`	Returns true if for each `ShapeElement` `a` in this shape, there is an element `b` in `other` such that `a.equivalent_to(b)` returns `True` and that no other element in this shape is equivalent to `b`.
`filter`
`filtered_to_attributes`
`is_embedded_in`	Returns `True` if for each `ShapeElement` `a` in this shape, there is an element `b` in `other` such that `a.is_embedded_in(b)` returns `True`.
`maximize_and_recalibrate`	Maximizes this shape in place and returns the newly maximized shape.
`query`	Computes all transformations `t` (see `Transformation`) of type `query_transformation` such that `t @ query.shape <= self` returns `True`.
`transform`	Apply a `Transformation` to all elements in this shape.
`union`	Compute the boolean union between this shape and another.

__add__(other: ndarray[3] | Shape) → Shape: Shifts a shape by other (if other is a vector) or performs union() (if other is a Shape).

__bool__(): Returns True if this shape is nonempty.

__le__(other: Shape): Calls is_embedded_in().

__len__(): Returns the number of elements (see ShapeElement) in this shape.

__rmatmul__(transformation: Transformation) → T_co: Computes transformable.transform(t) when performing t @ transformable for a Transformation t and Transformable transformable.

__sub__(other: ndarray[3] | Shape) → Shape: Shifts a shape by -other (if other is a vector) or performs difference() (if other is a Shape).

centered_at_origin() → Shape: Returns self - self.center.

difference(other: Shape, maximize: bool = True) → Shape

Compute the boolean difference between this shape and another.

Parameters:

other – The other shape.
maximize – If True, maximize the resulting shape.

Returns:

The difference of this shape and the other shape.

equivalent_to(other: Shape) → bool: Returns true if for each ShapeElement a in this shape, there is an element b in other such that a.equivalent_to(b) returns True and that no other element in this shape is equivalent to b.

filter(predicate: Callable[[ShapeElement], Any]) → Shape

filtered_to_attributes(attributes: Set[ElementAttributes]) → Shape

is_embedded_in(other: Shape) → bool: Returns True if for each ShapeElement a in this shape, there is an element b in other such that a.is_embedded_in(b) returns True.

maximize_and_recalibrate() → Shape: Maximizes this shape in place and returns the newly maximized shape.

query(query: ShapeQuery) → List[Transformation]

Computes all transformations t (see Transformation) of type query_transformation such that t @ query.shape <= self returns True. Currently only implemented for transformations of type Isometry, Similarity, and Affinity.

Parameters:: query – The ShapeQuery to use for computing transformations.
Returns:: All transformations t of type query_transformation such that t @ query_shape <= self returns True.

transform(transformation: Transformation) → Shape: Apply a Transformation to all elements in this shape.

union(other: Shape, maximize: bool = True) → Shape

Compute the boolean union between this shape and another.

Parameters:

other – The other shape.
maximize – If True, maximize the resulting shape.

Returns:

The union of this shape and the other shape.

property all_attributes: Set[ElementAttributes]

property all_concentric_carriers: bool: Returns True if all carriers in this shape are concentric.

arcs: The Arc instances in this shape.

property carriers: List[Carrier]: A list of all Carrier instances underlying the geometry of this shape. Provided as line carriers ( LineCarrier), then arc carriers ( ArcCarrier), then point carriers ( PointCarrier).

property center: ndarray[3]: The center of this shape.

property convex_hull: Shape

property elements_by_carrier_id: Dict[int, List[ShapeElement]]: A mapping of id(carrier) to all ShapeElement instances in this shape that have carrier as their carrier attribute.

lines: The Line instances in this shape.

property point_line_perpendicular_signature: ShapeSignature

A special ShapeSignature made of registration points (RegistrationPoint) at each point carrier (PointCarrier) and their perpendicular projection onto each line carrier (Line).

The spokes of each registration point are computed for the registration points on line carriers.

points: The Point instances in this shape.

property signature: ShapeSignature

This shape’s ShapeSignature.

A shape’s signature is created by marking all intersection locations of carriers. A RegistrationPoint is placed at each intersection with signature set as follows:

If the registration point is coincident with a PointCarrier or the center of a ArcCarrier, its direct_attributes includes that carrier’s attributes_set.
If the registration point is coincident to a LineCarrier, its spokes will include two spokes corresponding to that carrier.
- Each spoke corresponds to the half of the carrier in that direction.
- If there is not a Line in that direction from the registration point, the spoke’s type will be set to EMPTY.
- If there is a line in this direction, the spoke’s type will be set to FILLED.