Similarity

class Similarity(*transformations: HomogeneousTransformation)

A Similarity is any transformation composed of translations, rotations, uniform scales, and reflections. Under direct similarity, reflections are not included.

Its matrix will look like the augmented matrix:

┏           ┓
┃  M     T  ┃
┃           ┃
┃  Z     1  ┃
┗           ┛

Where M is a 3x3 orthogonal matrix with rank 3, T is a 3x1 vector, and Z is a 1x3 matrix containing all zeroes.

A CompositeHomogeneousTransformation is a CompositeTransformation closed under HomogeneousTransformation.

Parameters:: transformations – Transformations composing this transformation, supplied in the order of application (first-in, first-applied).

Attributes

transformations

Transformations composing this transformation, supplied in the order of application (first-in, first-applied).

Methods

`apply`	Apply this `CompositeTransformation` to a vector.
`closed_under`	Return `True` if composing a `CompositeHomogeneousTransformation` with `other` would result in creating another `CompositeHomogeneousTransformation`.
`compute`	Compute all `Similarity` transformations that might embed `query` in `target`.
`inverse`	The inverse `HomogeneousTransformation` of this one.

apply(vector: ndarray[3]) → ndarray[3]: Apply this CompositeTransformation to a vector.

classmethod closed_under(other: Transformation | Type[Transformation]) → bool: Return True if composing a CompositeHomogeneousTransformation with other would result in creating another CompositeHomogeneousTransformation.

classmethod compute(query: Shape, target: Shape, parameters: ShapeQueryParameters = ShapeQueryParameters(direct=True, indirect=True, indet_scale=1.0, indet_angle=0.0, indet_fit_max=False, indet_fit_uniform_scale=True)) → List[HomogeneousTransformation]

Compute all Similarity transformations that might embed query in target.

Parameters:

query – The shape to embed in target.
target – The shape to embed query in.
parameters – The parameters used to calculate the transformations.

Returns:

The list of all transformations t such that t @ query <= target and isinstance(t, Similarity).

inverse(): The inverse HomogeneousTransformation of this one.

transformations: Transformations composing this transformation, supplied in the order of application (first-in, first-applied).