mt.geo.transformation

Base tools to represent a geometric transformer and the act of transforming geometric objects (transformation).

Functions

  • transform(): Transforms an object using a given transformer.

  • transformable(): Checks if an object can be transformed using a transformer.

  • register_transform(): Registers a function to transform an object of a given type using a transformer of a given type.

  • register_transformable(): Registers a function to check if we can transform an object of a given type using a transformer of another given type.

mt.geo.transformation.transform(tfm, obj)

Transforms an object using a given transformer.

Parameters:
Returns:

the transformed version of obj

Return type:

object

Raises:

NotImplementedError – if the approx function has not been registered using function register_transform

mt.geo.transformation.transformable(tfm, obj)

Checks if an object can be transformed using a transformer.

Parameters:

  • tfm (Transformer) – a transformer

  • obj (object) – object to transform from

Returns:

whether or not the object is transformable using the transformer

Return type:

bool

Raises:

NotImplementedError – if the transformable function has not been registered using functions register_transformable or register_transform

mt.geo.transformation.register_transform(tfm_type, obj_type, func)

Registers a function to transform an object of a given type using a transformer of a given type.

Parameters:

  • tfm_type (type) – type or class of the transformer

  • obj_type (type) – type or class of the object to transform from

  • func (function) – transform function f(tfm, obj) -> obj to register

mt.geo.transformation.register_transformable(tfm_type, obj_type, func)

Registers a function to check if we can transform an object of a given type using a transformer of another given type.

Parameters:

  • tfm_type (type) – type or class of the transformer

  • obj_type (type) – type or class of the object to transform from

  • func (function) – transformable function f(tfm_type, obj) -> bool to register

Classes

  • Transformer: A mixin asserting that this is a class of transformers.

  • InvertibleTransformer: A mixin asserting that this is a class of invertible transformers.

  • LieTransformer: A mixin asserting that this is a class of transformers living in a Lie group, supporting the associative multiplication operator and the inversion operator.

class mt.geo.transformation.Transformer

A mixin asserting that this is a class of transformers.

A transformer is an object capable of transforming geometric objects of certain types into other geometric objects. It is usually parametrised by a transformation matrix. The mixin assumes that the act of transforming an object using the inheriting class is conducted via calling the global transform function. The mixin overloads the left shift operator.

Inheritance

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__lshift__(obj)

Transforms an object or raise a ValueError if the object is not transformable by the transformer.

__weakref__

list of weak references to the object (if defined)

class mt.geo.transformation.InvertibleTransformer

A mixin asserting that this is a class of invertible transformers.

The mixin assumes that a function self.invert() to return the inverted transformer has been implemented. It further overloads the right shift operator and the inverse operator.

Inheritance

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__invert__()

Returns the inverted transformer, invoking a given function self.invert().

__rshift__(obj)

Inversely transforms an object or raises a ValueError if the object is not transformable by the transformer.

invert()

Inverses the transformer

class mt.geo.transformation.LieTransformer

A mixin asserting that this is a class of transformers living in a Lie group, supporting the associative multiplication operator and the inversion operator.

Beside being an invertible transformer, the mixin additionally assumes that a function self.multiply(other) implementing the multiplication operator is available. It further overloads the multiplication, true division and modular operators, and provides a conjugate function.

Inheritance

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__mod__(other)

a%b = (~a)*b

__mul__(other)

a*b = Lie operator

__truediv__(other)

a/b = a*(~b)

conjugate(other)

Conjugate: self.conjugate(other) = self*other*self^{-1}

multiply(other)

Multiplies the transformer with another transformer.