# transform¶

The transform module.

class nutils.transform.TransformItem(todims, fromdims)

Bases: nutils.types.Singleton

Affine transformation.

Base class for transformations of the type $$x ↦ A x + b$$.

Parameters
• todims (int) – Dimension of the affine transformation domain.

• fromdims (int) – Dimension of the affine transformation range.

class nutils.transform.Matrix(linear, offset)

Affine transformation $$x ↦ A x + b$$, with $$A$$ an $$n×m$$ matrix, $$n≥m$$

Parameters
class nutils.transform.Square(linear, offset)

Bases: nutils.transform.Matrix

Affine transformation $$x ↦ A x + b$$, with $$A$$ square

Parameters
class nutils.transform.Shift(offset)

Bases: nutils.transform.Square

Shift transformation $$x ↦ x + b$$

Parameters

offset (numpy.ndarray) – The offset $$b$$.

class nutils.transform.Identity(ndims)

Bases: nutils.transform.Shift

Identity transformation $$x ↦ x$$

Parameters

ndims (int) – Dimension of $$x$$.

class nutils.transform.Scale(scale, offset)

Bases: nutils.transform.Square

Affine transformation $$x ↦ a x + b$$, with $$a$$ a scalar

Parameters
class nutils.transform.Updim(linear, offset, isflipped)

Bases: nutils.transform.Matrix

Affine transformation $$x ↦ A x + b$$, with $$A$$ an $$n×(n-1)$$ matrix

Parameters
class nutils.transform.Identifier(ndims, token)

Generic identifier

This transformation serves as an element-specific or topology-specific token to form the basis of transformation lookups. Otherwise, the transform behaves like an identity.