UnitaryTransformation

A metatype for representing a unitary transformation of 3D coordinates.

Attributes

A UnitaryTransformation object represents an affine transformation of space coordinates composed of a translation, $\vec{t}$ , and of a unitary linear transformation, $U$ , e.g. a rotation. It changes the space coordinates $\vec{r}$ to $\vec{r}'$ as:

$\vec{r}' = U \vec{r} + \vec{t}$

The UnitaryTransformation preserves angles and distances. It has the following attributes:

Name	Type	Description
translation	`double [3]`	Translation vector, $\vec{t}$ , in m.
matrix	`double [3][3]`	Unitary matrix, $U$ , representing the linear transformation, e.g. a rotation.

Constructor

The UnitaryTransformation constructor has 3 forms as detailed in the synopsis below.

Synopsis

pumas.UnitaryTransformation(translation, matrix)

pumas.UnitaryTransformation{translation=, matrix=}

pumas.UnitaryTransformation(transformation)

Note

In the second form arguments are optional, but for the sake of simplicity only the full form is reported. If not specified the translation attribute is set to the null translation and the matrix attribute is set to the identity.

Arguments

Name	Type	Description
translation	`double [3]` or `table`	Translation vector, $\vec{t}$ , in m.
matrix	`double [3][3]` or `table`	Unitary matrix, $U$ , representing the linear transform, e.g. a rotation.

transformation	UnitaryTransformation	Another UnitaryTransformation instance.

Note

When providing a Lua table as argument its length must be consistent with the corresponding C type.

Warning

The provided matrix must be unitary, e.g. representing a rotation or a reflection.