mathml

MathML Matrix

A Matrix is just Math.

MathML can show math inside of HTML.

To show a matrix as a MathML matrix, we just need to access the .MathML property.

(Scale3d 3 2 1).MathML

[\begin{matrix} 3 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]

A 2D Matrix (Matrix3x2) can be mapped to a 3D Matrix (Matrix4x4).

When we show a 2D Matrix's MathML, we show both the matrix and and it's equivalent matrix3d

(Scale 1 2).MathML

[\begin{matrix} 1 & 0 \\ 0 & 2 \\ 0 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]

A Quaternion ([Numerics.Quaternion]) can be mapped to a 3D Matrix ([Numerics.Matrix4x4]).

When we show a Quaternion's MathML, we show both the [Numerics.Quaternion] and and it's equivalent matrix3d

(Quaternion Identity).MathML

[\begin{matrix} X : 0 & Y : 0 & Z : 0 & W : 1 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]

MathML obviously works fine in html.

We can also preview the matrix by accessing another property: .html

(Scale3d 3 2 1).Html

By default, this will show the matrix twice.

Once in it's original form, and once transformed by itself.

[\begin{matrix} 3 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]

[\begin{matrix} 3 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]

A Matrix3x2 and a Quaternion can both be converted to a Matrix4x4

We show the equivalent matrix side by side

(Scale 1 0.5).MathML
(Quaternion 0.5 0.5 0.5 1).MathML

[\begin{matrix} 1 & 0 \\ 0 & 0.5 \\ 0 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 0.5 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]

[\begin{matrix} X : 0 & Y : 0 & Z : 0 & W : 1 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]

We can also attach our own .Content property to the matrix:

Scale -1 1 | 
    Add-Member NoteProperty Content "<h3>Backwards</h3>" -Force -PassThru |
        Select-Object -ExpandProperty Html