# MathTransform formulas

This file contains formulas written in MathML for inclusion in the Javadoc of some classes in the `org.apache.sis.referencing.operation.transform` package. Those formulas are provided in separated files for easier edition and for avoiding `javac` or `javadoc` “unknown HTML tag” errors with JDK 8. Fragment of this files are inserted in the Javadoc by the following tag:

>     {@include formulas.html#title}

where title is the text inside `<h2>…</h2>` elements just before the parts to copy in the javadoc. The `{@include}` taglet is defined in the `sis-build-helper` module.

## ProjectiveTransform

[ x' y' z' ] = [ u/t v/t w/t ]

> where u, v, w and t are obtained by

[ u v w t ] = [ m 00 m 01 m 02 m 03 m 10 m 11 m 12 m 13 m 20 m 21 m 22 m 23 m 30 m 31 m 32 m 33 ] × [ x y z 1 ]

## SwapAxes

[ 0 1 0 1 0 0 0 0 1 ]

## NormalizeGeographic

[ π/180 0 -λ 0 ⋅ (π/180) 0 π/180 0 0 0 1 ]

## DenormalizeGeographic

[ 180/π 0 λ 0 0 180/π 0 0 0 1 ]

## DenormalizeCartesian

[ a ⋅ k 0 0 FE 0 a ⋅ k 0 FN 0 0 1 ]