Changing a matrix from right-handed to left-handed coordinate system

Question

I would like to change a 4x4 matrix from a right handed system where:
x is left and right, y is front and back and z is up and down

to a left-handed system where

Answer 1

I think I understand your problem because I am currently facing a similar one.

• You start with a world matrix which transforms a vector in a space where Z is up (e.g. a world matrix).

• Now you have a space where Y is up and you want to know what to do with your old matrix.

Try this:

There is a given world matrix

Matrix world = ...  //space where Z is up

This Matrix changes the Y and Z components of a Vector

Matrix mToggle_YZ = new Matrix(
{1, 0, 0, 0}
{0, 0, 1, 0}
{0, 1, 0, 0}
{0, 0, 0, 1})

You are searching for this:

//same world transformation in a space where Y is up
Matrix world2 = mToggle_YZ * world * mToggle_YZ;

The result is the same matrix cmann posted below. But I think this is more understandable as it combines the following calculation:

1) Switch Y and Z

2) Do the old transformation

3) Switch back Z and Y