Maths

How to transform position and quaternions from a y-up coordinate system to a z-up coordinate system.

With the help of this transformation matrix

    matrix_yUp_to_zUp:
        (
            1,  0,  0,  0,
            0,  0,  1,  0,
            0,  -1, 0,  0,
            0,  0,  0,  1
        );

    matrix_zUp_to_yUp:
        (
            1,  0,  0,  0,
            0,  0,  -1,  0,
            0,  1, 0,  0,
            0,  0,  0,  1
        );

All you have to do is multiply your vector or matrix from the Z-up system with the transformation matrix which converts Z-up into Y-up:

yUp = someZupVectorOrMatrix * matrix_yUp_to_zUp

This flips the axes by taking the +Z as +Y and the +Y as -Z and will convert rotation and scale parts correctly, too. To convert from Y-up back to Z-up, just use the inverse() of the conversion matrix above which is

zUp = someYupVectorOrMatrix * matrix_zUp_to_yUp

or alternatively from y-up to z-up for position and quaternion:

float pxt, pyt, pzt, qxt, qyt, qzt, qwt = 0.0f;

pxt = rbData.x;
pyt = -rbData.z;
pzt = rbData.y;
qxt = rbData.qx;
qyt = -rbData.qz;
qzt = rbData.qy;
qwt = rbData.qw;