GLSL quaternion to 3x3 matrix

quat_to_mat3.glsl

mat3 quat_to_mat3(vec4 q) {
    // multiply by sqrt(2) to get rid of all the 2.0 factors in the matrix
    q *= 1.414214;

    float xx = q.x*q.x;
    float xy = q.x*q.y;
    float xz = q.x*q.z;
    float xw = q.x*q.w;

    float yy = q.y*q.y;
    float yz = q.y*q.z;
    float yw = q.y*q.w;

    float zz = q.z*q.z;
    float zw = q.z*q.w;

    return mat3(
        1.0 - yy - zz,
        xy + zw,
        xz - yw,
        
        xy - zw,
        1.0 - xx - zz,
        yz + xw,

        xz + yw,
        yz - xw,
        1.0 - xx - yy);
}