volume texture and GL_OBJECT_PLANE

I am using a 3D texture volume for the data and GL_OBJECT_PLANE for automatic texture mapping onto a cube. Everything works fine when it is at the origin, but as soon as I translate the model, the texture doesn’t map correctly anymore. Do I need to adjust my planes whenever I translate the model? Do I need to translate the TEXTURE matrix?

float xPlane[] = {1.0f, 0.0f, 0.0f, 0.0f};
float yPlane[] = {0.0f, -1.0f, 0.0f, 0.0f};
float zPlane[] = {0.0f, 0.0f, 1.0f, 0.0f};