How to drag 3d object only on axis parallel to the scene

im creating 3d editor by using css3drenderer and webglrenderer on top of it.

For moving object with mouse, im using dragcontrols.
It works fine when the scene 90 degree(in this case x and y is parallel axis),
3dobjects are moving only in x and y axis using dragcontrols.

but if we rotate the scene to 30 degree(in this case x and z is parallel axis)
still 3dobjects are moving in x and y.but i want to move only in x and z axis.

so i set position.y=0 on drag event of works somewhat but not efficiently,
3d objects lags much behind from mouse pointer when we try to move objects to the top of scene(i.e towards (-)z axis) same when we move towars (+) z-axis

so whatever the rotation of the scene,
i want 3d objects to be moved only parallel to the scene efficiently

Any help would be appreciated.