By making the beam polarization state in a cross prism having a dichroic function for an incident beam on a reflection type liquid crystal panel the same as that for a reflected ON beam, a small-sized, low cost projection type projector apparatus is provided. A keyboard operation module generates geometric shapes for display on a touch-screen display, each geometric shape corresponding to a respective finger of a user. In an embodiment of the invention, the display is partitioned into three areas comprising a user’s data area, an applications area, and another user’s data area.