1. An electronic cosmetic case comprising: a pair of image capturing units for simultaneously capturing facial images of a user from two different directions thereby obtaining two captured images; a stereo image display unit to receive the two captured images and simultaneously display one captured image to the left eye and the other captured image to the right eye, thus allowing the user to perceive a stereo image; a touch display panel for displaying a plurality of virtual cosmetics for the user to select; an optical pointing sensor for touching the touch display panel to select one virtual cosmetic from the plurality of virtual cosmetics, and touching a face of the user to make movements on the face according to the user operation, thereby simulating the application of makeup on the face of the user; a processing unit for determining a selected virtual cosmetic when the optical pointing sensor touches the plurality of virtual cosmetics, determining a movement track of the optical pointing sensor on the face and a thickness of the selected virtual cosmetic when the optical pointing sensor does the simulative makeup on the face of the user, doing the simulative makeup along the determined movement track on the stereo image, and creating a simulated stereo makeup image by filling the selected virtual cosmetic on the stereo image according to the determined thickness of the virtual cosmetic; and a repeat key for repeating a step of doing a simulation of makeup on the stereo image according to the user operation.