Home theater projectors; micro video projector; mini video projector; movie projectors; multimedia projectors; video projectors; image projectors; optical lenses; lenses for projectors; motion detecting sensors; motion recognizing sensors; sensors for determining position; displacement measurement instruments; projected capacitive touch sensors; touch sensitive electronic screens; computer firmware for motion sensing and tracking, as well as gesture recognition, for enabling responsive operation and control of third party personal computing and entertainment devices and global computer, communications, and entertainment networks; downloadable computer programs for motion sensing and tracking, as well as gesture recognition, for enabling responsive operation and control of third party personal computing and entertainment devices and global computer, communications, and entertainment networks; downloadable smart phone software application for motion sensing and tracking, as well as gesture recognition, for enabling responsive operation and control of third party personal computing and entertainment devices and global computer, communications, and entertainment networks; computer programs and software for image processing; augmented reality software for enabling a user to interact with virtual and mixed reality environments and content in the field of education, entertainment, art, games, music, performances, sports, communication, general interest, and business; augmented reality software for use in mobile devices for enabling a user to interact with virtual and mixed reality environments and content in the field of education, entertainment, art, games, music, performances, sports, communication, general interest, and business; software for processing images, graphics and text; data processing software for graphic representations; graphical user interface software; smart phone software application for motion sensing and tracking, as well as gesture recognition, for enabling responsive operation and control of third party personal computing and entertainment devices and global computer, communications, and entertainment networks; embedded computer operating software; gesture recognition software; digital signal processors; motherboards; circuit boards provided with integrated circuits; electronic integrated circuits; integrated circuit module; micro-computer; computer hardware; computer peripherals for the control of computers, tablets, smartphones, electrical appliances, household appliances, connected objects such as LED lights, cameras and GPS navigation devices