Abstract: Virtual Environment (VE) is a simulation environment,which fuses much information of cyber-soace to make the effect of immersion and interaction. To interact the virtual objects in VE , a series of geometric transformation should be offered .This paper studies the geometric transformation procedure,which exists in the coordinate system of VE. Especially, the research of fusing the information of the hand space and stereoscopic vision in virtual space is given.It assures the harmony of the interaction between human and the computer.