The trace is a space collection which the geometric elements are moved on given conditions. To find out the trace law of moving geometric elements, the projection method can be used to describe trace in the space. Due to principles of the trajectory of point, line and plane can form a curved surface, a trace in the space can be projected to different planes. The plane trajectories can return to space curved surface according to its moving regularities. The principal curvatures and principal directions at a given point on the curved surface can be obtained.