Although texture-based methods provide a very promising way to visualize 3D vector fields, their dense 3D texture hinders the visualization of a 3D volume. In this paper, we introduce the concept of 3D significance map, and describe how significance values are derived from the intrinsic properties of a vector field. Based on the 3D significance map, we can control transfer functions for comprehensible LIC volume rendering by highlighting significant regions and neglecting insignificant information. We also present a 3D streamline illumination model that can reveal the flow direction embedded in a solid LIC texture. Experimental results illustrate the feasibility of our method.