While many factors contribute to shape perception, psychological research indicates that the direction of lines on the surface may have an important influence. This is especially the case when other techniques (shading, silhouetting) do not present sufficient shape information. The psychology literature suggests that lines in the principal directions of curvature may communicate surface shape better than lines in other directions. Moreover, principal directions have the quality of geometric invariance so line directions are based on the surface geometry and are viewpoint and light source independent, and the lines do not move above over the surface during animation unless desired. In this work we describe principal direction line drawings which show the flow of curvature over the surface. The technique is presented for arbitrary surfaces represented by either 3D volume data or a polygonal surface mesh. The latter format is common in the field of computer graphics yet thus far has not been widely used for principal direction estimation. The methods offered in this paper can be used alone or in conjunction with other NPR techniques to improve artistic 3D renderings of arbitrary surfaces.