Abstract: This paper describes how the set of principal directions and principal curvatures can be understood to define a natural "flow" over the surface of an object and, as such, can be used to guide the placement of the lines of a stroke texture that seeks to represent 3D shape in a perceptually intuitive way. The driving application for this work is the visualization of layered isovalue surfaces in volume data, where the particular identity of an individual surface is not generally known a priori and observers will typically wish to view a variety of different level surfaces from the same distribution, superimposed over underlying opaque structures. This paper describes how, by advecting an evenly distributed set of tiny opaque particles, and the empty space between them, via 3D line integral convolution through the vector field defined by the principal directions and principal curvatures of the level surfaces passing through each gridpoint of a 3D volume, it is possible to generate a single scan-converted solid stroke texture that can be used to illustrate the essential shape information of any level surface in the data. By redefining the length of the filter kernel according to the magnitude of the maximum principal curvature of the level surface at each point around which the convolution is applied, one can generate longer strokes over more the highly curved areas, where the directional information is both most stable and most relevant, and at the same time downplay the visual impact of the directional information indicated by the stroke texture in the flatter regions. In a voxel-based approach such as this one, stroke narrowness will be constrained by the resolution of the volume within which the texture is represented. However, by adaptively indexing into multiple pre-computed texture volumes, obtained by advecting particles of increasing sizes, one may selectively widen the strokes at any point by a variable amount, determined at the time of rendering, to reflect shading information or any other function defined over the volume data.