Figure 1: Example showcasing our volumetric approach to hair growth. Left: polygonal model of scalp and hair serving as input to our method. Middle: Sparse volumetric velocity field shown as blue arrows that represent the flow of hair. Right: Final hair curves derived as streamlines from the sparse velocity field.Summary: We present a fast and flexible technique for creating hair styles directly from modeled geometry by advecting streamlines in sparse high-resolution velocity fields derived from surfaces or curves. Typically artists model hair styles as polygonal surfaces or curves representing sparse guide hairs. From this we automatically create a sparse, volumetric vector field with direction and magnitude derived from the tangents of the input geometry or curves. Additional hair styling is achieved by modifying this vector field, and curves representing the final hair model are computed as streamlines. This volumetric approach represents a significant paradigm shift from traditional curve-based hair modeling in that it allows artists to intuitively create and modify realistic hair styles directly from geometric surface models. Our technique also lends itself well to up-sampling of spares guide hairs without the need to employ explicit curve-based interpolation schemes.Surface Modeling of Hair: Typically the input to our hair grooming system is a collection of polygon (or NURBS) models for the scalp as well as surfaces of hair clumps. Thus, hair is effectively represented by proxy geometry rather than individual curves, which allows artists to work with high-level abstractions like silhouettes and surfaces using existing mesh editing tools. In preparation for the voxelization, the modeled surfaces are closed by procedurally polygonizing unshared edges.While the idea to generate hair curves from geometric surfaces is certainly not new we believe to be the first to propose a purely volumetric approach that offers interesting new possibilities in terms of artistic control. Notably [Yuksel et al. 2009] proposed a conceptually similar approach except they derived the hair curves by interpolation within polygonal cross-sections of the input meshes. Instead we convert the polygons into a volumetric representation of the tangent flow extended into the interior of the polygon model.Curve Modeling of Hair: Another common challenge encountered in hair modeling and rendering, is the problem of upsamling high-resolution hair curves from a sparse set of guide hairs. The common approach is to employ various interpolation schemes that operate on a sub-set of the guide hairs to generate new interpolated hair curves. Instead we propose rasterizing the tangent directions of the guide curves into a sparse velocity field. This field can then be combined, using standard volumetric compositing operations, with other flow fields e.g. generated from other hair styles represented either by polygonal surfaces or guide hairs. The resulting flow field is then used to generate new curves defined as streamlines.Volume Generation and Styli...

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