The final step is to designate an edge type similar to the edge flag described earlier, by setting an enumeration in the pixel shader input struct stating the edge type. This will enable us to color the edge and allows for explicit stylization and lighting based on edge type.

The three steps in the extrusion of an important edge: identifying the edge itself [left]; walk the vertices and output one in the original position and another in the direction of the normal a distance T as defined by the user [middle]; and create a new geometry [right].

Coplanar geometry drawn in a second pass results in z-fighting. To address this we transform the vertices a small distance epsilon toward the viewer [exagerated in figure for illustrative purposes] giving a much more visually appealing result.

Results

The choice to extrude geometry in the direction of the vertex normal gives a visually appealing silhouette edge in most cases. However, there is a visible gap if the model causes abrupt changes in the direction of extrusion when walking the vertices as they near a hard edge.

A hard edge is an edge where the triangles forming the edge share vertices with orthogonal normals. For example, a cube contains hard edges along its entire silhouette. A visual gap is noticeable at the transition point where the geometry changes from a silhouette edge (which is not also a hard edge), to a silhouette edge (which is a hard edge).

If a hard edge is present and inked as well, it occludes the transition point in most views. In practice, this visual gap is likely to be of little importance since both crease edges and silhouette edges are inked in most non-photorealistic rendering applications. The gap effect increases as the line thickness increases-it's not visible when the line is of typical thickness but is quite obvious when the thickness is large.

Increasing the line thickness increases the visible gap as the coincident vertex of a hard edge abruptly changes direction.

Aligning the fins to be perpendicular to the eye, instead of extruding along the normal, should also hide the discontinuity, although it would introduce z-fighting since there's no guarantee the silhouette would be rendered on a different plane than the geometry. One way to handle this predicament is to bias the z component of the silhouette's vertex position by a factor epsilon.

Future Work

It may also be worthwhile to explore implementing a more complex edge constructed as a closed manifold surface. While this would take significantly more resources, seeing as the amount of additional geometry required would increase greatly, it would allow for very complex stylization of the edges.

Silhouette and crease edge detection and extrusion on the GPU gives us several possibilities for future work. Stylizing the edges so they look similar to edges drawn by a human artist could also be possible within the geometry shader.

It's possible to do some quick real time edge stylization by biasing the extrusion direction or applying texture maps to the new geometry, but more advanced techniques could also be used in order to create stroke styles, ink styles, varying width, "shock" silhouettes, "dashed" silhouettes, "shattering" silhouettes, and other techniques in real time with DirectX 10 using the new capabilities of Direct3D 10 and Shader Model 4.0.

Joshua Doss is part of the advanced visual computing team in the Intel Software Solutions Group. Send comments about this article to jdoss@gdmag.com.

The author acknowledges support and review by Adam Lake, Matthew Williams, and David Bookout at Intel. Digital assets were designed by Jeffery A. Williams at Intel.

References

Marshall, Carl S. "Cartoon Rendering: Real-time Silhouette Edge Detection and Rendering," in Game Programming Gems 2. Hingham, Mass.:
Charles River Media, 2001.

Akenine-Moller, Tomas and Haines, Eric. Real-time Rendering Volume II, Wellesley, Mass.: AK Peters Ltd., 2002.

Lake, Adam, Marshall, C., Harris, M., and Blackstein, M. "Stylized rendering techniques for scalable real-time 3D animation," Non-Photorealistic Animation and Rendering archive, Proceedings of the 1st international symposium on Non-photorealistic animation and rendering. Annecy, France: ACM Press, 2000.

Gooch, Amy et al. "A Non-Photorealistic Lighting Model For Automatic Technical Illustration," in NPAR 2000, 13-20, 1998.

Tariq, Sarah at NVIDIA 2006. "DirectX10 Effects," Siggraph 2006.
http://developer.nvidia.com/object/siggraph-2006.html