Novel Techniques

This section describes the two novel techniques developed for this work. The two techniques combine principal-curvature texture with additional cues to the inter-surface distance; cast shadows and point-correspondence glyphs.

3_{The principal curvature directions for a point on a surface are the directions of minimum and maximum curvature.}

These directions are not always well defined. Both planar and spherical regions on the surface have the same curvature in all directions, thus these regions have no unique principal curvature directions. A technique using principal curvature directions to texture the surface may use an arbitrary choice of direction in such cases or attempt to avoid texturing these locations entirely.

Figure 4.6: The hill and tumor data sets visualized using principal curvature texture. The exterior surface is textured with cross glyphs locally aligned with the directions of principal curvature.

Principal-curvature texture with cast shadows

By casting shadows of the exterior surface curvature glyphs onto the interior surface, this tech- nique conveys additional cues to the distance between the interior and exterior surfaces. The distance between the image of the glyph and the image of its shadow reveals information about the distance between these regions of surface. See Figure 4.7.

Figure 4.7: The hill and tumor data sets visualized using principal curvature texture with cast shadows. The exterior surface is textured with cross glyphs locally aligned with the directions of principal curvature. The glyphs cast shadows onto the interior surface.

pattern such as a grid, is not a requirement for conveying the shape of two surfaces. Principal curvature texture does provide an irregular texture enabling users to quickly match glyphs to their corresponding cast shadows, thereby getting an estimate on surface shape and inter-surface distance. However, the same could be accomplished with other irregular texture patterns. Regular texture patterns also allow the same perception, though they may require a search for easy correspondences before arbitrary sections of the pattern and shadow can be visually matched.

Principal-curvature texture with point-correspondence glyphs

Casting shadows from one surface to another does give an additional cue to the distance between surfaces, but it has limited application. If texture patterns on the outer surface cast the shadows, as they do for the principal-texture technique employed herein, then the pattern must not be everywhere regular or it may be too difficult to discern which shadows are cast from which parts of the texture. Similar difficulties arise in using cast-shadow information when the surfaces are significantly distant from each other. For closed surfaces, regions of the textured outer surface cannot cast shadows onto the interior without multiple light sources (as might be used in non-photorealistic, technical illustra- tions [LHV04, LHV05]) or warping the shadow geometry.

Geometric glyphs4can be used to show the distance between two surfaces and can do so without the limitations of cast shadows. In this work, line glyphs show point correspondence between the two surfaces. Additionally, these point-correspondence glyphs show an upper bound on the local distance between the two surfaces. It is an upper bound on distance because the correspondence glyphs fol- low energy-minimizing paths rather than following the shortest paths between corresponding points. Section 4.4.3 discusses the computation of the correspondence glyphs in more detail.

The visualization technique combining principal-curvature texture and point-correspondence glyphs does so in a straightforward manner. The point correspondences are computed between exterior and interior surfaces, using the center of each principal-curvature glyphs as the end point on the exterior. As in the previous technique to use point-correspondence glyphs, the point of contact between interior surface and glyph is marked with a proximity glyph. The point of contact between the exterior surface and point-correspondence glyphs is usually hidden, so no proximity glyph is attached. See Figure 4.8. Early implementations of this technique did not use principal-curvature texture. This technique was conceived to look similar to the “plasma lamp” novelty toy, where arcing electricity excites gases trapped between two glass globes. The ends of each glowing arc in the plasma lamp spread out slightly at the points of contact with each globe. This technique initially used a simple disc texture on the exterior surface as the arc terminator. The arc terminators were expected to provide a local surface

4_{Geometric glyphsare geometric probes typically attached to surface geometry to visualize associated data. The visual}

Figure 4.8: The hill and tumor data sets visualized using the principal curvature texture with point- correspondence glyphs. The exterior surface is textured with cross glyphs locally aligned with the directions of principal curvature. The glyphs cast shadows onto the interior surface.

patch whose eccentricity and illumination would reveal the local surface orientation. Surprisingly, the cross glyphs seemed to provide much better shape cues when the two implementations were compared side by side (see Figure 4.9), so they were chosen for the user study. The discs were on the same scale as the crosses are in the final implementation, and also obscured the point-correspondence glyphs. The scale and density of the cross glyphs was believed to be near enough to an optimal balance that it was decided to use the crosses instead of finding parameters that better matched the discs.

Figure 4.9: The hills data set visualized using texture with point-correspondence glyphs. On the left, the texture is the cross glyph showing local principal curvature direction. On the right, the texture is a simple disc.