Conditions: Visualization techniques

The following sections describe the three visualization techniques included in this experiment: color mapping, principal curvature texture, and principal curvature texture with shadows.

Color mapping

The color mapping technique displays the geometry of one of the two intersecting surfaces. That surface’s color is mapped to the Euclidean signed shortest distance between the two intersecting sur- faces (Figure 5.3). A double-ended saturation scale, blue through grey to red, classifies inside, touch- ing, and outside as hue while also encoding distance as saturation. This scale is suggested by Ware as a possible scale for conveying ratio data, though Ware notes that conveying ratio data in color is “a tall order” [War04]. This color scale is also perceptible by those with deuteroanomaly, deuteropia, protoanomlay, or protopia, which are the most common forms of color blindness. Additionally, a

Figure 5.3: This is an example of the color mapping technique. The two surfaces on the left are used to produce the visualization on the right. The top left image is used as geometry, and the bottom left image is used to compute the distances mapped to the color scale.

simple grid texture projected orthogonally onto the surface along the Z axis appears on the visible surface to provide stronger shape cues. The color scale is normalized such that the range of the color scale maps to the range of values(−m,m)wheremis the maximum (unsigned) distance between the two surfaces. This maximizes the available perceptual precision in the saturation scale and would be expected practice if such a scale were applied to real data.

Color mapping is a frequently used visualization technique for displaying scalar values on sur- faces – a task for which it is well suited when used appropriately [Hea96, War88]. Applying a color scale to a surface can be quite effective for classification or metric estimation but is not a good per- ceptual technique for conveying geometric information. The color scale can only depict the values of a scalar-valued function at every point on a surface, but an arbitrary geometry can not necessarily be represented as a function over the surface. A color mapping technique is included because it is

Figure 5.4: This is an example of the principal curvature texture technique. The two surfaces on the left are used to produce the visualization on the right, and appear in the same colors. Regions of the surfaces labeledinteriorappear colored by the exterior, but are visualized as a neutral grey material with a regular-grid texture. Regions of the surfaces labeledexterior appear as principal-curvature glyphs textured onto a translucent surface.

a typically employed approach for comparing two surfaces. Though it conveys no perceptual shape information about one of the surfaces, the color scale directly encodes the metric for comparison in the distance task, and the gradient of the color scale encodes the metric for comparison in the local shape task (the magnitude of the color gradient tells how fast the local surface normals diverge).

Principal curvature texture

The second visualization technique is an adaptation of existing nested surface techniques. It is based on Interrante’s curvature-directed strokes [IFP96]. The technique employs textured glyphs which conform to both principal curvature directions, as suggested by Kim et al. [KHSI03], and

modulate translucency (Figure 5.4). The glyph is a elongated plus – the long axis indicates an estimate of the first principal curvature direction at the glyph center. Recall that the data includes noise, so the surface does not have significant regions with undefined principal directions (e.g. flat regions). Though one could replace the anisotropic glyph with an isotropic glyph to signify regions where the principal directions were undefined, this was not done here.

Red and blue are used to denote ownership of the exterior surface regions. Red regions belong to surfaceA, and blue regions belong to surface B. Though the apparent color is modified by the translucent exterior regions, the interior regions are rendered as a neutral grey. Neutral grey was chosen to minimize differences between this technique and the next, where I felt it important that the interior coloring provide better contrast for shadows than the red and blue color coding would. The interior is also textured with a simple grid to enhance shape perception.

Principal curvature texture with cast shadows

The third visualization technique adds cast shadows to the principal curvature texture (Figure 5.5). Again, red and blue denote ownership of the exterior regions of the two surfaces, while the interior is a neutral grey (tinted by the translucent exterior). Neutral grey provides better contrast for the cast shadows than would red or blue, helping the cast shadows to stand out against the interior and to be perceptually separable from the principal curvature glyph texture itself. The interior is also textured with a simple grid to enhance shape perception. Recall that the light source is fixed, thus when the surfaces undergo the rocking motion, the shadows move appropriately. I expected the cast shadows to enhance the ability to perceive inter-surface distance because cast shadows have been reported to help fix the frame of reference between caster and receiver [CL89].