Surface Rendering

The objective of surface rendering is to create the 3D appearance of a solid object by the use of visual cues such as intensity, cosine-shading, reflectance, perspective, and shadows. Radermacher and Frank (1984) developed a combination of intensity and cosine-shading first employed to obtain a surface representation of ribosomes (Verschoor et al., 1983, 1984). Similar algorithms were developed by other groups (van Heel, 1983; Vigers et al., 1986a). The intensity is used to convey a sense of distance, with closer parts of the structure made to appear brighter than more distant parts. Cosine-shading mimics the appearance of matte surfaces that are inclined relative to the viewing direction, with the highest brightness attached to surface elements whose normal coincides with the viewing direction, and zero brightness to surface elements whose normal is perpendicular to the viewing direction.

The schematic diagram in figure 6.8 explains how in general the distance of the surface from the viewer is derived from the 3D density distribution stored in the volume. First, a threshold density d0 must be defined, to create the distinction between ''inside'' (d>d0) and ''outside'' (d<d0). The choice of this threshold is critical in the visualization of the structure, as different choices may bring out different aspects of it (see below). With the given threshold, the algorithm scans the volume starting from a reference plane (which can be inside or outside the volume), counting the (normal) distance between that plane and the first encounter of a voxel that is equal to, or larger than, d0. The precise distance must then be evaluated by interpolation in the close vicinity of that boundary. The resulting distances are stored in the so-called distance buffer. On completion of the scan, the distance buffer contains a faithful representation of the topography of the molecule as seen from the direction perpendicular to the reference plane. The desired surface representation is now achieved by using the distance buffer in the computation of the two representational components,

Figure 6.8 Principle of surface representation combining shading and depth cue. The representation of a surface element is based on its distance from a reference plane measured normal to this plane. R and R', reference planes chosen inside and outside the structure, respectively, Si and S2, two portions of the surface. Si is hidden by S2 unless the interior reference plane R is used. O denotes the position of the observer; t1 and t2, the distances from two adjacent surface elements separated in the vertical direction by Ay. The slope of the plane seen from the viewing point, |ti — t2\/Ay, can be used to control the local shading, while the distance itself can be used to make elements close to the observer appear bright, and those far from the observer, dark. From Frank and Radermacher (1986), reproduced with permission of Springer Verlag.

intensity and shading, and mixing the two resulting signals. A 50:50 mixture of the two components is usually quite satisfactory.

Much more elaborate methods of representation incorporate one or two sources of light, a choice of surface texture, and the use of colors. In addition, ray tracing makes it possible to create effects associated with reflections of the surroundings on the surface of the structure. However, one must bear in mind that beyond conveying shape information, surface representations reflect no physical property of the molecule and that any extra effect has merely esthetic appeal. Examples of spectacular representations employing color to indicate segmentation are especially found in the virus field (e.g., Yeager et al., 1994; Bottcher et al., 1997; Che et al., 1998; Zhou et al., 2001a), but color is also indispensable in representing macromolecular assemblies of high complexity (e.g., Gabashvili et al., 2000; Stark et al., 2001; Davis et al., 2002). Particularly challenging is the need for the simultaneous representation of a density map and an X-ray structure fitted into it; in this case, one resorts to semitransparent surface renderings, often with reflections that reinforce the impression of three dimensions (e.g., Spahn et al., 2001a).

Surface representations are especially effective when shown in the form of stereo pairs. To achieve this, the representation is calculated for two viewing directions separated by 6° around the vertical axis, and the two images are mounted side by side with a distance equal to the average horizontal distance

Figure 6.8 Principle of surface representation combining shading and depth cue. The representation of a surface element is based on its distance from a reference plane measured normal to this plane. R and R', reference planes chosen inside and outside the structure, respectively, Si and S2, two portions of the surface. Si is hidden by S2 unless the interior reference plane R is used. O denotes the position of the observer; t1 and t2, the distances from two adjacent surface elements separated in the vertical direction by Ay. The slope of the plane seen from the viewing point, |ti — t2\/Ay, can be used to control the local shading, while the distance itself can be used to make elements close to the observer appear bright, and those far from the observer, dark. From Frank and Radermacher (1986), reproduced with permission of Springer Verlag.

between the two eyes, which is in the region of 6.5 cm (see figure 6.7c). Stereo viewing at a workstation is achieved by presenting the two frames alternately to the left and the right eye at a suitable rate, making use of synchronized switching of polarized glasses.

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