Figure 6 is a stereo line drawing of DNA as stick bonds with the patch boundary curves of the DNurbs. Bezier, B-spline patches with six patches per base pair are employed.
Figure 7 presents the rendering of a model of tRNA (11). Transparent DNurbs are overlaid on the complementary regions using B-spline, B-spline patches with four patches per pair.
Colour Plate 1 shows B-spline, B-spline DNurbs with eight patches per base pair. Colour and texturing are applied to illustrate the sequence and direction of the strands. Cutaway views give a feel for the fit to the underlying structure.
Colour Plate 2 illustrates more textured DNurbs. A Bezier, B-spline with only two patches per base pair gives the geometry. Textures are applied to indicate the chemical properties of atoms in the major and minor groves. The eight required texture patterns are also shown. For comparison, a space-filling model is drawn to scale.
The time required for computation of the control points is trivial once the coordinates are read into memory. The images shown in the Colour Plates cannot be rotated smoothly in real time except on high-end workstations. Table 2 gives rendering times in seconds for the boundary curves in Figure 6, the averages for the textured and non-textured DNurbs of the Colour Plates, and the atomic spheres of Colour Plate 2. A value of zero means real time transformation.
There appears to be a slight performance penalty in the Inventor environment compared to programs written directly in GL. Line drawings may be manipulated in near real time on even the lowest end workstation. This is the tack taken with Ribbons 2.0 on Indigo machines - manipulate the image as a line drawing, then turn on the solid rendering. The Sphere and NurbSurface objects in the Inventor environment may be rendered at a user-chosen ``complexity.'' The Colour Plates have the complexity of the NurbSurface objects set very high, while the complexity of the Sphere objects are set to the default. The DNurbs still look quite smooth with the default values, and the interactive response increases about threefold compared to the results given in Table 2.
Table 2. Rendering Performanc
Times (seconds) required to draw the images. Only the Indigo2 workstation is equipped with a special graphics board.
workstation space-filling textured non-textured line
CPU, graphics spheres DNurbs DNurbs DNurbs
----------------------------------- --- ---- ----- ------
Indigo R3000, low-end graphics 15 7 2.2 0.2
Indigo R4000, XS24 graphics 6 3 0.8 0.0
Indigo2 R4000, extreme graphics 1 2 0.2 0.0