Ray Integration

Table 1.4: Running times for various volume rendering ray integration approaches. Methods printed in blue represent implementations of previous work whereas methods printed in green are introduced in this dissertation.

Model	Ray Integration	Frames/sec			Tet/sec
Blunt Fin
	Average Luminance and Attenuation	1	.	314	328 K
	Linear Luminance and Attenuation	0	.	080	20 K
	Partial Pre-Integration	0	.	937	234 K
	Average Luminance and Opacity	1	.	312	327 K
	Linear Luminance, Average Opacity	1	.	196	298 K
	Linear Luminance and Opacity Approx	0	.	938	234 K
Oxygen Post
	Average Luminance and Attenuation	0	.	577	382 K
	Linear Luminance and Attenuation	0	.	028	18 K
	Partial Pre-Integration	0	.	338	224 K
	Average Luminance and Opacity	0	.	599	397 K
	Linear Luminance, Average Opacity	0	.	417	276 K
	Linear Luminance and Opacity Approx	0	.	337	224 K
Delta Wing
	Average Luminance and Attenuation	0	.	407	558 K
	Linear Luminance and Attenuation	0	.	029	40 K
	Partial Pre-Integration	0	.	313	430 K
	Average Luminance and Opacity	0	.	421	578 K
	Linear Luminance, Average Opacity	0	.	375	515 K
	Linear Luminance and Opacity Approx	0	.	309	424 K

Figure 1.4: Running times for various volume rendering ray integration approaches. The bars with the hatched fill represent implementations of previous work whereas solid fill represents methods introduced in this dissertation.

Table 1.4 compares the various methods for computing the volume rendering integral that I discussed in this dissertation. Figure 1.4 summarizes these results in a bar graph. Average Luminance and Attenuation is the approximation reviewed in Section 1.2.2 and Linear Luminance and Attenuation is the full computation of the volume rendering integral reviewed in Section 1.2.3. Partial Pre-Integration is the fast computation of linear luminance and attenuation introduced in Section 1.2. Average Luminance and Opacity is the same as Average Luminance and Attenuation except that the former averages opacity rather than attenuation. This method is similar to that used by Wilhelms and van Gelder [102]. Linear Luminance, Average Opacity and Linear Luminance and Opacity Approx are the approximations presented in Sections 1.3.1 and 1.3.2, respectively.

Note that I perform the ray integration for all these methods exclusively in the fragment processor and recall from the previous section that the renderer is fragment-processing bound for these tests. Therefore, the comparative rates shown in Table 1.4 are good indicators of the relative performance of the different methods.

The Average Color and Luminance approach pioneered by Shirley and Tuchman [86] has one of the fastest frame rates, but, as we see in the following sections, can have large errors caused by color averaging. The Linear Color and Luminance computation developed by Williams, Max, and Stein [105] has superior image quality but abysmal rendering rates. In contrast, the Partial Pre-Integration method introduced in this dissertation has a rendering speed competitive with the Shirley and Tuchman method yet, as we see in the following sections, its accuracy is competitive with that of the Williams, Max, and Stein method.

The Average Color and Opacity approach used by Wilhelms and van Gelder [102] also has excellent frame rates but poor image quality. Both the Linear Color, Average Opacity and Linear Color and Opacity Approx methods have competitive frame rates but more accuracy. The Linear Color, Average Opacity method is slightly faster, but the Linear Color and Opacity Approx is sometimes more accurate.