Cell Projection

The cell projection that performs adaptive transfer function sampling, described in Section 1.3, clips tetrahedra and renders them multiple times. Before analyzing the rendering rate of this cell-projection method, we must first understand how many more tetrahedra we must render to perform the adaptive transfer function sampling.

Table 1.2: Growth in data sets for adaptive transfer function sampling. This table gives the size of the original data set, the number of tetrahedra rendered by the adaptive transfer function sampling approach, and the growth in the number of tetrahedra rendered.

Data Set	Tetrahedra in Data Set	Tetrahedra Rendered	Growth
Blunt Fin	187,395	249,278	33%
Oxygen Post	513,375	662,625	29%
Delta Wing	1,005,675	1,373,010	36%

Table 1.2 gives, for each data set, the number of extra tetrahedra rendered. All the transfer functions selected require the adaptive transfer function sampling method to render about $33\%$ more tetrahedra.

Table 1.3: Running times for various volume rendering cell-projection approaches. Methods printed in blue represent implementations of previous work whereas methods printed in green are introduced in this dissertation.

Model	Cell Projection	Frames/sec			Tetrahedra/sec
Blunt Fin
	View Independent Cell Projection	3	.	296	618 K
	Balanced Cell Projection	4	.	498	843 K
	Adaptive Transfer Function Sampling	1	.	312	327 K
Oxygen Post
	View Independent Cell Projection	1	.	343	690 K
	Balanced Cell Projection	2	.	275	1168 K
	Adaptive Transfer Function Sampling	0	.	599	397 K
Delta Wing
	View Independent Cell Projection	0	.	721	725 K
	Balanced Cell Projection	1	.	556	1565 K
	Adaptive Transfer Function Sampling	0	.	421	578 K

Figure 1.2: Running times for various volume rendering cell-projection approaches. The bars with the hatched fill represent implementations of previous work whereas solid fill represents methods introduced in this dissertation.

Table 1.3 compares view independent cell projection with the two cell-projection methods defined in Chapter 1. Figure 1.2 summarizes these results in a bar graph. View Independent Cell Projection is the method developed by Weiler, Kraus, and Ertl [98] and reviewed in Section 1.1. Balanced Cell Projection and Adaptive Transfer Function Sampling are the methods presented in Sections 1.2 and 1.3, respectively. To highlight the running times of each cell-projection method, I used the least computationally intensive ray integration methods. For View Independent Cell Projection and Balanced Cell Projection, I used pre-integration to perform ray integration. For Adaptive Transfer Function Sampling, I simply averaged the color and opacity of each ray segment.

My Balanced Cell Projection is a modified version of View Independent Cell Projection, and the rendering times suggest that these changes do indeed speed up the rendering. Adaptive Transfer Function Sampling is the same as Balanced Cell Projection with the added ability to clip cells. We expect the added computation to clip cells to affect performance, and the data show that it does. In these ways, the comparative running times verify our preconceived notions of how well these cell-projection methods perform.

However, these results also differ somewhat from what I would expect. I would expect the improvements of the Balanced Cell Projection over the View Independent Cell Projection to be more dramatic. Furthermore, the penalty of the Adaptive Transfer Function Sampling is more costly than I would expect. I believe these results arise from the system being fragment-processing bound. If the fragment processing were the bottleneck, it would diminish improvements in the cell projection. Furthermore, the clipping performed in the Adaptive Transfer Function Sampling relies heavily on the fragment processor.

Figure 1.3: Effect of fragment processing on cell projection speed. All readings are taken from the Blunt Fin data set.

Figure 1.3 shows how the rendering rate changes as the image size (and consequently the number of fragments processed) increases. For all cell-projection methods, the rendering rate holds nearly constant until the image size reaches four thousand pixels. After that, the renderer becomes fragment processor bound and the rendering rate steadily decreases as the image size increases.