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2.4. VOLUME VISUALIZATION
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Figure 2.11 Comparison of sampling distances in slice-based volume rendering
(left) and volume rendering based on ray-casting (right). Only ray-casting guarantees constant sampling rates.
Software solutions for evaluating the volume rendering integral usually resort
to a different approach termed ray-casting. In this approach, rays are cast from a
hypothetical eye or camera position into the volume. Usually, exactly one ray per
pixel is generated by mapping 2D pixel coordinates to 3D world coordinates and
setting up parametric ray equations based on the viewer position and the derived
world coordinates. By successively incrementing the ray parameter, the volume
can then be sampled at regular intervals. Compared to slice-based volume rendering, the latter is a major advantage since it reduces artifacts (Figure 2.11).
The compositing, however, now has to be accomplished in a front-to-back order
which makes the blending operation more expensive: Cout = Cin + (1 − αin )αC;
αout = αin + (1 − αin )α. We will have more to say about the pros and cons of the
two approaches in Section 5.4.2.
In both ray-casting and slice-based volume rendering the volume is sampled
before the transfer function is applied. Thus, while the sampling frequency might
suffice for the original volume data, it might no longer suffice after the transfer
function has been applied (as, e.g., spikes might have been introduced). Preintegration is an approach developed to address this problem [18]. In this technique, the volume rendering integral is calculated in advance for pairs of sample
values. This calculation is performed in software and only for a relatively low,
fixed number of combinations. Thus, high-quality integration techniques with
adaptive sampling rates can be utilized to compute the contributions of the slabs
defined by the two samples. The price paid for the improved quality is the need to
sample the volume both on the front and back plane of the slab during rendering
and the need to re-compute the pre-integration table after changing the transfer
function. Pre-integration is used in Section 5.4.2.