5.5.2 Ray-casting

Ray-casting along the volume axis is trivial, since it is a simple traversal along adjacent voxels in the view direction. The gridpoints of the arrays of shaded colour, $C[x,y,z]$ and opacity $O[x,y,z]$ are averaged, in order to use values resampled at the voxel centers. Then, the application gives easily-computed top and front projected images of the volume.

However, rendering the volume from any viewing direction is a complicated task. Ray casting was implemented for arbitrary viewing direction in the xy-plane by rotating the image plane around the z-axis by $\theta_x$. Direction cosines were used to implement this feature (Sal99). Direction cosines generalize well from two dimensions to three. However, only the two dimensional representation was implemented. The idea is that image plane is rotated by an angle $\theta_x$ around the z-axis, the ray direction is computed perpendicular to the image plane. For each voxel a ray is cast in the view direction and unit samples located along the ray are calculated and the gridpoints around each sample are trilinearly interpolated in order to get the values at the sample point.