Brute-force Algorithm []

  Given a scalar valued 3D array of data samples of Voxels. A Voxel is defined by its position , i,j,k = 1,...,N its value (???), its color and the opacity .
The image is assumed to be an array of Pixels indexed by a vector .

Parallel rays are traced into the data from each pixel and a vector of colors and opacities is computed by resampling the data at W evenly spaced locations along the ray and by trilinearly interpolating from the eight voxels surrounding each sample location. Samples are indexed by a vector , where (u,v) identifies the ray (the location of the pixel the ray was cast from) and w = 1,....,W corresponds to the distance along the ray with w=1 being closest to the eye. The Color and opacity of sample U Uare denoted by and respectively. A fully opaque background is draped behind the dataset and the resampled colors and opacities are composited with each other and with the background to yield the color for the pixel .

Let and denote the color and opacity of pixel u uafter/before processing sample U U.

In a front-to-back algorithm color and opacity are calculated in the following way:

with .

After all samples along a ray have been processed, the color of the ray is given by