List of Figures

1. A photorealistic scene with translucent volumes (clouds).
2. Surface rendering versus volume rendering.
3. Volume representations.
4. Different renderings of two hexahedron cells.
5. Light transport through faces versus solids.
6. The standard graphics pipeline.
7. An illuminated volume.
8. Particle model of volumetric rendering.
9. Hierarchical pruning for ray casting
10. Cell traversal ray tracing.
11. Projected tetrahedra classes.
12. GATOR basis graph.
13. GATOR permutations.
14. Ray-cell-face intersection.
15. Ray-plane intersections at vertices.
16. A visibility cycle.
17. MPVO cell connectivity graph.
18. Shear-warp factorization.
19. Rectilinear volume slices.
20. Error in luminance averaging.
21. The calculations performed by a pre-integration table lookup.
22. Effect of aliasing of a transfer function.
23. Tetrahedron clipping.
24. Plot of $\Psi$ against ${\tau }_{\,\mathrm{b}}D$ and ${\tau }_{\,\mathrm{f}}D$.
25. Plot of $\Psi$ against ${\tau }_{\,\mathrm{b}}D$ and ${\tau }_{\,\mathrm{f}}D$.
26. Plot of $\Psi$ against ${\gamma}_{\,\mathrm{b}}$ and ${\gamma}_{\,\mathrm{f}}$.
27. Maximum error of $\Psi$ calculation using a lookup table.
28. Comparison of ray-integration approaches, linear attenuation.
29. Approximation of $\zeta$ for linearly interpolated opacity.
30. Approximation of $\Psi$ for linearly interpolated opacity.
31. Plot of $\zeta$ with linearly interpolated $\alpha$.
32. Plots the error of the $\Psi$ approximations.
33. Comparison of ray-integration approaches, linear opacity.
34. Sample data sets.
35. Running times of cell projection.
36. Effect of fragment processing on cell projection speed.
37. Running times of ray integration.
38. Error for linear attenuation approximations, $D=0.001$.
39. Error for linear attenuation approximations, $D=0.1$.
40. Error for linear attenuation approximations, $D=1$.
41. Error for linear attenuation approximations, $D=100$.
42. Error for linear opacity approximations, $D=0.001$.
43. Error for linear opacity approximations, $D=0.1$.
44. Error for linear opacity approximations, $D=1$.
45. Model used to study Mach bands caused by approximation errors.
46. Ganglion receptor response.
47. Cell boundaries with constant attenuation.
48. Cell boundaries with large attenuation in the back.
49. Cell boundaries with large attenuation in the front.
50. Cell boundaries with constant opacity.
51. Cell boundaries with large opacity in the back.
52. Cell boundaries with large opacity in the front.