Fig. 1. Principle of ray-casting algorithm

Fig. 2. Comparison of sampling method of improved algorithm and traditional algorithm

Fig. 3. Sampling frequency calculation method of improved ray-casting algorithm

Fig. 4. Calculation principle of linear interpolation

Fig. 5. Linear interpolation method of hierarchical grouping

Fig. 6. Calculation time of interpolation for improved algorithm and traditional algorithm

Fig. 7. Opacity and color synthesis (calculating order from front to back)

Fig. 8. Experimental results of smoke rendering in a fixed space scene. (a) Simulation rendering for 100th frame; (b) simulation rendering for 200th frame; (c) simulation rendering for 300th frame

Fig. 9. Experimental results of smoke rendering in the office. (a) Rendering result for 50th frame; (b) rendering result for 200th frame; (c) rendering result for 500th frame; (d) rendering result for 800th frame

Fig. 10. Experimental results of smoke rendering in the corridor. (a) Rendering result for 300th frame; (b) rendering result for 500th frame

Fig. 11. Experimental results of smoke rendering in a simple scene. (a) Traditional ray-casting algorithm; (b) ray-casting algorithm in Ref. [17]; (c) improved ray-casting algorithm

Fig. 12. Experimental results of smoke rendering in a complex scene with a farther viewpoint. (a) Traditional ray-casting algorithm; (b) ray-casting algorithm in Ref. [17]; (c) improved ray-casting algorithm

Fig. 13. Experimental results of smoke rendering in a complex scene with a closer viewpoint. (a) Traditional ray-casting algorithm; (b) ray-casting algorithm in Ref. [17]; (c) improved ray-casting algorithm

Fig. 14. Experimental results of smoke rendering frame rate