Visual Simulation of Turbulent Foams by Incorporating the Angular Momentum of Foam Particles into the Projective Framework

Round 1

Reviewer 1 Report

This article presents a foam-generation method. The proposed method takes the angular momentum of foam particles into consideration to enhance reality in the simulation.

Comments about the context are listed as follows:

1. Overall, this research contributes new ideas for foam generation in Virtual Reality (VR). This is the major contribution.
2. There are a lot of Physics properties, used in the equations, needing more explanation.  
3. Using the screen-space method to detect regions producing foams seems weird. Is there any Physics theory to support this approach? Or is it a heuristic method?
4. In page 6, line 178, the acceleration is computed by the difference of velocities at two consecutive time steps. It should be divided by the time step size.
5. Are foams regarded as balls and thus they have 3 radii, as shown in Eq. (3), page 6?  How to decide r_{p}? (line 186). The entries of the projection matrix should be shown. They are used in some equations.
6. Equation (5) needs some explanations. (i, j) are indices of the depth buffer? Why this equation works?
7. Do Equation (7) and (8) come from reference [38]? 
8. In Equation (6), how to compute k? The depth and acceleration maps are 2D spaces. 
9. In Equation (9), the variable "H" is different from the Height of the 2D space (in Equation (8)). It is better replaced by another letter. 
10. Equation (9) says the temporal variation of depth is equal to the mean curvature of the depth map. Is there any Physics foundation to support this ODE? 
11. Using the acting forces of neighboring particles to compute the torque is a great idea. However, Equation (11) needs more explanation, especially the smoothing weight function. Another suggestion, in Equation (11), torque would be a moment (a vector) not a scalar. Taking the 2-norm of the right hand side would be more proper.
12. In Equation 12, the angular momentum is incrementally updated. However, the torque has been computed in Equation (11) and the inertia of the particle is known, why bother to use this strange method?
13. Equation (13) is a simpler method to obtain angular velocity. Usually, we compute angular acceleration based on the variation of angular momentum and then update the angular velocity. 
14. Equation (14) computes the relative angular velocity between the foam and the underlying water particle. Is there any Physics theory to justify this equation? 
15. Equation (15) needs explanation too. Why do we need w_{p}? Can we just use w_{pf} to compute the tangential velocity?
16. In line 277, page 9, the scene is rendered by using ray-tracing? Is there any benefit to use ray-tracing method?  Can we use splatting methods, since the positions of particles had been projected onto the screen space?
17. Maybe I missed something. What is the frame rate of the simulations presented in Section 5, pp. 11-14?

Author Response

Attached file

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents the improvement of visual simulation of foams using the angular momentum of foam particles.

Below are some detailed comments that this reviewer thinks could improve the readability.

Please improve section 1.1 describing in a more clear and detailed way the problem statement along with Figure 1, Figure 2 and depth-based curvature to make the paper more self-contained. In the first paragraph do not duplicate "However".

English is good, but please check with a native English speaker the following points.

Lines 81-83: "every time" and "as the user wants": the concept is clear but English needs improvement

Line 85: "stably" is not commonly used, if possible check with a native English speaker

Line 99: method should be methods?

Line 100: method should be methods?

Line 109: "their" should be "its"?

Line 176: it seems that the real number set symbol is lacking in the two expressions.

Line 182: why is z_p outside the parentheses?

Equation (2): what is d in the last column vector?

Line 185: r should be italics?

Line 186: what is r_p?

Equation (4): if d_ij is an acceleration (line 177) what does compute argmin(z_ij)? Could you explain?

Line 197: gamma should be a Greek letter. Remove the commas in this sentence

Line 203: if possible check with a native English speaker the substitution of "as" with "with"

Line 206: if possible put in parentheses the recommendation

Equation (9): the variable H was previously used to represent horizontal resolution

Line 218: if possible put in parentheses the recommendation

Equation (11): what does mean the multiplication symbol?

Line 247: if possible check with a native English speaker the substitution of "as" with "with"

Line 255: if possible check with a native English speaker the substitution of "as" with "with"

Equation (14): what does mean the multiplication symbol?

Line 271: GHz

Line 280: if possible check with a native English speaker the substitution of "as" with "with"

Caption of figure 4 and following captions: if possible check with a native English speaker the substitution of "to" with "as"

Line 291: what does mean the multiplication symbol?

Line 293: what does mean omega=omega?

Figure 10 and following: please change color of red capital letters A, B, ... because are difficult to be read when printed in black and white (yellow could be better)

Line 390: please describe in more detail the parameters in Table 2

Author Response

Attached file

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

In the creation procedure of foams, some of the governing equations are based on physics while others are not. Briefly explaining the intuitions (heuristic concepts) would be better than citing published researches.