Efficient Construction of Voxel Models for Ore Bodies Using an Improved Winding Number Algorithm and CUDA Parallel Computing

Round 1

Reviewer 1 Report

Manuscript Title: “Efficient Construction of Voxel Models for Ore Bodies Using 2 an Improved Winding Number Algorithm and CUDA Parallel 3 Computing”

Manuscript Number: ijgi-2645413

My Suggestion

Abstract:

1.      The abstract should state briefly the purpose of the research, the principal results, and major conclusions. An abstract is often presented separately from the article, so it must be able to stand alone. Add some stronger conclusions to it.

Introduction

1.     The introduction section must be precise and reduced with the appropriate description.

2.     The authors should add more paragraphs/literature about the studies conducted with efficient construction of voxel models for Ore bodies.

3.     The authors did not provide a thorough explanation of the novelty of their work. Therefore, it is imperative to highlight the critical gap in the previous literature and emphasize the originality and innovation of this research.

  
Discussion

1.     More discussion must be needed to distinguish between previous literature.

2.     Limitations and recommendations must be added before conclusion.  

Conclusion:

1.      Please ensure your conclusions section underscores the scientific value added to your paper, and/or the applicability of your findings/results, as indicated previously. Please revise your conclusion in more detail. Basically, you should enhance your contributions, hypothesis retain/reject, limitations, implications/applications, advantages/disadvantages, policies, underscore the scientific value added to your paper, and/or the applicability of your findings/results and future study in this session.

Author Response

Response to Reviewer 1

Dear reviewer,

Thanks for you constructive and valuable comments, which help us improve our manuscript significantly. We break down your comments and provide our responses to each of your comments separately as shown below.

1. Comments: The abstract should state briefly the purpose of the research, the principal results, and major conclusions. An abstract is often presented separately from the article, so it must be able to stand alone. Add some stronger conclusions to it.

Response:

Yes, indeed. We revised the abstract and added texts to state briefly the purpose of the study (Page 1 Lines 13-17 of the PDF version).

We also added the description of relevant results and stronger conclusions (Page 1 Lines 20-23 of the PDF version).

2. Comments: 1). The introduction section must be precise and reduced with the appropriate description. 2). The authors should add more paragraphs/literature about the studies conducted with efficient construction of voxel models for Ore bodies. 3). The authors did not provide a thorough explanation of the novelty of their work. Therefore, it is imperative to highlight the critical gap in the previous literature and emphasize the originality and innovation of this research.

Response:

Thank you for your comments. Firstly, we carefully revised the introduction section.

Secondly, we added the relevant paragraph description of the literature on the construction of the ore body voxel model (Page 2 Lines 71-78 of the PDF version).

(Page 2 Lines 71-78 of the PDF version: Despite its worse edge-fitting effect than the GTP model, each voxel unit of the 3D voxel model can record ore body data, such as mineral phase and content, making it convenient for data analysis. Therefore, constructing the voxel model is integral to the current mine application model construction [27]. For example, Chang et al. and Jia et al. used voxels to analyze and predict the distribution of ore-forming points of ore bodies in combination with mathematical models [28,29]. They constructed an information-based three-dimensional ore body model to realize mineralization information mining. In addition, Wang et al. compared the interpolation effects of different mineral contents through the 3D voxel ore body model [30]. It can be seen that the voxel model is bene-ficial to constructing and analyzing the three-dimensional model of the ore body. An essential problem to be solved in the voxelization of a 3D model is the point in polygon test.)

Thirdly, we added texts to highlight the critical gap in the previous literature and emphasize the originality and innovation of this research (Page 3 Lines 110-118 of the PDF version).

(Page 3 Lines 110-118 of the PDF version: Compared to the drawbacks of the traditional Ray casting method and Winding number algorithm, our research introduce a novel method for network coding, Tri-Coding, which utilizes a triangulation model. Therefore, we proposed an improved Winding number with a Tri-Coding (WNTC) algorithm using the Delaunay triangula-tion model for voxelization model construction. The WNTC algorithm solves the problem by constraining the positive and negative values calculated by the internal and external directions of the triangular normal vector. The proposed WNTC algorithm eliminates the need for manual intervention in the modeling process, which makes it more conducive to 3D modeling program automation performance.)

3. Comments: 1). More discussion must be needed to distinguish between previous literature. 2). Limitations and recommendations must be added before conclusion.

Response:

Yes, indeed. We added texts to distinguish between previous literature (Page 14 Lines 376-379 of the PDF version);

(Page 14 Lines 376-379 of the PDF version: Compared with the existing 3D ore body voxel modeling research, this paper pre-sents an automated modeling scheme using the Winding number algorithm. Through the design and application of the Tri-Coding algorithm, the modeling process no longer needs artificial control.)

We also added texts to summarize the limitations (Page 14 Lines 380-392 of the PDF version) and recommendations (Page 14 Lines 393-405 of the PDF version) of our work.

(Page 14 Lines 376-379 of the PDF version, The limitations: (1) The Winding number with the Tri-Coding algorithm proposed in this paper only discusses the structure of the model, which is composed of triangular faces. When constructing a computer visualization model, polygons outside of triangles are allowed. The parameter structure must be adjusted accordingly if the algorithm is applied to a model constructed by polygons with more than three edges. That may involve in-creasing the number of calculations for the solid and dihedral angle. The proposed Winding number algorithm relies on inverse trigonometric functions, demands higher operation accuracy.

(2) Our study's GPU thread grid and block are relatively direct. The number of triangular faces of the stratum model used in this experiment is up to about 1000, which does not exceed the hardware environment limit of this experiment, so the number of triangles is directly used as the number of GPU thread grids to verify the effect of CUDA parallel computing design on the improvement of program running speed.)

(Page 14 Lines 393-405 of the PDF version, The recommendations: (1) When the model body is made up of polygons other than triangles, additional steps can be taken to adapt the algorithm using the abovementioned method. Alterna-tively, the polygons can be divided into triangles to meet the algorithm's parameters outlined in this paper. The latter method is more straightforward. However, it may in-crease the data in the model depending on the number and structure of the non-triangular polygons. Handling calculation accuracy with care during program de-sign is crucial to avoid any mistakes in the final judgment.

(2) When a model consists of a large number of triangular surface elements that exceed the capability of the GPU's hardware environment to handle thread meshes, the required threads can be grouped using software control. The CUDA parallel compu-ting process is then performed, with part of the host memory allocated to set registers, save pre-calculated results, and complete the operation via CPU coordinated control. )

4. Comments: Please ensure your conclusions section underscores the scientific value added to your paper, and/or the applicability of your findings/results, as indicated previously. Please revise your conclusion in more detail. Basically, you should enhance your contributions, hypothesis retain/reject, limitations, implications/applications, advantages/disadvantages, policies, underscore the scientific value added to your paper, and/or the applicability of your findings/results and future study in this session.

Response:

Yes, indeed. we revised the conclusion in more detail.

Firstly, the first paragraph (Pages 14-15 Lines 407-414 of the PDF version) summarizes the content of this paper and the experimental results and conclusions.

The second paragraph (Page 15 Lines 415-412 of the PDF version) expounds the innovation and the contribution of this paper.

Then, the third and fourth paragraphs (Page 15 Lines 423-433 of the PDF version) explain the value and the applicability of this study.

The last paragraph (Page 15 Lines 434-437 of the PDF version) provides the focus and development direction of the research content of this paper in the future research work.

Reviewer 2 Report

Dear Author Lei Liu,

The paper is thoroughly reviewed and I would like to suggest some minor changes. 

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 2

Dear reviewer,

Thanks for you constructive and valuable comments, which help us improve our manuscript significantly. We break down your comments and provide our responses to each of your comments separately as shown below.

1. Comments: Page No.2. Lines No. 49. Mentioned the various research fields

Response:

Yes, indeed. We added texts and related References to illustrate the various research fields of the Delaunay triangulation fields (Page.No.2. Lines No.46-49 of the PDF version).

(Page.No.2. Lines No.46-49 of the PDF version: The Delaunay triangulation network is a classic algorithm used in TIN, which is widely applied in various research fields. For example, it is applied to data analysis of meteor-ological stations in 2D GIS [16], the field of 3D printing, reinforcement of printed ob-jects [17], and 2D data conversion to generate data keys for data encryption [18].)

2. Comments: Page.No.2. Line No.58 removes the space issues

Response:

Yes, indeed. The space at the original Page No.2 Line No.58 has been removed.

3. Comments: why you used Voxel Models in this research? (write briefly)

Response:

We added relevant texts to explain why the Voxel Models is used in this research (Page.No.2. Lines No.56-57 and Lines No.61-63 of the PDF version).

In brief, the 3D voxel model has good geometric characteristics, with adjacent voxels and flexible particle sizes, and it's suitable for data analysis in 3D space and beneficial to the application of the model in mining engineering, for example, reserve estimation.

4. Comments: Figure.10. What do you mean KC and JC? (write briefly)

Response:

KC and JC are the stratum codes on the borehole data, which are used to distinguish different strata.

We added texts to explain the meaning of KC and JC (Page.No.11. Lines No.325-326 of the PDF version).

5. Comments: Increase the references

Response:

Yes, indeed. We increased the relevant references of the multi-domain application of Delaunay triangulation, the examples of the voxel model , and the research progress on voxel modeling of ore bodies. The number of references has increased from 35 to 46.

Reviewer 3 Report

Congratulations, this is a well-written manuscript. For 3D ore bodies modeling, the authors proposed the Winding number with triangle network coding (WNTC) algorithm, which provides a new method for 3D geological modeling. The manuscript is logically self-consistent, the method is somewhat innovative, and the results are reasonably analyzed, which makes it a manuscript with a high degree of completion.

Author Response

Response to Reviewer 3

Dear reviewer,

We gratefully thank you for your time spent reviewing our manuscript. The significance of your review work to us is profound. Thank you again, and best wishes.

Round 2

Reviewer 1 Report

Manuscript Title: Efficient Construction of Voxel Models for Ore Bodies Using an Improved Winding Number Algorithm and CUDA Parallel Computing

Manuscript Number: ijgi-2645413

The corrections suggested have been successfully completed. The authors have done clear explanation and included all the changes. The paper is addressed with the content and research perspective.

Thank you.