Method to Determine the Centroid of Non-Homogeneous Polygons Based on Suspension Theory

Round 1

Reviewer 1 Report

All comments are in the attached document.

Comments for author File: Comments.pdf

Author Response

[Comment] 1. Suggest shortened title to: Centroid of Non-Homogeneous Polygon Based on Suspension Theory.

[Response] Thank you very much for your suggestion. We think this paper places main focus on methodological contributions: propose a method to determine the centroid of non-homogeneous polygon. We feel so sorry for that.

[Comment] 2. Suggested rewrite of Abstract.

[Response] Thank you for your very constructive comments. The abstract has been restructured and redesigned. We have clarified the main focus and novelty of the proposed method.

 

[Comment] 3.

Line	Change	To
32	with its exact center	with its geometric center
...	...	...

[Response] Thank you for being so patient. We have tried our best to change so many language problems before resubmission according to your comments.

Author Response File: Author Response.docx

Reviewer 2 Report

Determine the centroid of non-homogeneous polygon is an important research in computational geometry, applied physics, and spatial information fields，and this study proposes an innovation method for centroid computing based on the suspension theory of physics. Although the research topic is of great interest and is easy to follow, there are still some shortcomings in this study, as follows:

1. In section Abstract, the research background and results are introduced clearly, but the technical key points of the proposed method were not clearly summarized, for instance how it uses the suspension theory of physics skillfully? What are the tricky things in the proposed method? Moreover, it is said “the traditional calculation method does not have a tangible connection with the center of mass of the object”, how does the study offer an innovative solution to shortcoming of traditional methods?
2. In section Introduction, the manuscript introduces some application backgrounds in details, but does not introduce and evaluate the related research work, especially, the related researches and developments about “the centroid of a non-homogeneous body”, which is the key work in this study.
3. In section “2.2. Method to Determine the Centroid”, the introduction of the proposed method and the calculation steps is relatively simple, authors can discuss the new advancements of the method and gives the physical interpretations of the conditions in the method.
4. In section “3. Centroid-computing Procedure of Different Type of Polygon”, the manuscript does not give a reason or a reference for choosing these three types of polygon. Are they representative polygons, or are they often used in similar studies?    
5. In section 3, the manuscripts uses the proposed method to determine the Centroid for the three types polygon, are there some objective indicators to identify the proposed method is better than other classic methods?
6. The experiments were not compared with other classical methods or studies, but the results were compared with administrative center. It cannot explain well the research advancement and feasibility of the proposed method. And the population data used in the experiment seem to be rough numbers rather than accurate ones, does it make sense?
7. Why “the proposed method is easy to implement using a GIS tools”? No explanation was given.
8. Add more references about related work, classical studies or meaningful strategies.

Author Response

[Comment] 1. In section Abstract, the research background and results are introduced clearly, but the technical key points of the proposed method were not clearly summarized, for instance how it uses the suspension theory of physics skillfully? What are the tricky things in the proposed method? Moreover, it is said “the traditional calculation method does not have a tangible connection with the center of mass of the object”, how does the study offer an innovative solution to shortcoming of traditional methods?

[Response]   Thank you for your very constructive comments. We have rewritten the Abstract section, and added the technical key points of the proposed method. The tricky things in the proposed method has also been illustrated. Sorry for our unrigorous description and we have modified this sentence: “the traditional calculation method does not have a tangible connection with the center of mass of the object”.

 

[Comment] 2. In section Introduction, the manuscript introduces some application backgrounds in details, but does not introduce and evaluate the related research work, especially, the related researches and developments about “the centroid of a non-homogeneous body”, which is the key work in this study.

[Response]   We have added the more related researches and developments about “the centroid of a non-homogeneous body” in section Introduction. The research contents mainly include the introduction of the traditional methods and analysis of the advantage and disadvantage of related centroid methods.

 

[Comment] 3. In section “2.2. Method to Determine the Centroid”, the introduction of the proposed method and the calculation steps is relatively simple, authors can discuss the new advancements of the method and gives the physical interpretations of 

the conditions in the method.

[Response]   Thank you for the suggestion. We have added more detailed explanation in the first paragraph of section 2.2 to help the audiences to better understand the following proposed method and the calculation steps.

 

[Comment] 4. In section “3. Centroid-computing Procedure of Different Type of Polygon”, the manuscript does not give a reason or a reference for choosing these three types of polygon. Are they representative polygons, or are they often used in similar studies?    

[Response]   We have added more details about the types of polygons and given the reason why we choose four types of polygons. However, in our humble opinion, self-intersecting polygon is often considered a topology error. So this type of polygon is not discussed in this paper.

 

[Comment] 5. In section 3, the manuscripts uses the proposed method to determine the Centroid for the three types polygon, are there some objective indicators to identify the proposed method is better than other classic methods?

[Response]   In section 3, we planned to present the proposed method and centroid-computing procedures. And in the section 4, we explained the comparison between the new method with other classic methods. We feel so sorry for that we have not found some suitable objective indicators.

 

[Comment] 6. The experiments were not compared with other classical methods or studies, but the results were compared with administrative center. It cannot explain well the research advancement and feasibility of the proposed method. And the population data used in the experiment seem to be rough numbers rather than accurate ones, does it make sense?

[Response]   In the section 4, we have added relative contents to compare the computing results of the new method with other classic methods (mean centroid, administrative center and weighted centroid). In addition, the population data set in section 4, which aggregated in 1000 m × 1000 m cells regarding the terrain and population density, are provided by the Data Center for Resources and Environmental Sciences, Chinese Academy of Sciences (RESDC) (http://www.resdc.cn). This is the most accurate population data we can get.

 

[Comment] 7. Why “the proposed method is easy to implement using a GIS tools”? No explanation was given.

[Response]   We are so sorry that we did not illustrate the terms clearly. We have modified this sentence to “the proposed method is easy to implement using ArcPy package” in manuscript.

 

[Comment] 8. Add more references about related work, classical studies or meaningful strategies.

[Response]   Thank you for the suggestion. We have added more detailed references about related work in section 1.

Author Response File: Author Response.docx

Reviewer 3 Report

This study proposed a new method to compute a centroid using the suspension theory.   The proposed method consists of four steps based on fundamental parameters setting. The proposed method was applied in practice to calculate the population gravity of Beijing. However, the critical challenges stated in the paper are not clear to me as follows.

 

Major comments:

The main drawback of this study did not present the proposed algorithm's performance. The authors must compare the proposed method with alternative methods regarding precision and runtime analysis. These comparisons will reveal the advantages/disadvantages of the proposed method. It is not easy to evaluate the performance of the proposed method in the current manuscript.

 

Although this study demonstrates the feasibility of the proposed method for non-homogeneous polygons, it is necessary to evaluate the proposed method's performance with different types of polygons (e.g., concave or self-intersecting polygons). It is reasonable to explain that the proposed method can handle all polygons.

 

Further, the proposed method requires three-parameter input (i.e., selection of original point, precision value, step length). It means the proposed method cannot be generalized. It can be random. It must be investigated how to determine proper parameter values.

Author Response

[Comment] 1. The main drawback of this study did not present the proposed algorithm's performance. The authors must compare the proposed method with alternative methods regarding precision and runtime analysis. These comparisons will reveal the advantages/disadvantages of the proposed method. It is not easy to evaluate the performance of the proposed method in the current manuscript.

[Response]   Thank you for the suggestion. We are so sorry we did ignore the issue. We planned to propose a new method to compute the centroid. In terms of algorithm's performance, ours is unfortunately worse than the traditional method. Because we should first find the two balance lines, and then compute the intersection of the balance lines to define the object centroid. However, we think the proposed method overcome the limitation of the traditional calculation method only considers the geometric coordinates of the boundary points of the polygon by the consideration of inside point value and distance.

 

[Comment] 2. Although this study demonstrates the feasibility of the proposed method for non-homogeneous polygons, it is necessary to evaluate the proposed method's performance with different types of polygons (e.g., concave or self-intersecting polygons). It is reasonable to explain that the proposed method can handle all polygons.

[Response] Thank you for your very constructive comments. We have added more details about the types of polygons and given the reason why we choose four types of polygons. However, in our humble opinion, self-intersecting polygon is often considered a topology error. So this type of polygon is not discussed in this paper.

 

[Comment] 3. Further, the proposed method requires three-parameter input (i.e., selection of original point, precision value, step length). It means the proposed method cannot be generalized. It can be random. It must be investigated how to determine proper parameter values.

[Response] Yes, three-parameter inputs need to be set according to specific application instances. To avoid the location uncertainty of centroid point, the selection of original point and step length should be determined according to 3.4.1 section: “if the starting and ending points are all set at the vertex of the line, which is an integral multiple step length. The intersecting points of different candidate centroid balance lines will gather at one unique point”.

For precision value, the G values on the left and right sides should be completely equal. However, it is difficult to achieve this in practice. We set the precision value is 0, if the difference is bigger than 0, we should adjust the end point coordinate to find the true balance line; otherwise, we think the current line is balance line. However, when no matter how you change the end point location, the difference is always hovering between some two values. We think current line is final balance line.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The new submission addressed my previous main concern. However there are some suggestions:

1. The related work added did not cite relevant literature well;
2. The English  language  of the revised portions should be improved;
3. The experimental results in Table 1. can be analyzed in more detail by the principle or advantages of the proposed methods.

Author Response

[Comment] 1. The related work added did not cite relevant literature well.

[Response]   Thank you for the suggestion. We have read and added more references and application cases in section 1. 

[Comment] 2. The English language of the revised portions should be improved.

[Response] Thank you for the comments and we have invited a native English speaker to help us polish the manuscript. 

[Comment] 3. The experimental results in Table 1. can be analyzed in more detail by the principle or advantages of the proposed methods.

[Response] Thank you for your very constructive comments. We have added more comparisons and analyses of the results in Table 1.