PONE-D-23-44182Generalized Bézier-like model and its applications to curve and surface modelingPLOS ONE

Dear Dr. Birhanu,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

The manuscript have many flaws need to be addressed are as follows: 1. Novelty of the work is missing2. In depth literature review need to added3. Mathematical expression have many error4. Lacking the presentation of Result and discussion section5. Need to improve the conclusion section

Please submit your revised manuscript by Mar 21 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Sameer Sheshrao Gajghate, PhD

Academic Editor

PLOS ONE

Journal requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. When completing the data availability statement of the submission form, you indicated that you will make your data available on acceptance. We strongly recommend all authors decide on a data sharing plan before acceptance, as the process can be lengthy and hold up publication timelines. Please note that, though access restrictions are acceptable now, your entire data will need to be made freely accessible if your manuscript is accepted for publication. This policy applies to all data except where public deposition would breach compliance with the protocol approved by your research ethics board. If you are unable to adhere to our open data policy, please kindly revise your statement to explain your reasoning and we will seek the editor's input on an exemption. Please be assured that, once you have provided your new statement, the assessment of your exemption will not hold up the peer review process.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Partly

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: Yes

Reviewer #3: N/A

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Manuscript ID: PONE-D-23-44182

The manuscript entitled "Generalized Bézier-like model and its applications to curve and surface modelling” proposes C^3 and G^3 continuity for curves, and G^1 and G^2 continuity for surface. This study is an extension of [1] and [2]. Hence, this work is the followed-up work. Overall, the paper has interesting results and significant contribution. However, the current of this work cannot be published until the following problems and remarks are addressed.

Minor comments:

1. There is typo in Equation (2.2) and (2.4) it should be U(F) since the author denoted the symbol for parametric curve.

2. Please mention that u and v are the x and y components of U(F), respectively for Equation (2.3) and (2.5).

3. In Equation (2.10), there is typo, it should be 0 ≤w, w1 ≤1.

4. Make sure the partition of each section is well organized. For example, Section 2.6 is for continuity of curve and surfaces but only discuss for curve only while Section 3 discuss for surface continuity.

5. In Section 3.2 first sentence, it should be G^0 continuity not G^1.

6. In Section 3.2 last sentence, it should G^2 continuity in w direction not t.

7. On page 13, last paragraph, please recheck which said figures.

Please check the manuscript for typos, grammatical mistakes, and undefined symbols.

Major remarks/comments:

1. The abstract should answer the following: What is the motivation of this study? What is the current limitation of the existing method? What is the advantage of the proposed method compared to the existing method?

2. Lack of literature review regarding G^1/G^2 continuity of Bezier-like surface. Consider the following work:

a) Hu, G., Cao, H., Wang, X., & Qin, X. (2017). G^2 continuity conditions for generalized Bézier-like surfaces with multiple shape parameters. Journal of Inequalities and Applications, 2017, 1-17.

b) Syed Ahmad Aidil Adha Said Mad Zain, Md Yushalify Misro. A novel technique on flexibility and adjustability of generalized fractional Bézier surface patch[J]. AIMS Mathematics, 2023, 8(1): 550-589. doi: 10.3934/math.2023026

3. Introduction has unclear motivation. What is the research gap? Next, what is the novelty of this research?

4. In Section 2.4 and 2.5, there is a lack of discussion regarding the geometric effect of shape parameters to the curves and surfaces. Please give details regarding the geometric effect of shape parameters, for example what will happen if the first shape parameter is increased while the other parameter is decreased and vice versa. What would happen if both increased/decreased?

5. In Section 2.6 paragraph 1, please elaborate regarding the reason C^3/G^3 continuity is smoother than C^2/G^2. What is the significant advantage of C^3/G^3 continuity compared to C^2/G^2 in terms of visualization? Please include the curvature comb or at least curvature plot to distinguish between C^2/G^2 continuity and C^3/G^3 continuity. You may refer to these references for curvature comb:

a) Farin, G. (2016). Curvature combs and curvature plots. Computer-Aided Design, 80, 6-8.

b) S.A.A.A. Said Mad Zain, M.Y. Misro, K.T. Miura, Curve fitting using generalized fractional Bézier curve, Computer-Aided Des. Appl. 20 (2023) 350–363.

6. In Section 2.6, it is preferable to include figures of C^2/G^2 continuity of gB-curves for comparison between C^2/G^2 and C^3/G^3 continuity.

7. In Section 3.2, 3.3 and 3.4 it is better to write the conditions and equations of G^2 continuity of surface in a proper theorem. It is quite weird because for Section 2.6 there is proper theorem for curve continuity. You can refer to reference in point (2).

8. Please recheck Eqn (3.9) and (3.10).

9. Please change title section 3.5 since it is confusing with section 3.3. Rewrite as the procedure and examples of constructing G2 surfaces using theorems.

10. Rewrite the conclusion by considering the motivation and advantages of the proposed method. Please also include the limitations of the proposed method.

If the author can address the comments, then I will recommend this manuscript for publication.

Reviewer #2: This paper is about the explanation of a novel Bezier-like curve definition. Apart from a few grammar errors, the text is well-written. However, it must be checked (again) by a native English-speaker. They used Bernstein-like functions as the basis of their construction. I didn't check all the equations and calculations of this paper. It looks like doable anyways. Therefore, I am more concerned with the idea and the novelty of the method this study proposes. I find them original and see it as positive contributions to the field.

Reviewer #3: This article extends the previous work of Amber et al. (2022a, 2022b) by introducing Generalised Bezier-like C^3 and G^3 curve and surface design.

Overall acceptable, but there are many typos exist in the present version. Below are comments to improve the paper.

1. Abstract: there is no evident in the article to support the proposed method is better than the standard Bézier curves and surfaces. This is the major issue in this article, show clearly how the proposed curve/surface better than traditional Bézier model.

2. pg.2: Before writing the short form, make sure to write the full form, e.g "H-BS", "GHT-BS" etc.

3. pg.2: the contribution of this paper is the continuity extension, the rest of the points are either redundant or has been established in Amber et al. (2022a, 2022b)

4. eq.(2.1) should;d be written as M =(u,v); this notation is inline with the rest of equations.

5. pg.3: U(Φ) should be written as M(Φ).

6. what is gB-like? state the full form first.

7. pg.4: define C_f stated in eq.(2.8)

8. eq.(2.10) typo: "0<=w,w1<=1", not "0<=w,w1<=r"

9. replace "talk" with "discuss".

10. Theorem 1: state for "parametric continuity C^3", the rest has been established in Amber et al. (2022a, 2022b).

11. C^f or C_f? be consistent.

12. Theorem 2: state for "parametric continuity G^3", the rest has been established in Amber et al. (2022a, 2022b).

13. what is φ?

14. Typo: the Fig.1, not Fig.2

15. State all the details to produce Figure 1. This applies for the rest of figures too, hence increasing reproducibility.

16. equatios stated after eq.(3.10) has typo: replace d(z) with d(w).

17. typo in eq.(3.12), m1?

18. typo in equation citing: Substituting (3.12) and (3.13) into (3.25)?

19. pg.13: typo Fig.3(a)....Fig.3(b)

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Attachments

Attachment

Submitted filename: Comment for PONE-D-23-44182.pdf

Generalized Bézier-like model and its applications to curve and surface modeling

PONE-D-23-44182R1

Dear Dr. Asnake Birhanu,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. If you have any questions relating to publication charges, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Sameer Sheshrao Gajghate, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #3: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #3: Partly

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #3: N/A

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The manuscript was improved according to the reviewer's comments and suggestions. Hence, I recommend the manuscript to be accepted for publication.

Reviewer #3: (No Response)

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #3: No

**********