New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation

Round 1

Reviewer 1 Report

Author Response

We have made the changes suggested by the reviewers in the language and we have clarified the concepts used.

Reviewer 2 Report

Please see the attached file.

Comments for author File: Comments.pdf

Author Response

Reviewer 3 Report

See the attachment.

Comments for author File: Comments.pdf

Author Response

Page 1 – Please do not use citations in the abstract. (At least without full description and even then it is not
advisable.) Your readers will read the abstract first and do not want to jump to references and back while
reading.
Response 1: We have made the changes suggested
Point 2: - Please extend the conclusions to outline in more detail the main results.
Response 2: We have made the changes suggested
Point 3: -Table 1. Typo: parallelogram
Response 3: We have made the changes in the text to introduce a measure for parallelograms
Point 4: -Figure 2. (b) some Spanish has slipped in.
Response 4: We have made the changes suggested
Point 5: -Page 6: First sentence is a bit odd. Perhaps a full stop after the reference
Response 6: We made the changes suggested.

Author Response File: Author Response.pdf

Reviewer 4 Report

- Page 1 – the title of the authors' affiliation must be translated to English language.

- Page 1 – The remark "These authors …" should be deleted.

-Page 1 – Abstract section – it is not usual to put the citation ("see [7]") in abstract.

- References are not denoted as per the order of appearance. Authors cannot start citing references with reference #7, the first should be #1, then others, in order. The order now is nonexistent. Please, rearrange the list of references accordingly.

- Page 2 – line 38 - the word "distorsioned" does not exist in English language. The proper term is "distorted".

- Page 2 – line 42 – "we will review …. we will propose…". The future tense cannot be used to describe the research that has been done. Please, reformulate.

- Page 2 – line 50 – Authors have to refer to the figure with its number, not the phrase "figure below".

- Page 3 – lines 93-94 – "…to decide whether that a quadrilateral is close to having the desired shape is distorted". This sentence is senseless, like some word is missing. Please, rephrase to make sense.

- Page 3 – lines 94-95 – "However, we have not noticed how it is that square or rectangle." Please, clear this context according to suggestion in the corrected manuscript. Indeterminate articles are missing.

Page 3 – line 96 – What is "Minrect 2015"? Authors cannot use the notions, phrases or terms that are very specific for the topic considered and obviously very familiar for them, without explaining/defining those for the readers. There might be some reader who is not familiar with this terminology.

- Page 4 – lines 119-120 – This is obviously unfinished sentence: "It is easy to construct an example for which the Robinson aspect ratio 1 but very distorted". Please, finish it to make sense.

- Page 5 line 124 – What does "Rectangles 2015" refer to? This is another example of undefined phrase.

- Page 5 line 146 – What does "Harmonic mean 2017" refer to? This is another example of undefined phrase.

- Page 5 – the statement of theorem 2 seems as unfinished sentence, since it starts with "if": "If m(T) is a good quality measure for triangles according to Field-Oddy in which for isosceles triangle the highest energy among all right triangles is achieved, so the harmonic mean (5), characterize squares at their maximum value."

- The phrase "Field-Oddy" also appears several times without explanation or reference [?].

- ALL the expressions and equations MUST be numbered, otherwise the reader would not be able to follow the line of calculations.

- Page 7 – the second line after line 182 – "For this reason some people are using the geometric mean …".

Authors cannot use the phrase "some people" for other researchers, whose work they obviously studied. It is derogatory. Plus, the auxiliary verb (are) is missing in this sentence.

Page 7 – line 189 – "y" is obviously Spanish for "and", but it should not be here. It also appears in several other places.

Page 7 – line 190 – the number 5) element of this list is not phrased properly. In this way it does not make sense. Please, rephrase this, to be the "natural" continuation of the main sentence before the listing (1 to 5).

- Page 8 – lines 193-194 – the abbreviated forms of verbs, like "let's" are not allowed in a scientific article, since that is considered as the casual expressing.

- Page – line 200 – What is "e-convex quadrilateral"? Another unexplained phrase.

- Page 9 – line 206 – "We have in consequence the follow definition …" This sentence makes no sense. Please, rephrase it. Maybe it should be "the following definition"?

- Pages 12 and 13 – figures 8 and 9 are neither mentioned – announced in the text prior to them, nor are they discussed afterwards.

- Page 13 – lines 254-256 – "Also we have proposed new functionals for grid generation that our computational tests, give us bases for using as alternative for area-orthogonal grid generation." This sentence makes no sense. Please, rephrase this context.

- Page 13 – the "Conclusions" section is not written properly. It should summarize the substance of the article with emphasis on what are its main contributions.

- Pages 13-14 – the list of references is not prepared according to the Journal's template.

The authors did not perform the check spelling of their manuscript, so there are some misprints, which is not allowed. Some letters from the Spanish language remained in the text.

The general remark, related to the content (the very topic) of the article. What are the benefits of these new "quality measures"? What kind of improvement do they introduce and how can that be quantified?

 The authors should consult the English language editor, as well.

 The scanned pages of the manuscript with marked errors and suggested corrections are enclosed.

Comments for author File: Comments.PDF

The authors did not perform the check spelling of their manuscript, so there are some misprints.

The authors should consult the English language editor, as well.

Author Response

Page 1 – the title of the authors' affiliation must be translated to English language.
Response 1: We have made the changes suggested 
Point 2: - Page 1 – The remark "These authors …" should be deleted.
Response 2: We have made the changes suggested
Point 3: - Page 1 – Abstract section – it is not usual to put the citation ("see [7]") in abstract.
Response 3: We have removed the references.
Point 4: - - References are not denoted as per the order of appearance. Authors cannot start citing references with reference #7, the first should be #1, then others, in order. The order now is nonexistent. Please, rearrange the list of references accordingly.
Response 4: It was a latex compile error
Point 5: - - line 38 - the word "distorsioned" does not exist in English language. The proper term is "distorted".
Response 5: We have made the changes suggested
Point 6: - -- Page 2 – line 42 – "we will review …. we will propose…". The future tense cannot be used to describe the research that has been done. Please, reformulate.
Response 6: We have made the changes suggested
Point 7: -- Page 2 – line 50 – Authors have to refer to the figure with its number, not the phrase "figure below".
Response 7: We have made the changes suggested
Point 8: - Page 3 – lines 93-94 – "…to decide whether that a quadrilateral is close to having the desired shape is distorted". This sentence is senseless, like some word is missing. Please, rephrase to make sense.
Response 8: We have reviewed  and made the changes suggested
Point 9: - - Page 3 – lines 94-95 – "However, we have not noticed how it is that square or rectangle." Please, clear this context according to suggestion in the corrected manuscript. Indeterminate articles are missing.
Response 9: We have reviewed  and made the changes suggested
Point 10: - Page 3 – line 96 – What is "Minrect 2015"? Authors cannot use the notions, phrases or terms that are very specific for the topic considered and obviously very familiar for them, without explaining/defining those for the readers. There might be some reader who is not familiar with this terminology.
Response 10: We have reviewed and made the changes suggested
Point 11: - Page 4 – lines 119-120 – This is obviously unfinished sentence: "It is easy to construct an example for which the Robinson aspect ratio 1 but very distorted". Please, finish it to make sense.
Response 11: We add an example to clarify the idea.
Point 12: -What does "Rectangles 2015" refer to? This is another example of undefined phrase.
Response 12: We removed the label that indicates a year to clarify the concept.
Point 13: - Page 5 line 146 – What does "Harmonic mean 2017" refer to? This is another example of undefined phrase.
Response 13: We removed the label that indicates a year to clarify the concept
Point 14: - - Page 5 – the statement of theorem 2 seems as unfinished sentence, since it starts with "if": "If m(T) is a good quality measure for triangles according to Field-Oddy in which for isosceles triangle the highest energy among all right triangles is achieved, so the harmonic mean (5), characterize squares at their maximum value."
Response 14: We have reviewed and made the changes suggested to clarify the concept
Point 15: - - - The phrase "Field-Oddy" also appears several times without explanation or reference [?].
Response 15: We made the changes suggested
Point 16: - - - - ALL the expressions and equations MUST be numbered, otherwise the reader would not be able to follow the line of calculations.
Response 16: We made the changes suggested
Point 17: - -- Page 7 – the second line after line 182 – "For this reason some people are using the geometric mean …".
Authors cannot use the phrase "some people" for other researchers, whose work they obviously studied. It is derogatory. Plus, the auxiliary verb (are) is missing in this sentence.
Response 17: We made the changes suggested

Point 18: - Page 7 – line 189 – "y" is obviously Spanish for "and", but it should not be here. It also appears in several other places.
Response 18: We made the changes suggested

Point 19: - Page 7 – line 190 – the number 5) element of this list is not phrased properly. In this way it does not make sense. Please, rephrase this, to be the "natural" continuation of the main sentence before the listing (1 to 5).
Response 19: We made the changes suggested

Point 20: - - Page 8 – lines 193-194 – the abbreviated forms of verbs, like "let's" are not allowed in a scientific article, since that is considered as the casual expressing.
Response 20: We made the changes suggested

Point 21: - -- Page – line 200 – What is "e-convex quadrilateral"? Another unexplained phrase.
Response 20: We rewrote the sentence to clarify the functional used.

Point 22: - -Page 9 – line 206 – "We have in consequence the follow definition …" This sentence makes no sense. Please, rephrase it. Maybe it should be "the following definition"?
Response 20: We remove the expression and rewrote the sentence.

Point 23: - - Pages 12 and 13 – figures 8 and 9 are neither mentioned – announced in the text prior to them, nor are they discussed afterwards.
Response 20: We rewrote the paragraph indicating how the mesh was obtained

Point 23: - - Page 13 – lines 254-256 – "Also we have proposed new functionals for grid generation that our computational tests, give us bases for using as alternative for area-orthogonal grid generation." This sentence makes no sense. Please, rephrase this context.
Response 23: We rewrote the sentence

Point 24: - - - Page 13 – the "Conclusions" section is not written properly. It should summarize the substance of the article with emphasis on what are its main contributions.
Response 23: We rewrote the sentence

Point 25: - - Pages 13-14 – the list of references is not prepared according to the Journal's template.
Response 23: We made the changes suggested.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors have submitted a greatly improved version. However, while the scientific content is fine, there are still some issues with the overall presentation that should be fixed before publication.

English is OK.

There are still some little issues such as 3.3 Rectangles quality measure -> Quality measure of rectangles

Line 20: Remove Basically (spoken language)

Line 200: the skew -> remove skew

Author Response

Page 1 – There are still some little issues such as 3.3 Rectangles quality measure -> Quality measure of rectangles
Response 1: We have made the changes suggested
Point 2: - Line 20: Remove Basically (spoken language)

Response 2: We have made the changes suggested
Point 3: -Table 1. Typo: parallelogram
Response 3: We have made the changes in the text to introduce a measure for parallelograms Point 4: -Line 200: the skew -> remove skew
Response 4: We have made the changes suggested

Author Response File: Author Response.pdf

Reviewer 4 Report

Majority of my remarks and suggestions for corrections are accepted. However, there are still some points that authors have to resolve:

- Page 1 – line 15 – cited is reference [1], then in line 30 next is cited reference [4].

References must be numbered in order of appearance in the text and the list of  references must be adjust accordingly.

- Page 7 – line 200 – number of the listed item should be 3), not 4).

- Page 12 – The "Conclusions" section is still not properly written. It must be longer and explain the conducted research and relate it to obtained results. Please, follow the "Instructions for authors" of the Journal.

- Pages 12 to 14 – Figures 9 and 10 should be placed before the "Conclusions" and "References" sections.

- Pages 12 to 14 – "References" section, i.e. the list of references is not written according to the requirements of the Journal's template.

The scanned pages of the manuscript with marked errors and suggested corrections are enclosed.

Comments for author File: Comments.pdf

Level of English language is satisfactory.

The scanned pages of the manuscript with marked errors and suggested corrections are enclosed.

Author Response

Page 1 – - Page 1 – line 15 – cited is reference [1], then in line 30 next is cited reference [4]. References must be numbered in order of appearance in the text and the list of references must be adjust accordingly. Response 1: We have made the changes suggested, now we have the references section is in the correct format.

Point 2: - - Page 7 – line 200 – number of the listed item should be 3), not 4).
Response 2: We have made the changes suggested
Point 3: -- Page 12 – The "Conclusions" section is still not properly written. It must be longer and explain the conducted research and relate it to obtained results. Please, follow the "Instructions for authors" of the Journal.
Response 3: We have made the changes suggested, we modified the conclusions section with the scope obtained and future work.
Point 4: -- Pages 12 to 14 – Figures 9 and 10 should be placed before the "Conclusions" and "References" sections.
Response 4: We have made the changes suggested
Point 5: -- - Pages 12 to 14 – "References" section, i.e. the list of references is not written according to the requirements of the Journal's template.
Response 5: We have made the changes suggested

Author Response File: Author Response.pdf