General Method for Extending Discrete Global Grid Systems to Three Dimensions
Round 1
Reviewer 1 Report
In this paper, the author proposes a general method that can extend any Discrete Global Grid Systems (DGGS) to the third dimension to operate as a 3D DGGS. They define encoding, decoding, and indexing operations in a way that splits responsibility between the surface DGGS and the 3D component, and allows for easy transference of data between the 2D and 3D versions of a DGGS. The algorithm is based on the well known algorithm. A very few algorithms are available to solve graph theoretical problem. But i think there exists no algorithm for fuzzy environment. For this reasons, this paper has a significant contribution. The result presented in this paper seems to be correct. Also the concept is also very interesting. Please carefully revise your paper according to my following suggestions.
1. Please clearly describe the contributions of this paper in the Abstract, the Introduction Section and the Conclusions Section of this paper.
2.'Abstract' should be refined. There are some grammar mistakes and redundant expression which may lead to misunderstandings.
3.Introduction' and 'Preliminaries' should be shortened. Some of the contents should be merged.
4.There are some typos. The authors must remove them.
5.Section 2 and Section 3 should be merged
6.The author should add the future work in the conclusion section.
7.There are some grammatical errors in this manuscript. The author must remove those.
8.The author must add some latest references . This reference are inconsistent. The author can add following reference
Author Response
Please see attachement for our response.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this manuscript the authors propose a method for constructing 3D grids for geo-spatial data, by transporting 3D grids from polyhedrons.
The manuscript clearly deserves publication in IJGI, but some improvements must be done:
- The introduction describing related work is very well elaborated, however, since the subject of the manuscript is 3D uniform refinable grids and volume preserving maps from polyhedrons to the ball, the authors should mention some papers in this topic (the constructions of volume preserving maps from polyhedrons to the 3D ball therein), for example
A. Holhos, D. Rosca, Uniform and refinable 3D grids of regular convex polyhedrons and balls, Acta Math. Hung., 2018, 156, 182-193.
Such papers are not published in "Geo-Journals", I suppose this is the reason the authors do not know them.- Figure 1, say in caption that the terms regular and semiregular will be explained two pages later.
- Figure 1 and lines 229-231. Explain more clear the meaning of R_min and R_max. They are distances from a fixed point O, or? The initial polyhedron is considered as inscribed in a sphere centered at O or is arbitrary polyhedron?
- Figure 3 and line 242. What is the meaning of regular? The red lines on the surface join midpoints of the triangle? If yes, take them midpoints in the figure, too, or at least write it. If not, explain why you used the term "regular". Also, if the vertices of the blue triangle are midpoints, as you write, then redraw the picture by drawing them as midpoints (no matter the view angle, a midpoints remains midpoint). I think the reader is confusing about this, until page 9, when you give more explanations about this.
- line 255, explain more clear what is "the maximum/minimum radius of a layer" and how r_min and r_max are taken. I am not sure I understood the meaning.
- line 348-349, then we have ... what? If there is no = in the formula, then vr_max/(x+1) are what?
- The terms "volume preserving maps" should be clarified. In [44] they introduce some different measures of volume preservation, which are not mentioned here. As I know, the standard definition of a volume preservation map f is vol(D)=vol(f(D)), therefore any other reconsideration of this definition must be mentioned (also precised in the abstract). A standard radial projection p:polyhedron ->sphere, p(A)=B (B = intersection of line passing through O and A with the sphere) does not preserves the volume, in the sense mentioned above.
- Formula after line 416 gives the expression for the map m as a linear function of r. I would like to see the expression of the corresponding map from the polyhedron to the 3D ball and a proof about its volume preservation (in the sense considered by the authors).
Author Response
Please see attachement for our response.
Author Response File: Author Response.pdf
Reviewer 3 Report
Very interesting and relevant paper, written by Benjamin Ulmer, John Hall and Faramarz Samavati. Faramarz Samavati is a well-known name in the research field of DGSS. Ulmer wrote (as first author) to the knowledge of this reviewer, one other paper on DGSS: Ulmer, B., Samavati, F. Toward volume preserving spheroid degenerated-octree grid. Geoinformatica (2020). https://doi.org/10.1007/s10707-019-00391-w This reviewer accessed the authors version of this paper through: http://pages.cpsc.ucalgary.ca/~samavati/pdf/paper-ben.pdf
This IIGI paper under review is quite related to the paper published in Geoinformatica. This is fair (as be part of PhD research), but it might be better to state in the introduction and/or related work to which extent the scope of this paper under review differs, has new findings, etc., in relation which the other, already published, paper in Geoformatica. It seems odd this other paper of the author is referenced only as [44] out of 48 references; should be expected to be in the top 10. Also, the kind of self-referencing seems somewhat detached from its own work: …”Furthermore, there are extensions of the method that improve the volume preservation of the grid without significantly sacrificing the efficiency of indexing [44].”, and “Using a similar methodology used in [44], we know that ….”
Line 127-129:
With the large amounts of 3D geospatial data being generated, such as 3D point clouds from LIDAR [32] and aircraft flight paths [33,34], there is emerging an increasing need for 3D global grids and grid systems [12].
> Ref [32] “Sirdeshmukh, N.; Verbree, E.; Oosterom, P.V.; Psomadaki, S.; Kodde, M. Utilizing a discrete global grid system for handling point clouds with varying locations, times, and levels of detail. Cartographica: The International Journal for Geographic Information and Geovisualization 2019, 54, 4–15.” is only be used to indicate the need for 3D global grid and grid systems for large amounts of 3D geospatial data, such as 3D point clouds. However, this ref [32] includes a section “3D DGGS” which states: “The 2D cells can be extended into 3D either on the base polyhedron or directly on the sphere/ellipsoid. This is ideal because DGGSs, although usually constructed using a polyhedron, can also be built on the sphere/ellipsoid directly. If a polyhedron is used as a base to construct the 3D cells, then a 3D hypercube is constructed on each face of the polyhedron and an 3-D Space Filling Curve (SFC) is created that traverses all of the cells of every hypercube.” This approach in [32], both constructing a 3D DGGS, as well the indexing, is not only developed for a specific application (see lines 168-169], but it is used as an indexing method. The same holds true for 4D-DGGS, using a 4D-SFC, to index time alongside X,Y, and Z. It would be fair to compare the methode in this paper under review into more detail with the method described in ref [32].
Ref [32] is only accessible behind a pay-wall. It could be the case the author has no access to it ….. Then, please check the authors copy at: http://www.gdmc.nl/publications/2019/DGGS_Cartographica.pdf
Line 387 Section 5.1. Radial Mapping / Line 464 6. Indexing Operations
“This property [area-preserving] is important for applications where the area of cells is frequently used, as this can be expensive to compute. Therefore, for a 3D DGGS, it may also be desired for each cell to have equal volume, or as close to equal as possible.”
Would be nice to link indexing directly to encoding and decoding, so there will be a direct relation between the index and the geometry, like be demonstrated in ref [32].
Author Response
Please see attachement for our response.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The manuscript can be published in this form.
