GIS tools are great for interpolating small-scale data, but when you want to interpolate data for the entire surface of a planet, it's problematic. The problem arises because the interpolation is done in -/+ 180 longitude and -/+ 90 latitude in terms of planar coordinates, even though the data are adjacent at the extremities. A further problem is that the distance between data points in this case can only be calculated using spherical geometry, which is not usually implemented in interpolation algorithms. In such a case, one has to write code, but I wonder what other people's experience is? Is there a program that handles this problem natively?
Hello Gaspar,
I do not know if there is a common software facing what you ask for.
I have a few question as I am trying to think of this question.
1. Do you intend to interpolate on a full spherical surface?
2. Are all the points in your database contribute in this interpolation procedure or are you going to set a max distance, to set limitations?
3. As the spherical surface has points on the opposite side (it is like a ball), are these points going to contribute to the interpolation procedure, if they are within the max distance?
4. If you set a max distance for the contribution of points in the interpolation procedure, is that distance long enough, that has to be faced as a spherical distance?
These are my question - thoughts for the moment.
Some details like the application would be helpful, and what the original dataset is. Are you attempting the 'interpolation' in a projected coordinate system rather than a geographic projection? The various scientific groups as NASA and ESA have analytical pipelines with associated tool chains suitable for whatever data representation and observations they deal with (Example https://www.nasa.gov/space-science-and-astrobiology-at-ames/division-overview/planetary-systems-branch-overview-stt/mars-climate-modeling-center/. Especially for tractable computation for those data sets. In a more general sense, 3D interpolation is common in ordinary application like LIDAR point cloud processing for closed shells like statues: Software like MeshLab ( https://www.meshlab.net/ )has several hundred built-in methods of interpolation with links to the journal articles explaining them, similarly Cloud Compare ( https://www.danielgm.net/cc/ ). In general, for a specific domain, 'interpolation can or does occur not in a single step, there is some sensor data, that is then transformed into some sort of tractable representation, there maybe one or several steps in an analytical pipeline, and then stored for a visualization step and comparison to previous or subsequent results.
We encountered this problem in an earlier study, when we tried to trace the forces that created the tectonic features from the lineaments and points on geological maps. The method therefore reconstructs a force field in the uppermost thin layer of the lithosphere from a phenomenon (trace line) observed on the surface. The reconstruction was performed in three steps: 1) the lineamens were converted into spatial planes as a function of their geodynamic parameters, and 2) a point cloud of 3D tensors was extrapolated around them on the surface, which was then 3) interpolated together with other lineaments' extrapolated tensors according to the direction components of the 3 tensors. The result was a continuous tensor field showing the relative stresses in the upper thin layer of the lithosphere. Since the mapped tectonic lines can be interpreted at several scale ranges, and most of the cases studied were regional in scale, we quickly ran into the problem of calculating distances using spherical geometry. We developed a code for it then, but since then there may be ready-made solutions. That's why I started this thread (out of curiosity). The theory is best illustrated by this poster, which is more of a medium scale region, but the figures provide a good overview of the workflow: https://www.researchgate.net/publication/301694737_Stress_field_modelling_from_digital_geological_map_data However, a new geological map of Mars was also published at that time, showing both compression and extension lines. As an experiment, we ran the model over the entire planetary surface and had to deal specifically with the adjacency of the extremities of the geographic coordinates (this was also solved by code). https://www.researchgate.net/publication/281405433_Map_of_ancient_tectonic_forces_on_Mars To touch on the questions Georgios Achilleos asked (although I hope that most of them have been answered above): 1) it is not usually global, but rarely is. 2) interpolation looks for data within a range to be interpolated. 3) even if it is global, there are no interpolation operations involving the opposite data points 4) in almost all cases it is necessary to use a spherical distance
NASA climate modelling applications are probably capable of modelling such data, even if the subject is different! Thanks for the idea Michael John Patrick!
Gáspár Albert INRE:"idea', if you found it useful, 'recommend' the answer so that others down the line can discover it.
What follows has a huge caveat, the specifics of your work is way over my head, but my work does have an aspect of dealing efficiently with all sorts of coordinate systems and data representations, so the following are more for possibly sparking trains of thought which someone far more capable than me might find useful - somewhat inspired by the false dichotomy between vector and raster formats in a GIS.
The 'spherical' issue is as old as geography itself, and up until now has been addressed piecemeal mostly by projecting geographic coordinate systems, and the performance limitations of computational infrastructure available. Relatively recently, the notion of DDGs (Discrete Global Grids) is undergoing an explosion of refinement as a 'sphere' ( ... and 'sphere-ish) as a recursive n-dimensional data representation (cursory, rough overview at https://spatialparalysis.xyz/blog/dggs-eli5/ but a quick Google Scholar finds more detailed descriptions: https://scholar.google.com/scholar?lookup=0&q=A+Review+of+the+Research+on+Discrete+Global+Grid+Systems+in+Digital+Earth ). Although on first appearance it would seem complex to calculate through these fields, there are now methods which mitigate this. These are already making their way into weather modeling ( https://www.abccolumbia.com/2019/01/11/ibm-to-deliver-worlds-highest-resolution-weather-model/ ).
From my naive reading of your project, it seemed to be analogous to a sort of 'weather' model, except with 'rock' instead of 'gas'.
The other vauge 'hunch' is how modern GPUs use quaternion representations and maths to short circuit the need for Cartesian calculations and transformations (quaternion interpolation) - and not just the 'spatial' sorts of computation, but for physics engines ( collision detection, etc. like when there are two spinning irregular objects with different rotational axes).
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