Minimum-error world map projections defined by polydimensional meshes

Kunimune, Justin

doi:10.1080/23729333.2020.1824174

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Over the last two thousand years, several map projections have been proposed. Map construction methods involve geometry projections, mathematical constructions [6][7][8][9], transformation and combinations [10][11][12][13][14][15], and approximation and optimization [16][17][18][19]. Modern computer software and libraries are also available for cartography and coordinate transformations, e.g., NASA's G.Projector and Open Source Geospatial Foundation's PROJ library [20,21].…”

Section: Introductionmentioning

confidence: 99%

“…As spheres and ellipsoids are not developable surfaces, distortions in map projections are inevitable [22,23]. The measurement and analyses of distortions [24,25] for different types of map projections are critical and still a challenging task for the design [16], categorization, evaluation, comparison, selection [26,27], and optimization [19] of map projections.…”

Section: Introductionmentioning

confidence: 99%

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Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs–Based Distortion Metric of Map Projections

Yan

et al. 2021

IJGI

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We studied the numerical approximation problem of distortion in map projections. Most widely used differential methods calculate area distortion and maximum angular distortion using partial derivatives of forward equations of map projections. However, in certain map projections, partial derivatives are difficult to calculate because of the complicated forms of forward equations, e.g., equations with iterations, integrations, or multi-way branches. As an alternative, the spherical great circle arcs–based metric employs the inverse equations of map projections to transform sample points from the projection plane to the spherical surface, and then calculates a differential-independent distortion metric for the map projections. We introduce a novel forward interpolated version of the previous spherical great circle arcs–based metric, solely dependent on the forward equations of map projections. In our proposed numerical solution, a rational function–based regression is also devised and applied to our metric to obtain an approximate metric of angular distortion. The statistical and graphical results indicate that the errors of the proposed metric are fairly low, and a good numerical estimation with high correlation to the differential-based metric can be achieved.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs–Based Distortion Metric of Map Projections

Yan

et al. 2021

IJGI

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“…BIOCMAN4 is close to a map of latitude, and BIOCMAN5 is high where there are monsoonal climates. Maps are presented in Danseiji V projection, which has low distortion in terrestrial areas at the cost of high distortion in the oceans(Kunimune, 2020). High resolution versions with full scale bars can be found in FiguresS9-S13).…”

mentioning

confidence: 99%

How many variables does Wordclim have, really? Generative A.I. unravels the intrinsic dimension of bioclimatic variables

Dinnage

2023

Preprint

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The 19 standard bioclimatic variables available from the Worldclim dataset are some of the most used data in ecology and organismal biology. It is well know that many of the variables are correlated with each other, suggesting there is less than 19 independent dimensions of information in them. But how much information is there? Here I explore the 19 Worldclim bioclimatic variables from the perspective of the manifold hypothesis: that many high dimensional datasets are actually confined to a lower dimensional manifold embedded in an ambient space. Using a state of the art generative probabilistic model (variational autoencoder) to model the data on a non-linear manifold reveals that only 5 uncorrelated dimensions are adequate to capture the full range of variation in the bioclimatic variables. I show that these 5 variables have meaningful structure and are sufficient to produce species distribution models (SDMs) nearly as good and in some ways better than SDMs using the original 19 bioclimatic variables. I have made the 5 synthetic variables available as a raster dataset at 2.5 minute resolution in an R package that also includes functions to convert back and forth between the 5 variables and the original 19 (https://github.com/rdinnager/biocman).

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Image-based approximation of derivatives of traditional differential metrics of angular distortion in map projections

Yan

Gao

et al. 2022

Cartography and Geographic Information Science

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Minimum-error world map projections defined by polydimensional meshes

Cited by 4 publications

References 14 publications

Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs–Based Distortion Metric of Map Projections

Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs–Based Distortion Metric of Map Projections

How many variables does Wordclim have, really? Generative A.I. unravels the intrinsic dimension of bioclimatic variables

Image-based approximation of derivatives of traditional differential metrics of angular distortion in map projections

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