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Enriching map projection diversity: An approach to fusion and distortion approximation

Version 2 2025-02-13, 09:11
Version 1 2025-02-13, 07:30
journal contribution
posted on 2025-02-13, 09:11 authored by Jin YanJin Yan, Jun Zhang, TianSheng Xu, Jing Gao, Guanghong Gong
  • gen_coords.jl: Pre-generates planar coordinate points for a series of projections and stores the results in the coords directory.
  • gen_opt_coords.jl: Uses Particle Swarm Optimization to perform non-proportional scaling on a series of projections, obtaining scaling factors that result in lower distortion projections. Using these scaling factors, planar coordinate points are generated and stored in the coords-opt directory.
  • fusion.jl: Performs pairwise fusion of projections from the coords and coords-opt directories using six different fusion methods and dozens of fusion coefficients.

For 220 projections in both coords and coords-opt, over 2 million new projections can be generated.

Each of the coords and coords-opt directories provides three sample projections.


  • opt-results.txt contains the optimized scaling factors.
    Example:

    Projection Name

    Equal-Area Projection

    Distortion Before Optimization

    Distortion After Optimization

    X Scaling Factor

    Y Scaling Factor

    moll

    true

    0.3856590420303463

    0.3716426296273295

    0.9059392884196235

    1.1038267274449063

  • fusion-arith-output.txt contains the arithmetic fusion results. (Results from the other five fusion methods can also be obtained using fusion.jl).
    Example:

Source Map Projection 1

Source Map Projection 2

Weighting

Number of HEALPix grids with NaN/Inf

Number of HEALPix grids with negative a or b

Ratio of negative a or b (i.e., anomaly rate)

Area distortion, angle distortion, and overall distortion using N_pix

Area distortion, angle distortion, and overall distortion after removing anomalies

moll

eqearth

-0.3

0

168

0.0008544921875

0.04759920095327961, 0.3863484915908265, 0.38926962492069384

0.04761955056832187, 0.3865136633356999, 0.3894360455087738

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