Myriahedral bibliography and source provenance

Documentation index · Geometric context · Implementation notes

Foundational publication

Jarke J. van Wijk, “Unfolding the Earth: Myriahedral Projections,” The Cartographic Journal, volume 45, issue 1, pages 32–42, 2008.

This is the primary description of subdividing a sphere into many faces, optimizing cuts through the dual graph, and unfolding the resulting tree into a planar map.

Previous implementation

Hannes Schulz and contributors, temporaer/myriaworld.

The repository describes itself as a rugged implementation of van Wijk’s method. The C++20 code in this repository reimplements its relevant forward geometry cleanly; it does not copy its runtime architecture or retain its external dependency chain.

Important primary files and records:

The pinned revision is the upstream head inspected while implementing this projection. Pinning makes line history and algorithm provenance reproducible.

Configuration evidence and adopted tree

The upstream README publishes this example:

./myriaworld --depth 5 --sigma 0.4 --wlon 3. \
  --output test --alpha 1 --rotate 0 \
  --clat 313 --clon -65 --roll -315 --render png

That command is valuable evidence for the intended depth, preprocessing pipeline, and available controls. It does not generate a tree that aligns with the black-and-white sample’s visible geographic branches. The upstream repository does not preserve a command line alongside each sample asset, and the configuration question remains recorded in upstream issue #2.

For this implementation, the historical preprocessing was reproduced with the exact face overlap data and candidate trees were compared against visible geographic anchors in the requested raster. The adopted compatibility configuration is depth 5, Gaussian sigma 0.7, wlat=0.5, wlon=0.1, clat=-60, clon=-65, full flattening, and a final 335 degree rotation. It is reproducible and visually registered, but it is not represented as the unrecoverable original command that created the PNG.

Geographic source data

Natural Earth provides public-domain map data at several scales. The historical workflow used the 1:10m countries and ocean datasets to estimate land coverage and choose favorable cuts.

Natural Earth and S2 geometry are preprocessing provenance only. Neither is a runtime dependency of a60::carto::myriaproj.

Local base raster

The registration asset is:

assets.static/myriahedral/black-white-downsampled.png

Properties verified during implementation:

Property Value
Dimensions 4480 x 2520 pixels
Canvas ratio 16:9
Color model 8-bit grayscale PNG
SHA-256 1228cae3fdcbdcb867952135e9eeaec7d894c092eb8dae828d0dd61ad8658fd7

The digest is identical to the upstream samples/black-white-downsampled.png at the pinned revision.

The raster supplies visual context and the 16:9 registration canvas. It is not sampled or used as a numeric lookup table by the forward transform. The current implementation deliberately uses van Wijk’s central gnomonic face-local method rather than preserving the historical program’s orthogonal chord-plane approximation, so subpixel coordinate differences from the raster’s generating lineage are expected and documented.

Licensing note

The cartofreako implementation is distributed under the license stated in its source headers and repository. The upstream author stated in myriaworld issue #1 that the code and sample image could be used under BSD terms. At the inspected revision, however, the upstream repository did not contain a standalone LICENSE file. That issue comment is therefore the available upstream record, not a substitute for legal advice or a newly invented license text.

Natural Earth states that its data is in the public domain. Van Wijk’s paper is cited for the projection method; no paper text or figure is incorporated into the implementation.