I really like the "one island" approach of the Fuller and AuthaGraph projections, seen below. My goal is to plot points (e.g. cities), shapes (e.g. modern and historical countries) and data (e.g. color gradients) on such a map. I'm interested in events on land, so ocean distortions and discontinuities are not a concern. Mapping topographical detail would be nice but very low priority.
My reading so far suggests that these projections are rarely, if ever, included in plotting libraries and tools. And it seems these projections, or even vaguely similar ones like Waterman, are restricted by copyright.
I would like a suggested "plan of attack" in terms of the tools I need to learn or build in order to achieve this goal. For example, do I need to start by inventing my own polyhedral map projection? Given a projection can I adapt existing plotting tools, or is this family of projections too weird? Given a plotting tool can I expect to consume publicly available data, or will I need a transformation step?
I am aware this is a very high-level question. I am not looking for detailed instructions. Instead I'm asking for an expert-guided "syllabus" to acquire the skills and tools needed to reach the end goal. Illustrative examples of programming libraries and tools are fine, if I run into compatibility or other technical issues I will find alternatives.
Example of plotting historical data (Source: Wikipedia)
Being able to recreate this map from raw data would be ideal. I believe this is the Airocean projection from the Dymaxion/Fuller/Airocean family.
Example of AuthaGraph projection (Source: Wikipedia)
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