How to match a spherical triangle to a flat triangle?

The gnomonic projector maps spherical triangles into right-angled right-angled triangles.

But I heard that Chamberlin’s trimetric projection has less distortion, so I would like to use this instead. Alas, when I use my (extremely rude and probably buggy) implementation of Chamberlin’s trimetric projection to display a spherical triangle formed by its three base points in the plane, I seem to get a shape that is almost a triangle, but three “lines” and bulges. Is this a mistake in my code, or should it do this?

Is there any other way to map a spherical triangle to a right-angled flat triangle that has less distortion than a glomonic projection?

EDIT: My goal here is to make the usual "multifaceted map" of the Earth. If you print something on the Map Fold-out page , you will have something similar to what I'm trying to do.

I have two triangles. One of them is a spherical triangle drawn on a three-dimensional globe. By definition, each edge of a spherical triangle is part of a large circle. When you look at this 3D globe, there are a bunch of cities, coastlines, etc. that (hopefully) are accurately drawn on this three-dimensional globe inside this spherical triangle.

Another triangle is a flat, two-dimensional (two-dimensional) right-angled Euclidean triangle. On paper. At the moment, the interior of this triangle is an empty white paper, but in the end I want to draw a copy of all these cities, coastlines, etc. In this area.

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http://en.wikipedia.org/wiki/Chamberlin_trimetric_projection

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Source: https://habr.com/ru/post/1755883/


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