Proposal: Support for Trapezoidal Map Projections in PROJ

[gwahak]

PROJ supports a wide variety of map projections, yet provides almost no direct support for simple trapezoidal world map projections based on equidistant or equal-area principles. This is somewhat surprising considering that PROJ already supports projections such as Eckert I projection, Eckert II projection, Collignon projection, Albers equal-area projection, HEALPix projection, and Tissot's equidistant conic projection, many of which already exhibit trapezoidal geometric structures or related frame characteristics.

Currently, PROJ already supports several related projection families, including trapezoidal projections in which the pole collapses to a single point (effectively forming a triangular map), conic projections that can be interpreted as trapezoidal frames wrapped into a circular-sector shape, and world map projections in which the polar width is reduced to exactly half of the equatorial width.

[kbevers]

For this issue to be actionable, please provide more information on which projection(s) your think are missing and guidance on how to implement them. In the current state this issue is too vague to act on. Reference relevant papers describing the desired projection(s).

[gwahak]

Thank you for the clarification request.

In many practical cases, trapezoidal projections use an isosceles trapezoidal frame. Parallels are represented as straight horizontal lines, while meridians are represented as oblique straight lines connecting corresponding points between parallels.

Such projections may be defined in at least two different ways:

By directly specifying the trapezoidal geometry itself, or

By specifying one or more standard parallels with correct scale properties, similarly to how projections such as the Albers equal-area conic projection are parameterized.

In particular, an equal-area trapezoidal projection can be constructed from the Albers equal-area conic projection by replacing:

the radial height component with a vertical Cartesian height coordinate, and

the circular arc length of each parallel with a horizontal straight-line parallel of identical length.

Ideally, multiple parameterization methods could eventually be supported. However, for an initial implementation, I would suggest starting with the standard-parallel-based approach, since it is conceptually closer to existing PROJ projection families such as Albers equal-area conic and equidistant conic projections.

[kbevers]

I'm afraid this is still way to hand-wavy to be of any practical use. Please provide proper reference papers for the specific projection(s) you are interested in.