correct projection (PROJ.4 string) to rotate map

Question

I want to project a map as being rotated by x degrees (as opposed to the standard "north is up" orientation).

So far I'm able to get some arbitrary rotation using these projections:

Two Point Equidistant as used in this Gist

+proj=tpeqd +lat_1=35 +lat_2=35 +lon_1=-80 +lon_2=-122  +x_0=0 +y_0=0 +ellps=WGS84 +units=m +no_defs

Azimuthal as described here: Rotating ~90° using Two-Point Equidistant projection with Proj4

+proj=aeqd +ellps=sphere +lat_0=90 +lon_0=-90

However, I'm having trouble actually converting a value in degrees (like 45°) to a corresponding PROJ.4 string for a specific map. Can anyone point me in the right direction?

EDIT: I'm using Mapnik to render the maps.

Answer 1

Note: I have not tried this.

You could try to use oblique Mercator. Here's an example of a PROJ string for a statewide Michigan projected coordinate reference system:

PROJ.4 : '+proj=omerc +lat_0=45.30916666666666 +lonc=-86 +alpha=337.25556 +k=0.9996 +x_0=2546731.496 +y_0=-4354009.816 +no_uoff +gamma=337.25556 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs'

Check out the alpha and gamma parameters: +alpha=337.25556 +gamma=337.25556

alpha rotates the cylinder used by oblique Mercator, AKA it happens early in the algorithm. gamma is applied near the end of the algorithm to re-orient the data. If you use the same values in alpha and gamma, grid north will be close to geodetic/true north in the center of the projection. So you can adjust alpha and gamma to rotate the coordinate reference system.

+no-uoff also influences it, but I've never figured out exactly how.