Variant A would be implemented in Carmenta Engine by giving a ScaleFactor but not any StandardParallel.

Variant B would be implemented in Carmenta Engine by giving a StandardParallel, while letting ScaleFactor remain 1.

Variant C is similar to B, in that it is the StandardParallel that is given, not the ScaleFactor. But in addition, the true origin - the point whose projected coordinates are FalseEasting and FalseNorthing - is in variant C on the intersection of the standard parallel and the central meridian, by definition. (In variants A and B, the true origin is the central pole.) Variant C cannot be implemented directly in Carmenta Engine, but it can be emulated. First, define an auxiliary projection, PolarStereographicB, with the same parameters as variant C requires, except that instead of the intended value FN for FalseNorthing, you use a FalseNorthing of zero. This will in effect give you a PolarStereographic constructed as variant B. Use this in an auxiliary Coordinate Reference System, CrsB (with the intended GeodeticDatum). This is not the Crs you want, but the only difference is a constant offset in the northing values. So, take the true origin of variant C, the intersection of the central longitude and the standard parallel, and project to easting and northing by CrsB. Let N be the northing you get. Now, start over and build a new PolarStereographicC projection with the same parameters as PolarStereographicB, except that the FalseNorthing this time is FN - N, instead of zero. This is the projection you want. (To make things interesting: what we call the true origin for variant C, the EPSG calls the false origin. But our usage of "true origin" is widely accepted.)

Variant A would be implemented in Carmenta Engine by giving a scaleFactor but not any standardParallel.

Variant B would be implemented in Carmenta Engine by giving a standardParallel, while letting scaleFactor remain 1.

Variant C is similar to B, in that it is the standardParallel that is given, not the scaleFactor. But in addition, the true origin - the point whose projected coordinates are falseEasting and falseNorthing - is in variant C on the intersection of the standard parallel and the central meridian, by definition. (In variants A and B, the true origin is the central pole.) Variant C cannot be implemented directly in Carmenta Engine, but it can be emulated. First, define an auxiliary projection, PolarStereographicB, with the same parameters as variant C requires, except that instead of the intended value FN for falseNorthing, you use a falseNorthing of zero. This will in effect give you a PolarStereographic constructed as variant B. Use this in an auxiliary Coordinate Reference System, CrsB (with the intended GeodeticDatum). This is not the Crs you want, but the only difference is a constant offset in the northing values. So, take the true origin of variant C, the intersection of the central longitude and the standard parallel, and project to easting and northing by CrsB. Let N be the northing you get. Now, start over and build a new PolarStereographicC projection with the same parameters as PolarStereographicB, except that the falseNorthing this time is FN - N, instead of zero. This is the projection you want. (To make things interesting: what we call the true origin for variant C, the EPSG calls the false origin. But our usage of "true origin" is widely accepted.)

Variant A would be implemented in Carmenta Engine by giving a scaleFactor but not any standardParallel.

Variant B would be implemented in Carmenta Engine by giving a standardParallel, while letting scaleFactor remain 1.

Variant C is similar to B, in that it is the standardParallel that is given, not the scaleFactor. But in addition, the true origin - the point whose projected coordinates are falseEasting and falseNorthing - is in variant C on the intersection of the standard parallel and the central meridian, by definition. (In variants A and B, the true origin is the central pole.) Variant C cannot be implemented directly in Carmenta Engine, but it can be emulated. First, define an auxiliary projection, PolarStereographicB, with the same parameters as variant C requires, except that instead of the intended value FN for falseNorthing, you use a falseNorthing of zero. This will in effect give you a PolarStereographic constructed as variant B. Use this in an auxiliary Coordinate Reference System, CrsB (with the intended GeodeticDatum). This is not the Crs you want, but the only difference is a constant offset in the northing values. So, take the true origin of variant C, the intersection of the central longitude and the standard parallel, and project to easting and northing by CrsB. Let N be the northing you get. Now, start over and build a new PolarStereographicC projection with the same parameters as PolarStereographicB, except that the falseNorthing this time is FN - N, instead of zero. This is the projection you want. (To make things interesting: what we call the true origin for variant C, the EPSG calls the false origin. But our usage of "true origin" is widely accepted.)

Variant A would be implemented in Carmenta Engine by giving a scaleFactor but not any standardParallel.

Variant B would be implemented in Carmenta Engine by giving a standardParallel, while letting scaleFactor remain 1.

Variant C is similar to B, in that it is the standardParallel that is given, not the scaleFactor. But in addition, the true origin - the point whose projected coordinates are falseEasting and falseNorthing - is in variant C on the intersection of the standard parallel and the central meridian, by definition. (In variants A and B, the true origin is the central pole.) Variant C cannot be implemented directly in Carmenta Engine, but it can be emulated. First, define an auxiliary projection, PolarStereographicB, with the same parameters as variant C requires, except that instead of the intended value FN for falseNorthing, you use a falseNorthing of zero. This will in effect give you a PolarStereographic constructed as variant B. Use this in an auxiliary Coordinate Reference System, CrsB (with the intended GeodeticDatum). This is not the Crs you want, but the only difference is a constant offset in the northing values. So, take the true origin of variant C, the intersection of the central longitude and the standard parallel, and project to easting and northing by CrsB. Let N be the northing you get. Now, start over and build a new PolarStereographicC projection with the same parameters as PolarStereographicB, except that the falseNorthing this time is FN - N, instead of zero. This is the projection you want. (To make things interesting: what we call the true origin for variant C, the EPSG calls the false origin. But our usage of "true origin" is widely accepted.)