Blended projection: The projections American Polyconic an...

[Piotr]

When I blend American Polyconic and Werner, I get this error:

Blended projection: The two projections are incompatible.

[daan]

You will find many incompatible combinations. The reasons vary: Some are topologically incompatible. Some are just bugs in a difficult algorithm.

— daan

[Piotr]

But how is it possible for projections to be topologically incompatible? How does Geocart 3 blend projections? Also, in case of American Polyconic and Werner, are they topologically incompatible, or just bugs in a difficult algorithm?

[daan]

But how is it possible for projections to be topologically incompatible?

If the result overlaps itself, I consider it to be topologically incompatible.

How does Geocart 3 blend projections?

It is a simple linear weighting.

Also, in case of American Polyconic and Werner, are they topologically incompatible, or just bugs in a difficult algorithm?

My guess is a bug. I would not expect overlaps in this combination as long as you use the same projection center for both.

Cheers.
— daan

[Piotr]

But blending Hammer and Briesemeister results in an overlap.

[Piotr]

Second incompatible pair: Mercator and Stereographic (equatorial, range up to 85.05 vertically and 90 horizontally, which is nearly a hemisphere)

[Piotr]

Bump - In fact, I haven't found a conformal pair to blend that does not result in an error, except for projections that are the same. Not even Mercator and Lambert conformal conic with equator standard parallels with the same boundaries works.

[daan]

The blended projections functionality definitely needs a lot of work.

— daan

[Piotr]

The blended projections functionality definitely needs a lot of work.

— daan

Considering the problems with conformal projections, I agree. I've also tried finite projection pairs, like elliptic conformal and circular hemisphere-symmetrical Lagrange; they didn't work either.

Apparently blending two equal-area projections does not necessarily produce an equal-area projection for averaging or linear weighting. Does averaging two conformal projections, if it didn't return an error, produce a conformal projection?

[daan]

Apparently blending two equal-area projections does not necessarily produce an equal-area projection for averaging or linear weighting. Does averaging two conformal projections, if it didn't return an error, produce a conformal projection?

Yes, it does, although you have to be careful of the projection folding back onto itself if the topology of the two projections differs significantly. You could have that problem with blending something in polar aspect with something in equatorial aspect, for example.

— daan