[Proj] Oscar van Vlijmen reply

[Michael Ossipoff]

Oscar van Vlijmen quoted me:

Repeating the first paragraph from Michael's announcement: > This list¹s 
main topic is solutions for co-ordinate transformations. But > this posting 
isn¹t off-topic, because it¹s about co-ordinate transformations > too: I 
claim that, for data maps in atlases, the transformation from the > map¹s X 
& Y co-ordinates to the latitude/longitude co-ordinates should be > easy and 
convenient for everyone, and I suggest a solution that I haven¹t > read 
mentioned anywhere.

…and then  replied:

I can only comment: After 3 weeks of discussion I still haven't seen any 
solution.

I comment:

The solution (to the need for more usable data maps) that I was referring to 
there, the one that I haven’t seen mentioned anywhere, is the graduated 
equidistant cylindrical, which has the linearly interpolable positions 
property.

Other obvious solutions, also sharing the linearly interpolable positions 
property, are the ordinary equidistant cylindrical, and the sinusoidal. I’ve 
  mentioned all three of those solutions  on this list. I mentioned the 
first two in my first posting.
.
Though the equidistant conic and graduated equidistant conic don’t have the 
LIPP, they allow for easier lat/long determination than the projections 
usually used for data maps. I mentioned those in my postings too, including 
my first posting.

I emphasize that all of those were mentioned in my first posting (except for 
the sinusoidal, which I suggested after Daan advocated the need for 
equal-area for data maps.

Oscar continues:

Where are the equations or code for forward and inverse?

I comment:

I want to assure Oscar that the cylindrical equidistant, the graduated 
equidistant cylindrical, and the sinusoidal are not mathematically difficult 
to construct. He can find equations for the their construction and inverse 
construction of the equidistant cylindrical and the sinusoidal in books that 
cover such things.

The graduated equidistant cylindrical won’t be difficult either, since it 
merely consists of the equidistant cylindrical, with different north-south 
scale in different latitude bands.

I encourage Oscar to let me know if he has trouble constructing the 
equidistant cylindrical, the graduated equidistant cylindrical, and the 
sinusoidal.

I want to emphasize that very easy determination of X and Y map co-ordinates 
from lat/long co-ordinates, and very easy determination of lat/long 
co-ordinates from map X and Y co-ordinates are the whole point of the 
projections that I’ve been suggesting for data maps.

Maybe Oscar is asking specifically about the graduated equidistant 
cylindrical, since the ordinary equidistant cylindrical and the sinusoidal 
are already well-described, an their equations of construction and inverse 
construction are surely easy for anyone to find.

Let me repeat my clear definition of the graduated equidistant cylindrical 
projection:

It is the equidistant cylindrical, but with different north-south scale in 
different latitude bands. Each two consecutive parallels shown on the map 
bound such a latitude band. In that latitude band, the north-south scale is 
the geometric mean of the east-west scales along the two depicted parallels 
that bound that latitude band.

Obviously something different must be done, on a world map, for the 
northernmost and southernmost latitude bands, because obviously, like 
Mercator, this projection can‘t show the poles.. As one way of dealing with 
this, I suggest letting latitude 85 be the extreme poleward limit of a world 
map on this projection,  and the poleward bounding latitude of the most 
poleward latitude bands. So the most extreme latitude bands would be from 
latitude 80 to latitude 85. Obviously other ways of dealing with polar 
regions could be suggested too.

Of course it won’t always be desired to show the Earth all the way from 85 
south to 85 north.

[end of definition of the graduated equidistant cylindrical projection]

Oscar, let me know if you have trouble writing equations for the 
construction and inverse construction of that projection, and I’ll help you 
out.


Oscar continues:

If no one can come up with a practical solution, then for that reason the 
discussion thread in this list should probably end.

I comment:

1. I have proposed practical solutions to the problem of finding projections 
for more usable data maps.

2. Yes, the thread should probably end, since everything to be said on the 
subject has been said--unless someone has a constructive suggestion.

Michael Ossipoff