# [Proj] Oscar van Vlijmen reply

Peter Galbraith GalbraithP at dfo-mpo.gc.ca
Mon Aug 20 09:21:44 EDT 2007

```Michael,  your posts are hard to read.  Consider using this form of

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Oscar van Vlijmen <ovv at hetnet.nl> wrote:

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

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.

> Where are the equations or code for forward and inverse?

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.

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
out.

> If noone can come up with a practical solution, then for that reason the
> discussion thread in this list should probably end.

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
```