
Linearized map of Lake Michigan: a matter of perspective - r0muald
https://somethingaboutmaps.wordpress.com/2015/09/28/a-matter-of-perspective/
======
gus_massa
> _Taking the square root of the data de-emphasizes the densest areas, helping
> fix this. Actually, I’ll tell you a secret: I showed the 2.25th root of
> density, not the square root, because I’m way too detail obsessive._

This is an important detail. I used something similar before. Never assume
that the best conversion from data to color is linear. The monitor is not
linear, the eye is not linear, who knows if the printer is linear.

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VLM
Not to be a wet noodle on the cerebral art explanation or ignore the technical
discussion, both of which were interesting, but as an extremely practical
matter a former coworker of mine had a life goal to row a boat around the
perimeter of Lake Superior (a little bigger, and to the north) and this
linearized map is kinda what he saw, which is both cool and would be an
interesting way to document his photos and stories and it might have been a
useful navigational tool for him, if zoomed in to human scale.

And no he didn't live in his boat and do it in one trip, it took him years
(decades?) of his life. He'd do city B to city C on one vacation and city C to
city D on some weekend etc.

Social media photo sharing sites are kind of "done" as a startup idea (or are
they?) but I could see something like this, generalized to work on cars,
planes, and bikes, being kinda popular to scroll and zoom thru someones trip
photos as an unusual kind of map display. Maybe for navigation apps, scroll
along a long line...

~~~
dalke
In case you didn't make it to the end of the page, there's a "bonus" map of
Lake Superior.

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gvb
We have a sailboat on Lake Michigan. That map of Lake Michigan is, for the
most part, how we experience it when we do a "sailing adventure" because we
are going port-to-port along the coast.

~~~
hugs
I've wanted to do this for a long time. Have you posted anything online about
how you planned your trips, or have any favorite planning sites/books?

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ableal
Nice work. A few compass roses tossed on the page at suitable intervals might
help orientation (as in "which way is the sunset here?").

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dj-wonk
A comment on the math: the article portrays it as quite verbose to say the
least, which I think might indicate to some that it is "scary" or really
complicated. I get the hunch that it need not be that way, if approached
differently.

Affine transformations, conceptually, are quite elegant:
[https://en.wikipedia.org/wiki/Affine_transformation](https://en.wikipedia.org/wiki/Affine_transformation).
Figuring out the values to use for a particular transformation is the key
here. This is where the blog post gets really verbose in the math.

The complexity of the solution, as written, seems much higher than the
inherent complexity of the problem. So my intuition suggests the mechanics of
the solution (e.g. the amount of notation required, at least, if not the
amount of computation) can be dramatically simplified if done a different way.
I'd think that playing around with polar coordinates and various frames of
reference would help find an elegant calculation.

~~~
bazzargh
those aren't affine transformations he's using, they're plane projective
transformations (parallel lines aren't preserved). Yes, you can express what
he means more simply, but as an 8x8 matrix problem - then just use a maths
library to solve it. (see eg
[http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/EPSR...](http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node11.html)).

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tfgg
Lovely map.

> I once briefly understood why we were doing what we were doing, but that
> knowledge has since vanished into the ether

Looks like generalized barycentric coordinate over the quadrilateral? Sort of
like UV mapping, though it'd be good to hear from someone that knows more.

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bazzargh
I've often thought about doing something like this for documenting my bike
trips; a 'somewhat straightened' map would work great down the side of the
page with the story. The straight line route maps that used to appear in AA
map books are a bit dull, I wanted something more like
[http://w.faringdon.org/alljpg/hy%20Map%20London%20to%20St%20...](http://w.faringdon.org/alljpg/hy%20Map%20London%20to%20St%20Davidsjpg.JPG)

However I got sidetracked in the notion of how to linearize the map. What I
want, is roughly: start with the route, smooth it so that the original route
still wiggles on the final map (eg
[https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93...](https://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm),
then interpolate with splines)

Simply using straight line distance to the curve won't work, places can be the
same distance from multiple points on the route (unless you divide space up as
in the article).

So what I thought of instead was, treat the smoothed line as a charged wire,
and map POIs as opposite charges. Electric field lines do not intersect, and
if a POI 'charge' is allowed to fall towards the 'wire', the distance it
travels and the place it lands give me coordinates. These calculations are
relatively straightforward (see eg
[http://lampx.tugraz.at/~hadley/physikm/apps/linecharge.php](http://lampx.tugraz.at/~hadley/physikm/apps/linecharge.php)),
and I never need to figure out a closed form for the transformation, which I
guess would be horrendous.

I'm not sure what you'd call this coordinate system; it bears some similarity
with isobaric coordinate systems in meteorology though.

Edited to add: these things are called 'strip maps' in the literature btw,
there's a survey of examples here:
[http://www.geovista.psu.edu/publications/MacEachren/MacEachr...](http://www.geovista.psu.edu/publications/MacEachren/MacEachren_ALinearView_86.pdf)

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JoeAltmaier
Ok, as I understand it, there is no canonical way to unfurl a lakeshore. Sure,
a map of the lakeshore can be drawn differently. But there is no real
parameterization of a shoreline. Its called the 'coastline of England' problem
or some such. I.e. an approximate shoreline might be 200 miles. Draw every
nook and cranny - 300 miles. Draw the accurate line around every grain of sand
that's wet on one side and dry on the other - 20000 miles. What is the 'real
shoreline'?

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curtis
This reminded me of wooden maps carved by the Greenland Inuit, for example the
"Ammassalik wooden maps"
([https://en.wikipedia.org/wiki/Ammassalik_wooden_maps](https://en.wikipedia.org/wiki/Ammassalik_wooden_maps)).

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TrevorJ
The stretch of beaches between Grand Haven and Saugatuck are some of the best
spots to spend a summer (all 5 weeks of it in the Michigan climate).

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eponeponepon
I love this. It's brilliant how enormous the cultural dependecies are in what
we think of as completely uncontroversial geographic facts - like how "Upper"
and "Lower" Egypt are the 'wrong way round' from a modern frame of reference -
i.e. Upper Egypt was the south, because it was where the Nile flowed from.

~~~
dalke
"wrong way round' from a modern frame of reference"?

Isn't the modern use the same as the Egyptian one; that "upper" means
"upstream", no matter the direction of river flow?

For example, in
[https://en.wikipedia.org/wiki/Ob_River](https://en.wikipedia.org/wiki/Ob_River)
you can see "The upper Ob valley, in the south, grows grapes, melons and
watermelons, whereas the lower reaches of the Ob are Arctic tundra."

At
[http://www.protectingourwater.org/watersheds/map/upper_st_jo...](http://www.protectingourwater.org/watersheds/map/upper_st_johns/)
you can see "The Upper St. Johns River Basin extends from the headwaters of
the St. Johns River in Indian River and Okeechobee Counties to the confluence
of the St. Johns and Econlockhatchee Rivers in Seminole County".

At [http://aep.alberta.ca/lands-forests/forest-
management/forest...](http://aep.alberta.ca/lands-forests/forest-
management/forest-management-facts-statistics/documents/FMU-FMA-LUF-Map-
Apr302011.pdf) you can see a map showing that the Upper Athabasca and Upper
Peace are to the south of Lower Athabasca and Lower Peace.

~~~
Jtsummers
Up/Down have come to mean North/South in the way many people speak in English
(US-centric? Not certain how other English speaking countries handle this). I
think that's what GP post was referring to.

That it's actually referring to upriver/downriver in the case of Egypt is lost
on those who aren't more closely familiar with the geography. It makes sense
once explained, but it's non-obvious if you've become accustomed to up and
down being synonymous with North and South.

Side note: There's a discussion about Common Core math and a comment by DanBC
about how students may correctly fill out many math worksheets without
developing any actual understanding just by coincidence (some idiosyncratic
algorithm or method that's technically wrong, but happens to work for the
worksheets). The same thing happens with language. If people only encounter an
idiom in a limited context, they may come to misunderstand what the idiom
actually expresses. In this case that it's not strictly the cardinal
directions, but the direction of the rivers.

~~~
dalke
While I agree that many people use north=up/south=down, I'm not convinced that
it's meaningful to talk about the 'modern frame of reference' in this way.

We have one major river in the US which flows south, the Mississippi. It's
such a big influence on the local views that people in New Orleans may use
"north" to mean "up river" even in a bend where the river flows from
geographic south. The Mississippi is very influential in US history. Northern
slavers used the threat to "sell down the river" to the South.

We also have the Hudson River, which is important for New York. Someone sent
"up the river" was being sent to the Sing Sing Correctional Facility, thirty
miles north of New York City.

So it's not surprising that those set a baseline for a lot of people.

But if you're from Portland, OR, then the river flows (locally) west. If
you're from Jacksonville, FL, the river flows (locally) east, after coming
from the south. If you're from Nebraska, the Platte flows mostly east. In
Boston, the Charles flows mostly northeasterly. (And to double-check, the
Upper Charles River Reservation is indeed 1) upstream, and 2) southwest of the
mouth.)

To say that the modern frame of reference has changed, I would want to see
evidence for change. Where is the "upper" part of a river system used for
something other than upstream?

Otherwise, my belief is that eponeponepon is asserting a personal view that is
not really backed by the evidence.

~~~
Jtsummers
My point was that upper and lower seem to (anecdata) be disconnected from the
context of rivers. Upper and Lower Egypt make sense once reminded of this, but
for many (anecdata) it seems upper and lower mean north and south so their
intuitive sense is that the naming is "wrong" or seems off.

~~~
dalke
Yes, I think I understand your point. Yes, there are many people who use
"upper" and "lower" as rough equivalents to "north" and "south".

Here is but one of many examples - "Up and down can be confusing when one
talks about Egypt. In ancient times the term Upper Egypt actually meant
heading downwards into Africa, while Lower Egypt meant heading upwards on the
map, to the Nile Delta." [http://motherdaughterbookreviews.com/guest-post-the-
magic-of...](http://motherdaughterbookreviews.com/guest-post-the-magic-of-
maps-in-middle-grade-books-by-fiona-ingram/)

My point, however, is that the phrase 'modern frame of reference' is
meaningless. At best it's "personal sense of reference" or "a common mistake."

That is, our 'modern' use now seems to be identical to what it was when the
terms "upper" and "lower" Egypt were coined.

Also, note that that book review is wrong. At least, according to Wikipedia,
'Lower Egypt was known as Ta-Mehu which means "land of papyrus"' and 'Upper
Egypt was known as Ta Shemau which means "the land of reeds"', so it's not
like modern English uses a direct translation of the Ancient Egyptian.

So, when was this earlier time that's supposed to be different from now?

