Timeline for Project map to a particular shape
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 15, 2018 at 17:42 | comment | added | Tyler Durden | @barrycarter I don't think. If the perimeter as treated as dimensionless and has no visible features, then there is no visible discontinuity. | |
| Jul 15, 2018 at 17:11 | comment | added | user1722 | @TylerDurden Wouldn't that mean there's a "break" point at some distance from the perimeter where you switch from one algorithm to the other? It seems like things would get ugly there. | |
| Jul 15, 2018 at 16:59 | comment | added | Tyler Durden | @barrycarter Well, the points of the perimeter do not have to be constructed with the same rule as the points on the interior. In the algorithm I used the perimeter is constructed differently than the interior. That may be a flawed method, but was my original thinking. | |
| Jul 15, 2018 at 16:46 | comment | added | user1722 | @TylerDurden If I understand correctly, the map should have two properties: 1) a fixed scale (no distance distortion), and 2) all points 5 miles from a coastline (for example) would map to a circle. In this case, I'd think the center of your map would be the point in the USA most distant from any coastline, not the geographical center? | |
| Jul 15, 2018 at 14:43 | comment | added | Tyler Durden | @HenrikSchumacher For my purposes, I care most that the distance to the nearest point on the coastline are close to their geodesic distance. The angle to a distant point is not important. | |
| Jul 15, 2018 at 14:40 | comment | added | Henrik Schumacher | @Tyler Any such mapping would introduce distortion of distances. Conformal maps have the nice property that they still preserve angles. | |
| Jul 15, 2018 at 14:35 | comment | added | Tyler Durden | The Stephenson suffers from the same problem mentioned in my comment to the original question in that it distorts the map in areas of complex perimeters. The "great lakes problem". Eg in the example shown you can see how the gray dot is distorted. In a map projection this point should be relatively close to the coastline, because it is close to the coastline in the geodesic data. You may want to read the question more closely and think about how maps are designed to answer better.. | |
| Jul 15, 2018 at 14:15 | comment | added | Joseph O'Rourke | @TylerDurden: I only know it has been implemented (perhaps not in Mathematica). I added a link. | |
| Jul 15, 2018 at 14:14 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
added 299 characters in body
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| Jul 15, 2018 at 14:06 | comment | added | Tyler Durden | How is this implemented in Mathematica? | |
| Jul 15, 2018 at 13:09 | history | edited | Joseph O'Rourke | CC BY-SA 4.0 |
added 177 characters in body
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| Jul 15, 2018 at 13:01 | history | answered | Joseph O'Rourke | CC BY-SA 4.0 |