Is there a non-trivial, exact analytic (symbolic) conformal map from some polygon to some rectangle?

I’m looking for any example of a conformal map m: P -> Q where P is some polygon of at least 4 sides, Q is a rectangle, and and m is not linear (so P and Q are not merely scaled, rotated, & translated copies of each other). FWIW, Q must in general depend on P, which is why I’m not specifying Q further here.

  1. I don’t care how many sides P has for this example — I want it in order to validate some more general work. (Especially helpful if the number of sides is “small”, say < 7 or even 10. Even better if it has 4 sides (not all right angles), but that’s not necessary.)
  2. I understand that m won’t be unique. I’m just looking for ANY such m.
  3. Crucially, I need m to be exact, symbolic, constructed, and fully “worked out”. By that, I mean no limits, no implicit functions (or ones with only an existence proof but no construction), no indefinite unevaluated integrals, etc. I am flexible in what class of functions is used to express m, but think of those in, say, Abramowitz & Stegun, or implemented in the core of MATLAB. E.g., elementary, incomplete beta, Bessel, and elliptic-integral functions are all fine.

The reason I phrase #3 that way is that I want to be able to inspect m, look at its derivatives, etc., which will be opaque if the function is not explicitly written in terms of such functions. What makes the conditions of #3 useful for that is that those functions (a) satisfy various analytic and algebraic relations, with published theorems behind them, and (b) have already been implemented in code according to established standards of accuracy and numerical stability (something which might not automatically be true of their inverses, BTW).

views – Geofield Map – Filter attachment result by clicking marker

So You have 2 views on the Page
1 view is the Map
and another view is the “attachment”

You need to look in to how to use Contextual filters look at the Url Arguments in A view (see | and

A Very Quick Way to get this done is, in your Map View
add 2 new fields Content id and a Global: Custom text field
then in your new custom field view add

 <a href="{{ nid }}" class="use-ajax btn">Quick View</a>

where /map is the path to your map page,

Then open your Map FORMAT Settings and scroll until you see

in Marker Infowindow Content from select your new field

Then save the map view.

Open Your “attachment” view and add a CONTEXTUAL FILTERS

selecting “ID” in the Content Category.

config like

tick Provide default value

Type = Query parameter

Query parameter = show

this will give you

enter image description here

this is not 100% exactly what you want but then you can start to add a custom js file to target the marker click event and auto trigger the window link – good luck !

javascript – In WordPress, how to embed a google map to a form, let the user draw on the map, and submit the custom area as an image or a PDF?

There are some plugins available that do similar things, like this one:

How to Draw in google maps

…but no plugin has this functionality as far as I can tell.

We need to send the image with the user-selected area as part of the form.

Maybe we could convert the map with the area to a screenshot on submit event, then in JS base-64 encode it and then wrap it in a div and assign the base-64 encoding as a jpg bg image of that div, and have all of that stringified and injected into a hidden input field and submitted with the rest of the form.

Ideally, the admin should receive an email with the area in PDF or as an image, with the rest of the form’s data (the usual stuff – contact info).

Any ideas? Hopefully, a plugin 🙂 Here’s google maps relevant documentation I could find:

monogame – How can I get correct coordinates from a diamond isometric map created in Tiled?

I am rendering a diamond isometric map created in Tiled using Monogame.Extended.Tiled package.

Here is where I’m trying to spawn a player with an object at coordinates 224,224 on my map


Here is where it actually spawns within the game world.
Actual game

I have some debug info at the top of the screenshot. 0, 0 in the gameworld is where the first tile is in the middle of the screen.

I understand how to get the correct coordinates when it is a staggered map. I know for a diamond it involves something with the halving the screen size and height but I’m personally stuck and have tried searching for this answer somewhere.

I just want to be able to convert the coordinates Tiled puts out, into the world space. If it comes to it, I will just use my own map renderer and go back to staggered but I would prefer not to.

As usual, any help is appreciated and will provide any extra information.

usa – Choosing between 2 google map routes

Google Maps takes into account traffic when the data is available. Of course when planning a trip ahead of time, conditions may not be as anticipated. You can set a day and time in the near-future but those are less reliable. If you want to know the best route, check the day you are leaving but for such a long trip, it means that you may not be able to know where exactly will be a good point to stop.

As you can see from your screenshot, Google shows you the distance and estimated time. This makes it easy to calculate the average speed which is more useful than the maximum speed since that is not always possible due to traffic. Even if you manage to go over the limit at times, it won’t make as much difference compared to how much sleep to you take, how long you stop for meals, etc.

For the quickest travel time, follow Google Maps Live which requires a data connection. This allows Google to change the route while your trip is already in progress since traffic conditions will certainly change during that 29+ hour trip. Accidents and road closures allow the drive to adapt dynamically and so the final path may be none of the above.

If you want to plan ahead, reserve a night of hotel in the middle, choose restaurants to stop too, pick one route and plan to follow it with only minor detours. There is some overlap with the two shorter routes and time does not vary that much that it won’t be much loss if it turns out the other one had better traffic the day of your trip.

polygons – Question about error executing RegionResize of map

I want to resize the map of the country as below.

region = EntityValue[Entity["Country", "SouthKorea"], "Polygon"] /. g_GeoPosition :> g["LongitudeLatitude"]
newregion = RegionResize[region, 10]

However, newregion often stops with no results.
Also, all previously executed information will be erased.

mf = RegionMember[newregion]; mf[{125, 35}]

I want to discriminate the inside and outside of the data with a resized map.
Could the error be caused by the map being disconnected? How can I solve this?

geography – Plot a Map of German Bundesländer with specified colors assigned to them

I would like to draw a map of the German states (“Bundesländer”) with Mathematica 12.

I found examples how to outline countries. But I need the next smaller levels.

I have not found anything how to highlight the administrative divisions of a country of the first level (in DE: Länder, in France Region), of the second level (in DE: Regierungspräsidium, in FR: Département) etc. at all on a map.

How do you find out for which keywords there are geographical data in the Wolfram database?

How do you get a map with these entities outlined and how do you assign colors to them?

migration – Map profile_id based on previously mapped uid when migrating user profiles from CSV file

I’m trying to migrate users and user profiles to site, where both entities might be already present. In this case I would like to overwrite specified fields and leave others in the original state. I’m trying to map profile_id like this:

    plugin: migration_lookup
    no_stub: true
    # previous user migration
    migration: mayors_users
    # property in the source data
    source: lau
    plugin: entity_lookup
    entity_type: profile
    value_key: uid
    source: '@uid' 

However, this fails with error:

Destination field type integer is not a recognized reference type.

Do you happen to know, how can I use entity_lookup plugin for this?

A linear map $T:Vrightarrow W$ maps zero vector to zero vector i,e. $T(0)=0$. Is the converse also true??

A linear map $T:Vrightarrow W$ maps ${0}$ to ${0}$ i,e. $T(0)=0$. Is the converse also TRUE? Can we say that if a map $T$ maps ${0}$ to ${0}$ then its a linear map?

Providing a C interface to a ‘Region’ map

I decided using a C++ map or unordered_map is the most appropriate option to store ‘Regions’ where which can be loaded in arbitrary patterns

The rest of the project is written in C, so I made a C interface:

#include <unordered_map>
#include "Region.hpp"
static std::unordered_map<uint64_t, void *> Regions;
extern "C" {
void *GetRegion(const uint16_t X, const uint16_t Z, const unsigned char Y) {
    const uint64_t Key = X|((uint64_t)Z<<16)|((uint64_t)Y<<32);
    return Regions.count(Key) ? : NULL;
void *CreateRegion(const uint16_t X, const uint16_t Z, const unsigned char Y) {
    const uint64_t Key = X|((uint64_t)Z<<16)|((uint64_t)Y<<32);
    if (Regions.count(Key)) {
    void *const Region = GenerateARegion(X, Z, Y);
    Regions.insert({Key, Region});
    return Region;
bool DeleteRegion(const uint16_t X, const uint16_t Z, const unsigned char Y) {
    return Regions.erase(X|((uint64_t)Z<<16)|((uint64_t)Y<<32)) != 0;

I am wondering if there is an elegant way to eliminate the repeated X|((uint64_t)Z<<16)|((uint64_t)Y<<32)