layout – Setting a default value to the Region field in the checkout

I’ve been using Magento_Checkoutlayoutcheckout_index_index.xml to set predefined values in some of the fields like this:

<item name="company" xsi:type="array">
    <item name="config" xsi:type="array">
        <item name="default" xsi:type="string">Some value here</item>
    </item>
</item>

And it works fine for company for example. But when I try to do the same with region it doesn’t work.
I understand there’s some behind the scenes stuff going on with it depending on the country you choose.

Is there some way to set a default/predefined value for the region field in the checkout?

performance tuning – Speed up Region Intersection in 9D

I have nearly 2000, 9-d regions represented in terms of ImplicitRegion[]. I need to find the intersection between them. Although RegionIntersection[] works fine, it is very slow. I show below the first 4 Simplex, which gives me the ImplicitRegion later.

M[1]=Simplex[{{0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,1}}] ;
M[2]=Simplex[{{0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,1}}] ;
M[3]=Simplex[{{0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,1,0},{-1,0,0,0,-1,0,0,-1,-1}}] ;
M[4]=Simplex[{{0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,1,0},{0,0,0,1,1,1,1,1,1}}] ;

I obtain the regions using the following code, making use of RegionMember[].

RR={x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[9]} ;
 Do[B[i] = 
   Refine[RegionMember[M[i], RR], 
     RR [Element] Reals] /. {GreaterEqual -> Greater, 
     LessEqual -> Less}; 
  R[i] = ImplicitRegion[B[i], Evaluate[RR]], {i, 1,4}];

Now the problem is when I consider RegionIntersection.

In[134]:= RegionIntersection[R[1],R[2],R[3],R[4]]//Quiet//AbsoluteTiming

Out[134]= {0.405168,EmptyRegion[9]}

I searched a bit and tried to use M[i] directly inside RegionIntersection[] but it didn’t work. Any idea how to speed up the RegionIntersection[] part. As I have nearly 2000 such regions and similar code leads to 3 hours.

safety – In Germany, Is/are there any city or a special region in a city which is/are dangerous for non-white people to go to?

I have been living as a white, non-obvious foreigner in Germany for more than 25 years. Nationalism used to be frowned upon until recently, at least the subject was rarely discussed openly, but there are strong, dormant xenophobic tendencies in large parts of the German society, even if noone speaks about it. In the last few years, the nationalist and racist political party AfD has experienced a huge increase in support and is in several municipalities in the eastern parts of Germany the largest political party by number of votes. Expressing racist and xenophobic hatred has definitively become more wide-spread and socially accepted just during the last few years.

I am personally not at all easily scared, but there are for sure areas which I would have avoided, if I had looked obviously ‘different’, at least some districts in Berlin and many rural areas in the eastern parts of Germany. There are also a few ‘nazi villages’ in eastern Germany, of which Jamel in Mecklenburg probably is the most famous.

There is of course a large step from having an opinion and to act out violence against foreigners. It is not self-evident that in certain areas of Germany, someone will wait for you behind every rock, looking forward for any chance to beat up a non-white. Racial motivation has been recorded in crime statistics since 1990 and since then, there have been about 200 racially motivated murders. In the recent years, there have been some 1000 to 2000 yearly cases of racially motivated violence across the country. With millions of foreigners living in Germany and many more millions visiting Germany every year, the chances that anything will happen to you are as you can see in general very small. There are however areas with much more violence than in other areas and you might want to avoid them.

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How do I fill a region in Roblox?

I try this:

workspace.Terrain:FillRegion(Region3.new(Vector3.new(2048, -256, 2048), Vector3.new(-2048, -512, -2048)):ExpandToGrid(4), 4, Enum.Material.Basalt)

I get the error Region cannot be empty. What gives? Of course the region is empty, I am trying to change that. Is :FillRegion() broken?

differential equations – Discrepancy in Rectangular Region Specification for NDSolve

I am working through the Finite Element Method tutorial and having difficulty with the region specification. The first example is straightforward:

ufun = NDSolveValue[{-Laplacian[u[x, y], {x, y}] == 10, u[x, 0] == 0, 
    u[x, 1] == 1}, u, {x, 0, 1}, {y, 0, 1}];
Plot3D[ufun[x, y], {x, 0, 1}, {y, 0, 1}, ColorFunction -> "TemperatureMap"]

ndsolve_sol_1

Note that the region is specified by {x,0,1},{y,0,1}. It then states that an arbitrary region, reg, can be specified with Element[vars,reg], for example Element[{x,y},reg], such that RegionQ[reg] returns True. It suggests the tutorial Element Mesh Generation for more details.

So I define a rectangular region with the same dimensions as the region above, and check that it is a valid region:

reg = Rectangle[{0,1},{0,1}];
RegionQ[reg]

Which does indeed return True. But when I substitute this into the code above, errors are generated:

ufun = NDSolveValue[{-Laplacian[u[x, y], {x, y}] == 10, u[x, 0] == 0, 
    u[x, 1] == 1}, u, Element[{x, y}, reg]];

enter image description here
enter image description here
enter image description here

Have I made an error, or is there nuance here I’m missing?

integral equations – Question with Integrate and Region

Let’s say I’ve got a 2D region r=Region(Polygon({{0,0},{1,0},{1,1}})). I can do integrals like Integrate(1,{x,y}(Element)r), or Integrate(y,{x,y}(Element)r), to calculate areas and area moments.

I’d like to do an integral like Integrate(c^2,{x}(Element)r), where c is the height (ymax-ymin) of the region at a particular value of x.

Any ideas appreciated.

-David

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