Calculate surface normal and area for a non-planar quadrilateral

Given the four coordinates of the vertices, what is the best possible approximation to calculate surface area and outward normal for a quad?

I currently join the midpoints of the sides, thus dividing the quad into four triangles and a parallelogram, and find the normal to the plane of the parallelogram, but that doesn’t give me correct results when the original four vertices aren’t coplanar.

Is it possible to use isoparametric transformations for this purpose? (This calculation is a part of a bigger FEM code)

I want to add a slide on my homepage by using Elementort but it shows content area missing

I am using a WP theme in my website . When i am trying to create a slide on my homepage after mune by using elementor plugin , it shows “content area was not found on your page . please call the_content function . But i don’t Where to add this function .

    get_header(); $  show_on_front = get_option( 'show_on_front' ); if ( $  show_on_front == 'posts' ): 	$  banner_count = get_theme_mod( 'newspaper_x_show_banner_after', 6 ); 	$  banner    = get_theme_mod( 'newspaper_x_banner_type', 'image' );  	?> <?php the_content(); ?>     <div class="row">         <div id="primary" class="newspaper-x-content newspaper-x-archive-page col-lg-8 col-md-8 col-sm-12 col-xs-12">             <main id="main" class="site-main margin-top" role="main"> 				<?php 				$  banner_count_index = 0; 				if ( have_posts() ) : 					?>                     <div class="row"> 						<?php 						while ( have_posts() ) : the_post();  							if ( fmod( $  banner_count_index, $  banner_count ) == 0 && $  banner_count_index != 0 ) { ?>                                 <div class="row">                                     <div class="col-xs-12 newspaper-x-image-banner"> 										<?php get_template_part( 'template-parts/banner/banner', $  banner ); ?>                                     </div>                                 </div> 								<?php 							}

i want a slide show after menu

When can I reenter the Schengen area if I received a fiktionsbescheinigung?

I just returned to the U.S. from Germany after my work visa was rejected

I entered the Schengen zone on July 30th, 2018 and began looking for work out there casually. I received a job offer from a start-up and began applying for a work permit. In the meantime, as my Schengen time was nearly up, the ausländerbehörde gave me a fiktionsbescheinigung.

Later, this office rejected my request for a visa. I left the Schengen zone to the states on the 12th of December.

I am wondering how long I have to wait in order to return to the Schengen zone, so that I can begin to look for work out there again. I am looking for a company to support an EU-blue card and in my opinion it is best to look there rather than attempt to find a position from the states.

Spherical Triangles: Area and mapping to Euclidean space

If we take a sphere of radius 1 and travel a quarter-circumference south from the north pole, turn 90 degrees, travel another quarter circumference, then return North, we form a triangle with an angle of 270$ ^\text{o}$ . According to Mathworld, the area of such a triangle would be given by $ $ \Delta=R^{2}[(A+B+C)-\pi]$ $ With A, B and C the angles of the triangle.

Now if we consider lines of latitude and longitude (I understand these always intersect at $ 90^\text{o}$ ), and shift the base of the triangle closer to the north pole but so that it remains on a line of latitude, this would suggest that the base of the triangle still meets the two longitudinal lines at 90$ ^\text{o}$ . This would suggest that the area stays the same, which seems very wrong.

I am also unsure of the maximum sum of angles of a spherical triangle. On the same Mathworld page it states

The sum of the angles of a spherical triangle is between $ \pi$ and $ 3\pi$ radians (180 degrees and 540 degrees; Zwillinger 1995, p. 469)

However, considering a very small triangle (s.t. the sum of interior angles tends to 180$ ^\text{o}$ , and taking this as the outside of the triangle (and the rest of the sphere as the inside) this would create a ‘triangle’ with angles summing 900$ ^\text{o}$ . My guess would be that this might not count as a triangle because it perhaps cannot be mapped appropriately to Euclidaen space. So then, what would be an appropriate mapping to Euclidean space? Would it result in a ‘triangle’ with curved sides?

Staging area

I am pretty new to web design but am starting to build sites for myself and others.
I am looking for some help/support/advice on how to best setup staging sites on my existing domain.
So while I am building these sites I can give the staging address to the person that I am building for so that they can see the progress of the site and suggest changes.


I think the correct way to do this is through Cpanel using subdomains plus all my sites will…

Staging area

Sanya tourist area

I am at a conference at TSIMF, and the featured outing is an excursion to “the tourist area” tomorrow afternoon. I thought this was just informal terminology, but the (sparse) program materials refer to paying an entrance fee, and TSIMF’s Sanya tour page features a picture of the Nanshan Cultural Tourism Zone, which I guess is what is meant.

When I hear “tourist area”, I think of a place that I want to avoid, far from paying to enter, where mainly it’ll be a game of avoiding the people who want to sell me things. I am much more interested in seeing the nature on the island (as in my other question). However, the picture and brief description on the TSIMF page actually looks kind of appealing, even within these constraints. Does anyone have experience on whether it is worth it to pay to enter this area, and how enjoyable it is if you want mainly to see the sights rather than to shop?

Stavropol City, surrounding area – Safety

This is my first time posting here. Thank you in advance to anyone who reads and comments.

I have the possibility of going to Stavropol City, Russia for work. I will be staying in the city then traveling to the city of Nevinnomyssk about 60km South of Stavropol to visit the Client’s factory.

If I go, I will be staying about 3 days and 2 nights. Each night I will stay at a hotel in Stavropol and leave to Nevinnomyssk to have meetings with clients during the day.

I know the surrounding regions can be quite volatile and the US/UK embassies warn against all travel to Stavropol Krai for any reason.

However, when I checked online a bit there seems to be a number of cases of people visiting Stavropol and having wonderful experiences but I am hesitant to rely on anecdotal accounts.

Does anyone have solid information on this area? Namely Stavropol City and Nevinnomyssk.

Again thank you for reading and any information is highly appreciated.

Criar polígono e calcular a área em python

Preciso de ajuda para ler um arquivo .mif que tem coordenadas que formam um polígono e calcular a aulas deles em python

Segue a lista de coordenada que tem no arquivo mif.

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How to Fix (when needed) Scanner “Large Area Spatial Crosstalk”

What is it?

“Large Areas Spatial Crosstalk” is the terminology used by the IEC standard for scanners, 61966-8. It refers to the affect of nearby colors shifting the scanned colors towards the neighboring colors.

What problems does it cause?

The effect can produce large differences in the colors of scanned photos which makes it sometimes impossible to scan a photo and get a colorimetrically accurate image file. These aren’t often noticed in complex photos but some are quite susceptible. A scanned picture of a hot air balloon against a bright sky will tend to lighten the brighter sky more than the balloon.

Accurate reproduction is highly desired for, inter alia, precision duplication and retaining historical images.

Here’s a scanned image from a moderately high end, V850 Epson Scanner. It’s large, shifted L* values are labeled underneath each circle. The three, circular, patches on the left were printed the same as the three on the right. The lighter ones were RGB(240,240,240) while the darker ones were RGB(118,118,118). The circles surrounded by white have scanned L*s about 6 higher than the same ones on the right. This shift is from “Large Area Spatial Crosstalk.”

Scan with Large Area Spatial Crosstalk

This problem is caused by light reflecting off nearby parts of a document, getting scattered around and bouncing off the translucent, illuminating white rails on either side of a horizontal aperture through which the CCD scan is captured. It’s as if the Lux levels on the right side white surround area were boosted over 20%, the increase in light needed to increase L* from 85.7 to 92.7.

Question: Are their any reflection desktop scanners that have addressed this issue in their design and/or is there any software that corrects or is looking to correct this defect?

How to manage the Notification under the upper “Notification” area inside our sharepoint online classic team site

I am not sure how we can manage the notifications which are shown under the Notification area:-

enter image description here

For example we have our “Site Pages” library linked to managed metadata column (named “Category”). so when users add new modern pages they can link them with the managed metadata column, as follow:-

enter image description here

we got a request from our customer, asking that when a News modern page is created and this modern News page is linked to a specific term inside the “Category” property, to show this action inside the Notifications section. so can anyone advice on this please? is there a way to define when notifications should be shown for users?

Of course i am not talking about users’ alerts, i am referring to the Notification section as shown in the above picture. Thanks