dnd 5e – How does Hunger of Hadar behave in confined space?

Hunger of Hadar has a curious wording:

A 20-foot-radius sphere of blackness and bitter cold appears, centered on a point with range and lasting for the duration.

Compare this to Fireball:

A bright streak flashes from your pointing finger to a point you choose within range then blossoms with a low roar into an explosion of flame. […] The fire spreads around corners.

And Darkness:

Magical darkness spreads from a point you choose within range to fill a 15-foot radius sphere for the duration. The darkness spreads around corners.

Total cover rule here states:

A target with total cover can’t be targeted directly by an attack or a spell, although some spells can reach such a target by including it in an area of effect.


What would allow or require Hunger of Hadar to appear in a different shape or size?

Most simply this would be mundane walls, though I guess manufacturing a glass container of desired shape wouldn’t be hard, and then there’re spells like Force Cage and Leomund’s Tiny Hut. These would block most spells, but the HoH spell description is very explicit… a 20-foot radius sphere appears, no buts, no ifs. Is there a rule which would override the HoH description?

What interval x must be confined in a given distance?

The question asks me to find the interval x must be confined within a given distance

$$ lim limits_ {x to a} x ^ 2 = 4, epsilon = 0.1 $$

Anyone know how to fix this problem?

algorithms – How to get confined spaces from a series of connected nodes

I have a bunch of connected walls in a list and the data for them are as follows:

Wall
{
   Node A;
   Node B;
}

Node 
{ 
   float x; 
   float y; 
}

I want to find connected wall pieces as an array of connected dots to represent the perimeter of each room.

Here is a visual example of what I'm trying to find:
enter the description of the image here

The red dots are the nodes, and the lines are the walls, the numbers are the identified pieces that the walls have created.

The walls can be in any angle, I do not know if it matters.

I wonder what algorithms exist that can help me solve this problem, what is the best way to approach that?

Pathfinder 1e – What is the best wild form of melee combat for confined spaces?

I play a level 9 Druid and seek advice on combat forms. In general, I use voluminous shapes and focus on vital attacks at the strikes and tail in combat. However, this strategy does not work when I'm in a dungeon with 5-foot corridors.

What are the best alternative forms of wild form for druids per level that correspond to a 5-foot corridor?

I am looking for something focused in melee with a high DPR but that is quite simple and easy to play. I also want something generic rather than situation.

Until now, I have considered using medium-sized animals in the wild, but these do not seem very interesting because of bad statistics. Maybe there are some basic shapes or something else that I missed?

$ frac {n} {n!} = frac {1} {(n-1)!} $? true for $ n confined?

I'm trying to derive that $ frac {d} {dx} sin {x} = cos {x} $and I have a priori that $ e ^ x = sum_ {n = 0} ^ { infty} frac {x ^ n} {n!} $, So $ e ^ {kx} = sum_ {n = 0} ^ { infty} frac {k ^ nx ^ n} {n!} $ (all this in order to differentiate by distributing the derivative on $ frac {e ^ {ix}} {2i} – frac {e ^ {- ix}} {2i} $), in addition, I try to differentiate this $ e ^ {kx} $ and I proceed as follows:

$$
begin {equation}
tag {1} frac {d} {dx} e ^ {kx} = frac {d} {dx} sum_ {n = 0} ^ { infty} frac {k ^ nx ^ n} {n !}
end {equation}
$$

$$
begin {equation}
tag {2} frac {d} {dx} sum_ {n = 0} ^ { infty} frac {k ^ nx ^ n} {n!} = sum_ {n = 0} ^ { infty } frac {d} {dx} frac {k ^ nx ^ n} {n!}
end {equation}
$$

$$
begin {equation}
tag {3} sum_ {n = 0} ^ { infty} frac {d} {dx} frac {k ^ nx ^ n} {n!} = sum_ {n = 0} ^ { infty } frac {nk ^ nx ^ {n-1}} {n!}
end {equation}
$$

Then, recalling that $ n! $ is defined recursively as $ n (n-1) (n-2) (n-3) (…) (1): n geq 0, n in mathbb {Z} ^ + cup {0 } $given $ frac {nk} {n!} = frac {nk} {n (n-1) (n-2) (…) (1)} $, the postman $ n $ splits and we get $ frac {k} {(n-1) (n-2) (…) (1)} = frac {k} {(n-1)!} according to the definition of my factorial.

$$
begin {equation}
tag {4} sum_ {n = 0} ^ { infty} frac {nk ^ nx ^ {n-1}} {n!} = sum_ {n = 0} ^ { infty} frac { k ^ nx ^ {n-1}} {(n-1)!}
end {equation}
$$

But obviously, when $ n = $ 0 so we have the case of $ (- 1)! $ in the denominator, which is not defined by my definition; and according to Wolfram ($ Gamma (0) $) this is $ bar { infty} $.

Where did I go wrong in my derivation?

Local NGINX reverse proxy to confined applications

I installed my server years ago and installed NGINX. Recently, I added Gitlab as a container and added Nextcloud (also as a container). Now, I wanted to check if my configuration is well built and add other applications. In all manuals, for example Django, NGINX is also added to the docker-compose file. Until now, I understand this NGINX as a web server and not as a proxy. However, I can not find any instructions describing my constellation. In short: the NGINX proxy is installed locally, then container with the NGINX web server and APP.

My NGINX proxy also supports certificates. Is the following configuration correct or are there any errors? What would be the default behavior for redirecting a proxy to a container?

site.conf:

server{
server_name cloud.my-site.de;
listening [::]: 443 ssl http2;
listen to 443 ssl http2;

server_token off;

error_log /var/log/nginx/cloud.error_log warn;

location / {
proxy_pass http://127.0.0.1:4321/;
proxy_set_header Host $ host;
proxy_set_header X-Forwarded-For: $ proxy_add_x_forwarded_for;
X-Real-IP proxy_set_header: $ remote_addr;
proxy_set_header X-Forwarded-Proto $ scheme;

# ...
#ssl cert configuration
#
}

It would be very useful to have a reference. What I have not yet understood are the different networks and the way to correctly connect the reverse proxy to the containers.

Can you tell me these sources of information?

pathfinder – Spell fighting in confined spaces, are there sanctions?

I have a Vigilante Brute who also likes to take a Enlarge the person potion now and then (we decided that the gross capacity is do not magic and can stack with magical widening).

I've read and applied the rules on compression, but that does not dissuade him (and that's fine), he likes to be The Hulk.

Now the problem arises when the magician of the spell, a mage, must pass to join the fight and cast a spell. I've set up compression constraints on the fight (-4 to AC, -4 to hit), which also means that the Magus's turn can not end on the same box as the Brute (a pain for the mage, as this would enhance the effectiveness of Spellstrike. / Easier). The question then is: can the mage sneak into a shared space (with a 5-foot step) and use spell combat?