Convex hull on set of squares

Imagine a set of two to six squares within 3D-space. The goal is to generate a convex hull around these squares as efficiently as possible.

The following constraints are known:

  • Each of the two to six squares consists out of 4 vertices (a vertex being a 3D-vector).
  • Each vertex will be part of the convex hull (none of them will be on the "inside").
  • During the creation of the convex hull vertices may not be connected to other vertices from within the same square (otherwise the squares would "degenerate").

Is there an especially fast/efficient way to create a convex hull for this very specific geometry?

Fit in squares in a dedicated space

A random number between 2 and 100, What I want to do is; create a number of squares(doesn’t have to be, any shape is ok) that will fit accordingly inside the dedicated space for them(let’s say half of the screen, etc).

if the number is 2, create 2 squares that are 1/2 space size big. if the number is 10, create 10 squares 1/10 space size big. maximum squares per rows and columns are 10… Example: enter image description here

How can I achieve something like this, any tutorial or idea?

When using a reach weapon, which squares around me can I attack?

Considering a medium creature, with 5ft of reach, wielding a reach weapon such as a longspear.

By the rules:

With a typical reach weapon, you can strike opponents 10 feet away, but you can’t strike adjacent foes (those within 5 feet).

Squares within 5 feet would be all adjacent squares to the creature, including diagonal ones (first diagonal being counted at 5ft).

It appears clear that the weapon will allow attacks into four squares: those 5ft away from the creature in the north, east, south and west directions. They are 2 squares away in a straight line, thus 10ft away, within reach.

But now, what about the squares diagonally away, beyond 5ft, north-east, south-east, south-west and north-west of the creature? According to the rules, the second square of a diagonal line is considered 15ft away when it comes to movement. Does this also apply to attack distances?

Also, what about squares reachable by going diagonally once, then straight up/down/left/right? This would usually count at 10ft of movement, so are they attackable?

Here’s a diagram:

??x?? ?...? x.C.x ?...? ??x?? 

C is the creature, dots are where I assume you cannot attack, Xs are where I assume you can attack and question marks are where I’m not sure you can.

EDIT:

The Case of the Missing AOO

I’ve come across an interesting point on the Paizo forums. If you are in one of the far corners and you consider these not threatened, then you can diagonally move towards the character and never provoke an AOO (that is, per RAW)… and yet, logically, a threatened area should make an uninterrupted circle around the creature. This may explain why 3.5 made an exception out of this.

When using a battlemap, can a lightning bolt be directed between squares to affect both?

Lightning bolt is listed as having a width of 5 feet.

When using a battlemap, can the line of the spell be directed between squares to affect creatures on both sides with full damage?

Does Lightning Bolt affect everyone in its line of effect? suggests this would be true for Pathfinder rules. Its answer suggests that even if the lightning bolt passed a tiny corner of a square – the creature would take full damage. Does this hold true in 5e?

Does a reach weapon allow you to threaten squares 10 feet away or not?

In D&D 5e, does a reach weapon allow you to threaten squares up to 10 feet away for the purpose of Opportunity Attacks or does it just allow you to attack squares up to 10 feet away?

There is some confusion because PHB p.147 says that a reach weapon adds 5 feet to your reach when you attack with it, which can be interpreted to mean that, if an enemy is 10 feet away on his turn, he isn’t actually in your reach (since you aren’t attacking with the weapon yet) so you don’t get an Opportunity Attack. Is this interpretation correct and you only threaten 5′ away, or does a reach weapon always increase your reach for the purpose of threatening distance?

How does increasing in size affect adjacent squares and enemies?

Inspired by this question and effectively asking the opposite question. Assuming play is on a grid, what squares can a creature occupy when it goes from being medium size (1×1) to large size (2×2)? Does the square it already occupied when it was medium need to be included in its new form? What are the options for the three additional squares, can they simply be any that would make the creature 2×2? How does increasing in size interact with the “Moving Around Other Creatures” rule which states:

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

So if there were a creature in one direction would you not be able to include its current space in your new form/size? What if you were surrounded by creatures, could you increase in size at all?

Some hopefully helpful diagrams: You are C, monsters are X, empty spaces are #.

Can

###   #C#   ###    

change into:

CC#   CC#   ###   

or

#CC   #CC   ###   

What can

XXX   #C#   ###   

change into?

What can happen from this last scenario:

XXX   XCX   XXX 

Note: I am looking for an answer that is rooted in RAW, but if no answer exists there an answer from experience with this issue would also work.

Examples of why this might matter:. If you end up occupying the same space as an enemy then a spell like fireball would no longer be able to target you.
If you push the creatures out of the way this could do things such as pushing then into a moonbeam spell.
If you are not allowed to occupy the same space as the monsters then I am confused what would happen if you were initially surrounded.

What squares can you occupy when your size increases, and do other nearby creatures impact this?

Can Create Bonfire be placed in a way that affects multiple squares?

The Create Bonfire cantrip creates a bonfire which “fills a 5 foot cube”. It deals comparable damage to other cantrips, making one assume it’s meant to only deal it (reliably) to a single target. But, if playing on a grid, is there something actually preventing a character from making the 5 foot cube be placed at an intersection, possibly damaging four creatures?

Font Awesome Icons only squares

I have a problem with the icons of font awesome. They are showing, though not all. Some icons just show a square and I don’t know how to fix it.

So this is how it looks like:

enter image description here

If I go to the console and remove the tick on “font” and “font-family” it will appear again correctly. I can’t understand why

enter image description here

So how can I delete these properties?