What are Hero Points in DnD5e

I’ve just Downloaded an Excel Character Sheet and it has a slot for Hero Points. I have Players Handbook, MM, DMG, SCAG, VGtM, MToF, XGtE and I’m fairly sure it isn’t in any of them.

Is it Homebrew, or from a different realm, is it just a different name for something I know about or am I just being thick?

Do multiple sources of temporary hit points combine, or do you only get one set?

Do multiple sources of temporary hit points combine, or do you only get one set?

For example, say you cast armor of Agathys and false life on yourself. Do you have two separate pools of temporary hit points, or do you have to pick one of the two? By separate pools, I mean that you have 5 temp HP from AoA and 8 temp HP from FL. If you take 10 damage, can you pick one of the two pools of temp HP and take the leftover damage to your real HP, but still have the other pool to protect against a second attack?

I ask because a warlock player in my game insists that she gets both pools, but I think it should be either-or.

How do multiple sources of temp HP interact with one another?

Algorithm for identifying polygons (set of points)

Are there any known algorithms for uniquely identifying some set of points despite scaling, moving and with some amount of threshold?

I have an “ideal” set of points with coordinates and I need to check if other set matches the ideal one. Other set could be rotated, scaled or distorted a bit (points could be placed with slight offset).

All sets have one common property: there are 2 points located farthest apart. This can be used to, at least, negate rotation. We do know angle (45deg) that line between farthest points create with axis, and we do know needed distance between them.

I’ve tried following algorithm:

  1. Rotate “other” set to some point (so that farthest points create line that is 45 degrees to “x” axis);
  2. Scale set so farthest points distance = “ideal” distance;
  3. Use sort of GeoHashing algorithm to get point hash with some accuracy (like threshold).

But that approach gave nothing. “GeoHashing” produces semi random results and probably not suitable for 1000×1000 calculations. And using geometric operations furthermore reduced accuracy (initial distortion of points + inaccuracy of some geometric methods).

Algorithm to find what points are the nearest to other points

I have two lists:

  • Location list, it contains point of interest

  • People list, it contains coordinates of every person. One single person could be in the list multiple times, depending from the log time. Someone who is out for a walk will result in two different locations in two different hours.

I would find out what people where near every point of interest.

I could approach the problem with brute force: external loop check for every point of interest the entire people list finding out who was there.

I would obviously avoid brute force. I thought about Nearest Neighbour, for sure multiple people will be in the same spot so I could look for a point of interest in the cluster.

Solutions?

Intersection algorithim for finding the intersection points of two arbitrary mathematical curves

I’m looking for an intersection algorithm for finding the intersection points of two arbitrary mathematical curves. Websites like Desmos, GeoGebra, and WolframAlpha allow you to graph and/or input two(Or more but I’m only interested in two) curves to find their intersection points. I know all of the services I’ve listed have some form of API, my problems with those APIs are the technical and practical restrictions. Therefore, I’d like to just use the algorithms they use under the hood. Problem comes when I don’t even know the names of those algorithms or even whether they’re public domain. I’ve done some searching around but I can’t seem to find what I’m looking for. So I guess what I’m asking for are some basic design descriptions/requirements for these algorithms so I can implement one of them. I figured this problem wasn’t really a question for the mathematics StackExchange or StackOverflow So I decided to place it here. Let me know if that’s a problem.

Articulation points (or cut vertices), but only subset of vertices need to be connected

I know we can find all articulation points efficiently in a graph using DFS.

But what if not all nodes need to be connected, but instead we have set of node pairs that need to communicate (there is a path between them). How to efficiently find all nodes (vertices) which removal will cause some of mentioned pairs to be disconnected (can’t communicate with each other)?

For example, we can have different cases for image below (undirected graph):

  1. If pairs are A-B and C-D, then 2 is not vertex cut, because pairs remain connected.
  2. If pairs are A-C and B-D, then 2 is vertex cut, because pairs can’t communicate (there is no path between them).

If we know set of pairs that need to communicate, what is the most efficient way to find all “vertices cuts”? enter image description here

Cast Sleep spell and the hit points are exactly tied, which creature falls asleep?

so playing DnD 5e, what happens if I cast the first level Sleep spell, get 27 for my roll, but there are two 15 hit point creatures in the area of effect?

I did not roll high enough to put both creatures to sleep. Only one can fall asleep (27-15=12). How do you determine which of the two creatures falls asleep?

Caster’s choice? Random chance? Higher constitution modifier?

Sleep spell text:

This spell sends creatures into a magical slumber. Roll 5d8; the total is how many hit points of creatures this spell can affect. Creatures within 20 feet of a point you choose within range are affected in ascending order of their current hit points (ignoring unconscious creatures). Starting with the creature that has the lowest current hit points, each creature affected by this spell falls unconscious until the spell ends, the sleeper takes damage, or someone uses an action to shake or slap the sleeper awake. Subtract each creature’s hit points from the total before moving on to the creature with the next lowest hit points. A creature’s hit points must be equal to or less than the remaining total for that creature to be affected. Undead and creatures immune to being charmed aren’t affected by this spell.

Thanks for your time!

How do you use spell points as a Sorlock?

I am currently playing an Elf that is a level 5 Warlock / level 3 Sorcerer. My DM has graciously let me take a few short rests in the morning after my trance and before we start the adventuring day letting me create extra level 2 spell slots (level 3 warlock spell slots get converted to 3 sorcery points, 3 sorcery spell get converted to level 2 spell slots). My group tested the spell point variant rule want to use it. How does converting warlock spell slots to sorcery points to sorcerer spell slots work with the spell point variant rule from the DMG?

Optimization Problem to Maximize Points Given Cost Constraints

I have 2 groups of items: A and B. Each item has an associated cost c i and points p i. I need to choose 3 items from group A, and 2 items from group B such that the sum of points of those 5 items is maximized. There is a constraint where I have limited funds to choose those 5 items. Suppose I have $ 500 to work with, then my constraint is:

$ $ 0 \leq 500 – C_{A1} – C_{A2} – C_{A3} – C_{B1} – C_{B2}$ $

and I want to maximize the sum of their points:

$ $ max = P_{A1} + P_{A2} – P_{A3} – P_{B1} – P_{B2}$ $

For some A1, A2, A3, B1, and B2 provide the maximum # of points. I have the data representing the costs and points for each item.

Thanks in advance.