How many power points do I gain from Psionic Talent?

Psionic Talent, in Dreamscarred Press’s Psionics Unleashed, is a feat that grants bonus power points.

Benefit: When you take this feat for the first time, you gain 2 power points.

That’s all well and good, but the trouble is that it can be taken multiple times.

Special: You can take this feat multiple times. Each time you take the feat after the first time, the number of power points you gain increases by 1.

The benefit’s “When you take this feat for the first time” doesn’t play with “Each time you take the feat after the first time” in any defined fashion. I can see people reading it for five different progressions, as follows:

2 -> 2+3 -> 2+3+4 -> 2+3+4+5 (+14 pp: The effects of the feat stack, and each feat gives one more power point than the last.)
2 -> 3+3 -> 4+4+4 -> 5+5+5+5 (+20 pp: The effects of the feat stack, and each feat gains the increase to the number of power points it grants.)
2 -> 2+1 -> 2+1+1 -> 2+1+1+1 (+5 pp: The effects of the feats stack, but each subsequent feat gives only +1 PP.)
2 -> 2, 3 -> 2, 3, 4 -> 2, 3, 4, 5 (+5 PP: The effects of the feat don’t stack, but each feat grants one more set power point than the last.)
2 -> 2, 1 -> 2, 1, 1 -> 2, 1, 1, 1 (+2 PP: The effects of the feat don’t stack, but each subsequent feat gives only +1 PP.)

From what I’ve seen, the most popular reading is the +14 reading, but it’s only been as well-argued as the +5 readings in my opinion. My question, then, is how many extra power points do you have after taking Psionic Talent four times?

Mantle of inspiration movement with temporary hit points

The ability mantle of inspiration is worded this way:

Mantle of Inspiration When you join the College of Glamour at 3rd level, you gain the ability to weave a song of fey magic that imbues your allies with vigor and speed.

As a bonus action, you can expend one use of your Bardic Inspiration to grant yourself a wondrous appearance. When you do so, choose a number of creatures you can see and who can see you within 60 feet of you, up to a number equal to your Charisma modifier (minimum of one). Each of them gains 5 temporary hit points. When a creature gains these temporary hit points, it can immediately use its reaction to move up to its speed, without provoking opportunity attacks.

The number of temporary hit points increases when you reach certain levels in this class, increasing to 8 at 5th level, 11 at 10th level, and 14 at 15th level.

If you already have temporary hit points when you would gain these new temporary hit points (and you had more before, thus not gaining any from this ability, because temporary hit points don’t stack), would you still be able to use your reaction to move up to your speed?

My understanding would be that no, you couldn’t because if you could, the ability should have been written like this:

When a creature would gain these temporary hit points, it can use its reaction to move up to its speed, without provoking opportunity attacks.

Anyways, let me know if you can or not, in fact, use your reaction if you don’t actually gain these temporary hit points (maybe they are gained but overwrtitten by the higher source right from the get-go and its possible to use your reaction?)

If you cast Darkness using sorcery points (Shadow Sorcerer) do you need material components?

Shadow Sorcerers at 3rd level gain the spell Darkness which doesn’t count against spells known. In addition, you can cast this spell by expending 2 sorcery points. I wanted to know if you could circumvent the material cost by using sorcery points. I’m assuming you do need the components as sorcery points seem to function like auxiliary spell slots.

Generate triangular surface mesh of convex hull spanned by 8 points in 3D-Space

I am looking for a numerically efficient algorithm to get a triangular surface mesh of the convex hull given by 8 points in three-dimensional space.

For context, the use case is the following:

I have a numerical Simulation calculating the time evolution of a field with three components on a lattice. Say we have lattice coordinates $ (i,j,k)$ , then every lattice point $ (i,j,k)$ has a field vector $ (\phi_1, \phi_2 , \phi_3)$ attached.

For relevant physics, I need to now take unit cells on my lattice, so the 8 corners of a little cube of my lattice. I take the field vectors $ (\phi_1, \phi_2 , \phi_3)$ of every corner of my unit cell and then interpret their convex hull as a closed volume in $ \phi$ -space, with $ \phi$ -space being the 3D space given by the $ (\phi_1,\phi_2,\phi_3)$ coordinates.

I am now interested if the volume spanned by these 8 points in $ \phi$ -space does the following things:

  1. If it contains the origin, $ (0 ,0 ,0 )$

  2. If a Ray traveling from the origin in $ (-1,0,0)$ -direction pierces my given volume

The idea to evaluate both 1.) and 2.) at the same time is to decompose the surface of the convex hull into triangles. For a triangle in 3-Dimensional space, it is easy to evaluate whether it is pierced by my given Ray in $ (-1,0,0)$ direction. I can then count how many triangles are pierced. If exactly two triangles are pierced (because of convexity), I know the cell satisfies condition 2.). If exactly one triangle is pierced, I know the origin has to lie inside my volume, that is condition 1.) is satisfied. Lastly, when no triangles are pierced, none of the above apply.

I think this approach is probably relatively fast. Speed is critical, because I have approximately $ 10^6 … 10^9$ cells to evaluate per sweep across my lattice.

I’d be interested in any other approaches as well, though.

Update: So, I think possibly a 3D-Gift-Wrapping algorithm would atleast produce the required result, because it creates the convex hull by consecutively finding triangles on the surface? I will have to try that out tomorrow.

Can I do better than that in terms of efficiency?

K Closest Points to Origin C# solution deemed too slow by Leetcode.com

LeetCode challenge

I know I could simply use the built in .Sort or .Order by to solve this question in 1 line. However, for interviews I would need to show the whole workings of my solution.

I am using a min-heap to calculate and store the distances from the origin. Then I simply return the K number of distances.

My code fails due to the “Time limit exceeded” error, indicating my code is too slow. However, it does return the correct answer.

Is there a more efficient way of using a min-heap? Or should my code be using a completely different algorithm and data structure?

public class Solution {     public int[][] KClosest(int[][] points, int K)     {         var lists = new int[K][];          Heap head = new Heap();          for (int i = 0; i < points.Length; i++)         {             int a = points[i][0];             int b = points[i][1];             var testMin = a * a + b * b;             var newNode = new Node             {                 val = testMin,                 index = points[i]             };             head.Add(newNode);         }          for (int i = 0; i < K; i++)         {             lists[i] = head.Pop().index;         }          return lists;     } }  class Heap {     public Node head;     public Node tail;      public void Add(Node newNode)     {         if (head == null)         {             head = newNode;             tail = newNode;         }         else         {             newNode.parent = tail;             tail.next = newNode;             tail = tail.next;         }         HeapifyUp();     }      void HeapifyUp()     {         Node curr = tail;         while (curr.parent != null)         {             if (curr.val < curr.parent.val)             {                 var tVal = curr.val;                 var tIndex = curr.index;                  curr.val = curr.parent.val;                 curr.index = curr.parent.index;                  curr.parent.val = tVal;                 curr.parent.index = tIndex;             }             curr = curr.parent;         }     }      public Node Pop()     {         var tempHead = new Node         {             index = head.index,             val = head.val         };          // Set head value to tail value         head.index = tail.index;         head.val = tail.val;          // Deference tail         if (tail.parent != null)         {             tail.parent.next = null;             tail = tail.parent;         }         else         {             tail = null;             head = null;         }          HeapifyDown();          return tempHead;     }      void HeapifyDown()     {         Node curr = head;         while (curr != null && curr.next != null)         {             if (curr.val > curr.next.val)             {                 var tVal = curr.val;                 var tIndex = curr.index;                  curr.val = curr.next.val;                 curr.index = curr.next.index;                  curr.next.val = tVal;                 curr.next.index = tIndex;             }             curr = curr.next;         }     } }  class Node {     public int[] index;     public int val;     public Node next;     public Node parent; } 

functionality similar to ACF repeater? User to add points

I have custom post type called “tours” , user adds post called “london tour” as a title . And then i want user to be able to add tour stops, which will be displayed in front end with fontawesome icons , as a stylised list . I don’t want to include full text editor, just some kind of field with ability to add next field.

My only though was to have a simple list in content editor, and to use javascript to stylize ‘li’ items etc.

How many Ki points can a monk spend per turn?

Flurry of Blows, Patient Defense, and Step of the Wind each cost 1 Ki point to use and use a bonus action. Does that mean I can only use 1 per turn, since I can only take 1 bonus action per turn?

At the same time it feels like Ki points are kind of like spell slots, and maybe if I get the ability to spend more Ki I can use more of these abilities in a turn.

Can anyone clarify this for me?

How many skill points should I give my players for winning an encounter?

I am about to start my first game with The Dark Eye system, and I am wondering how many skill points I should give my players for winning an encounter (not necessarily combat).

Specifically, I am asking for experiences other GMs have made with The Dark Eye and for a rough estimate that I should aim for when rewarding my players. The rulebook only states that a “small adventure” should offer about 5-10 and an “adventure that spans over 2-3 evenings” should be about 15-25 points. However, I like to give rewards on a per-encounter and not on a per-adventure basis, so these estimates aren’t really worth much to me.

How many skill points should I give my players for winning an encounter?

How many skill points should I give my players for winning an encounter?

I am about to start my first game with The Dark Eye system, and I am wondering how many skill points I should give my players for winning an encounter (not necessarily combat).

Specifically, I am asking for experiences other GMs have made with The Dark Eye and for a rough estimate that I should aim for when rewarding my players. The rulebook only states that a “small adventure” should offer about 5-10 and an “adventure that spans over 2-3 evenings” should be about 15-25 points. However, I like to give rewards on a per-encounter and not on a per-adventure basis, so these estimates aren’t really worth much to me.

How many skill points should I give my players for winning an encounter?