Can you escape from Dimensional Shackles as easily as by polymorphing?

The intent of Dimensional Shackles (which block all kinds of teleportation or interplanar travel on their victim) is clearly to prevent spellcasters from escaping.

But what happens if a Dimensional-Shackled spellcaster casts polymorph on himself (and then drops his concentration)? Is he then free from the Shackles and thus able to teleport away? Or are the Shackles somehow linked to him and will still be applied to him, still preventing him from teleporting/planeshifting/etc. until he actually escapes by succeeding on the DC 30 Strength check?

How does the Dimensional Loop’s Fold Space ability interact with areas of effect?

The magic item Dimensional Loop (Acquisitions Incorporated, pg. 220) has an ability called Fold Space which says:

Choose a space you can see within 60 feet of you (no action required). You treat that space as if it were within 5 feet of you until the end of your turn. This allows you to move immediately to that space without provoking opportunity attacks, or to interact with objects or creatures in that space as though they were next to you (including allowing you to make melee attacks into that space).

Suppose Jim Darkmagic is having a dual with another mage, and they are 50 feet apart. The mage uses its action to hold a fireball spell until he sees Jim casting a spell. On Jim’s turn, he uses the Fold Space ability of his Dimensional Loop and chooses the space the mage is occupying. Until the end of Jim’s turn, the mage’s space is treated as if it were within 5 feet of Jim. Next Jim starts casting inflict wounds on the mage. Seeing this, the mage uses his reaction to cast fireball centered directly on Jim.

Is the mage considered to be within the area of effect of his own fireball?

Similarly, does Jim need to be wary of casting his own fireball on the mage until next turn?

Data Structure for high dimensional data with nullable coordinates

Are there alternatives to uniform grid spatial partitioning when considering data structures for data with nullable or missing coordinate values?

For example with uniform grid spatial partitioning it is fairly trivial to extend it to allow nulls: Given a point P in nullable R3, (x?, y? ,z?), like (5, null, 1) we can assign this point a bin (i?, j?, k?) like (2, null, 1). We can then search neighboring bins by slicing the data structure like bins[i-1:i+1 or null, :, k-1:k+1 or null] (assuming that j bin coordinate was null). Basically, in the null dimensions the point becomes a hyper-plane of sorts.

This is more of an academic question. I can probably use the spatial partitioning approach just fine, but wanted to know if someone might be familiar with alternatives.

Do Dimensional Shackles share any of the properties of Manacles?

The Dimensional Shackles state:

You can use an action to place these shackles on an incapacitated creature. The shackles adjust to fit a creature of Small to Large size. In addition to serving as mundane manacles, the shackles prevent a creature bound by them from using any method of extradimensional movement, including teleportation or travel to a different plane of existence. They don’t prevent the creature from passing through an interdimensional portal.

You and any creature you designate when you use the shackles can use an action to remove them. Once every 30 days, the bound creature can make a DC 30 Strength (Athletics) check. On a success, the creature breaks free and destroys the shackles.

Does the bolded text mean that they actually have all the properties of regular Manacles?:

These metal restraints can bind a Small or Medium creature. Escaping the manacles requires a successful DC 20 Dexterity check. Breaking them requires a successful DC 20 Strength check. Each set of manacles comes with one key. Without the key, a creature proficient with thieves’ tools can pick the manacles’ lock with a successful DC 15 Dexterity check. Manacles have 15 hit points.

In particular then:

  • Can Dimensional Shackles be escaped with a DC 20 Dexterity Check?
  • Can you break them with a DC 20 Strength check?
  • Can somebody else break them with a DC 20 Strength check? (The DC 30 check only applies to the bound creature)
  • Do they come with a key?
  • Can they be opened with a DC 15 Dexterity Check using Thieves’ Tools?
  • Do they have 15 hit points?

For example, if they only have 15 hit points, couldn’t you simply headbutt them until they broke, which would take maybe 30 turns with a +1 Strength modifier, quite far from one try per 30 days.

How do dimensional shackles work in an antimagic field

I’m sorry I have a few questions. As such my very first question is to clarify something I’m unsure about: In stack exchange are we allowed to post multiple questions in one thread? I’m new to stack exchange and don’t know if I should separate my questions over multiple threads. Because I don’t know, I will avoiding asking them all at once and limit it to my main question:

Main question: How do dimensional shackles work in an antimagic field? Will they remain on the bound creature? If so, will they still have a DC 30 strength check to break, or will the be broken by a 20 (mundane manacles)?

In addition to serving as mundane Manacles, the shackles prevent a creature bound by them from using any method of extradimensional Movement, including teleportation or Travel to a different plane of existence. They don’t prevent the creature from passing-through an interdimensional portal.

The bolded sentence suggests they work as mundane manacles, but does that mean they work even when they become mundane? I noticed unlike manacles there is no DC for using thieve’s tools, that led me to noticing that the pictures I have seen of the dimensional shackles don’t seem to have a lock (by the picture it could be a lock of some sort in the middle, but it is unclear), or anything holding them together for that matter. Additionally the one who uses the manacles and anyone he designates when he uses them can just take the shackles off. That is the premise for the question I asked, back to the question: Are they held together by magical means and fall off in an antimagic field, or do they become mundane manacles in the field? If they become mundane manacles are they as hard to break as they were outside (DC 30), or do they have the same difficulty to break as mundane manacles (DC 20)?

How big/little of an opening does a boggle need to use its Dimensional Rift ability?

I’m creating a giant wasp hive in the boughs of a tree in the Feywild, and it happens to have a boggle in it.

The upper sections of the hive have smaller, narrow, rigid, doorway-type openings everywhere that the boggle can use for dimension shifts.

My concern is about the bottom two sections of the hive. The doorway-type openings throughout the bottom two sections are ten or twenty feet square on those levels (so, 15’x20′ or 20’x20′ or whatever).

I’m concerned that these openings might be too big for the Boggle’s dimensional rifts. How large/small of an opening does a boggle need to use this ability?

Arranging Colors in a Grid; Two Dimensional TSP?

I am working on an interesting problem, which I believe can be solved algorithmically. I have a 6×8 on which I am attempting to arrange 48 color swatches, such that the transition from each swatch to its neighbor is as smooth as possible.

I can compute perceptual color differences using LAB-space encoding, so it is simple to generate a matrix of color differences. If I were attempting to simply order these colors, it would essentially be the traveling salesman problem; and I could use some heuristic solutions to get a near optimal result.

However, arranging the colors into a grid introduces a new dimension. In the interest of symmetry, we can wrap the edges of the grid so that each swatch has exactly 4 neighbors.

I have a hunch that this problem reduces to the following graph problem: Given a fully connected weighted graph of 48 nodes, find a subset of this graph such that the resulting graph is fully connected, each node has exactly 4 edges, and the sum of edge weights is minimized.

Any ideas on existing algorithms that might be helpful in solving this problem? Approximate solutions and heuristic solutions are acceptable as I imagine this problem is in EXP.

How to calculate the power spectrum and cross spectrum for two dimensional data?

I have two sets of data:

G={{G_1,x_1,y_1},{{G_2,x_2,y_2}},…..,{G_{n},x_n,y_n}}

H={{H_1,x_1,y_1},{{H_2,x_2,y_2}},…..,{H_{n},x_n,y_n}}

where H_{n} and G_{n} are values of G and H in the point (x_{n},y_{n}). I want to calculate the power spectrum and the cross spectrum . Can you help me ? Thanks.

How to calculate the power spectrum and cross spectrum for two dimensional data?

I have two sets of data:

G={{G_1,x_1,y_1},{{G_2,x_2,y_2}},…..,{G_{n},x_n,y_n}}

H={{H_1,x_1,y_1},{{H_2,x_2,y_2}},…..,{H_{n},x_n,y_n}}

where H_{n} and G_{n} are values of G and H in the point (x_{n},y_{n}). I want to calculate the power spectrum and the cross spectrum . Can you help me ? Thanks.