What are the circumstances of Traxigor’s transformation and do they explain how he retained his magical abilities as an otter?

Traxigor is an Archmage with a rather unique morphology, who is encountered during Baldur’s Gate: Descent into Avernus:

Traxigor was polymorphed into an otter years ago, and decided he preferred the new form to his original one (that of a wizened old man). His otter form was made permanent by a wish spell. He uses the archmage stat block, but is a Tiny beast with a Strength of 3.

What exactly happened here? Are the circumstances of this transformation recorded in any official source material (from any edition)?

This answer establishes that (in D&D 5e) the spell polymorph would not allow a spellcaster to retain their spellcasting abilities while polymorphed into a beast, and this answer establishes the same for true polymorph. On the surface, this seems like an inconsistency (which wouldn’t be surprising), but do the circumstances of Traxigor’s transformation into an otter resolve this inconsistency somehow?

Ordering eigenvectors for basis transformation

Let’s say I have a matrix $ H$ represented in some basis, $ a$ , and I’d like to transform this to be represented in a different basis, $ b$ . The only difference between the bases is that $ b$ is a basis of eigenvectors of a reflection operator, $ \hat{\sigma}$ . So in theory, what I want to do is find the eigenvectors of $ \hat{\sigma}$ , but them into a matrix that I’ll call $ U$ , and then compute $ H_b = U^\dagger H U$ . My problem is that the basis $ a$ is ordered according to an order I want to preserve, but Mathematica by default sorts the eigenvectors of $ \hat{\sigma}$ by the eigenvalues (which are all either +1 or -1 since this is a reflection operator). How can I keep the ordering of the eigenvectors locked to the original basis so I can indeed use this as a basis transformation without mixing up the subblocks of my existing matrix?

Here’s a code example of what I want:

Ha = {{298.1, -0.7, 0., 0., 0., 0., 0., 0.}, {-0.7, 296.8, 0., 0., 0., 0., 0., 0.}, {0., 0., 298.1, -0.7, 0., 0., 0., 0.}, {0., 0., -0.7, 296.8, 0., 0., 0., 0.}, {0., 0., 0., 0., 298.1, -0.7, 0., 0.}, {0., 0., 0., 0., -0.7, 296.8, 0., 0.}, {0., 0., 0., 0., 0., 0., 298.1, -0.7}, {0., 0., 0., 0., 0., 0., -0.7, 296.8}}; 

Note that Ha is blocked in 4 2×2 blocks. When I change bases, I expect this to become blocked in 2 4×4 blocks.

Now, my operator $ \hat{\sigma}$ can be represented as:

sigma={{0, 0, 0, 1., 0, 0, 0, 0}, {0, 0, 1., 0, 0, 0, 0, 0}, {0, 1., 0, 0, 0, 0, 0, 0}, {1., 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1.}, {0, 0, 0, 0, 0, 0, 1., 0}, {0, 0, 0, 0, 0, 1., 0, 0}, {0, 0, 0, 0, 1., 0, 0, 0}}; 

But then when I call Transpose[Eigenvectors[sigma]].Ha.Eigenvectors[sigma], I get a matrix that is horribly off-diagonal, which is just showing that the eigenvectors of sigma are not sorted properly. So, how do I keep everything sorted correctly?

How to decompose a 4×4 TRS transformation matrix with negative scale?

As the title says I need to decompose 4×4 TRS transformation matrices and extract the proper scale vectors and the proper rotation vectors (or rotation quaternions).

I know how to extract those information when the upper 3×3 matrix determinant is not negative. The problem is that those matrices can have that negative determinant and as far as I could understand, this negative determinant indicates a flip or mirrored transformation.

What do I have to do to extract the proper values for scale and rotation in those cases?

What is an efficient way to get a look-at direction from either a quaternion or a transformation matrix?

So, I have an object in my custom engine (C++), with a column-major transform in world space. I’m using a package that takes a look-at direction as an input. What’s the most efficient way to get a look-at direction from this transform? Do I extract the rotation matrix? Do I try to extract a quaternion?

Transformation of an object into parameter value on submission of request

Today I saw rather a weird phenomeon, when submitting a request spontaneoulsy.

The URL I typed looked something like below:

https://example.com/en/trade/pro?layout= and when submitted it transformed into https://example.com/en/trade?layout=pro

If I correctly perceived that the pro object moved to a value of layout (if not just visually).

It didn’t work for https://example.com/en/trade/test?layout= and when submitted should transform into https://example.com/en/trade?layout=test, that didn’t work.

It did only work for the pro object.

Is this a behavior made by developers of the site or could this eventually lead to something interesting?

How to adjust a PC statistics when undergoing a (semi)permanent transformation into a different creature?

The Monster Manual contains guidance for Player Characters as Lycanthropes (p. 207) or Vampires (p. 295).

Is there any other guidance on how to handle player characters (semi)permanently transforming into another creature where they could retain their class levels and statistics but also take on characteristics of that creature?

Possible examples I am thinking of might be a transformation into a lich, a dragon, a fiend/celestial, etc.

I am specifically looking for solutions where the character can still function as a PC, gaining EXP, levels, and interacting with other player mechanics.

I am looking for answers based on official content, however, if there is no useful rules/guidance in DnD 5e, I would be interested in how other editions handled this idea or even DM/player table experience and solutions.

Can any of the found greater steeds benefit from the weapon proficiencies granted by Tenser’s Transformation?

The mount summoned by the 4th level Paladin spell find greater steed has this interesting ability:

While mounted on it, you can make any spell you cast that targets only you also target the mount.

The 6th level wizard spell Tenser’s tranformation grants weapon proficiencies;

You have proficiency with all armor, shields, simple weapons, and martial weapons.

After casting Tenser’s transformation while riding my found greater steed, technically my mount would have proficiency with all simple and martial weapons.

Obviously the primary issue here is going to be the question of “appropriate anatomy” – can magic that makes the uncoordinated wizard with no weapon skills a martial juggernaut also give my griffon the basic ability to firmly grasp a short sword? Are any of the mounts listed1 able to make use of any of the weapon proficiencies granted by Tenser’s transformation?

1 a griffon, a pegasus, a peryton, a dire wolf, a rhinoceros, or a saber-toothed tiger.

How to hide race transformation [closed]

I am playing AD&D1st/2nd. My knight are getting transformed into Drow(by ego Item), the transformation will be complete in like 30 days and My party is like elves, gnomes, and humans. How can I possibly hide my transformations?

Thank you for your answers in advance.

Some additional info I am Lvl 4 Human Knight(Cavalier)/Pal, I use full plate armor+helmet (but haven’t done my training yet), playing a Lawful evil character (the item I picked up is Demonic/evil). If I would be good the item would simply posses me. Item was forged by Drow, thus it thinks that only Drow should use it, that’s why it tries to transform me into the Drow. I do have a bunch of non-weapon profs(Diplomacy, Government, Heraldry, Strategy, Geography, Economics, Captaincy / Command), but they are useless when trying to hide the changes in my body. (Yes, It is homebrew Item)

P.s Sorry for not giving enough information , I started playing D&D a week ago, still don’t know a lot of things…Thank you for your understanding

How to calculate the transformation such that two points with different position, orientation and origins line up?

Let’s say you have two different 3D Objects which both contain a node that is off center (not at the origin) and have an orientation. How do you calculate the transform for one of the object so that both of these nodes line up? As in both nodes end up at the same position in space and the same orientation?

In gaming terms, both 3D objects have “snap” points and I’d like to calculate how to transform one of them so that they snap together at that specific node.

for illustration purposes The cubes are the 3D objects, the X/Y/Z axis represent the origin of each of these objects, and the arrow is the node. The goal would be in this case both arrows overlap and thus the cubes end up at the exact same place. Note the origin is NOT at the same spot for both objects.

How well will the max transformation rounds in Keepassx deter an attacker for the next twenty years?

Keepassx lets you decide how many transformations rounds need to be run in order to unlock your Keepass database. In my version of Keepassx (2.0.3) the max value seems to be 999,999,999. With that setting it takes my laptop about 22 seconds to unlock the database. I imagine that a beefy workstation would take less time than that. With that in mind, how well can this setting deter someone else from accessing your database, assuming that they managed to get access to it? Let’s just say an individual (not an organization) with a computer made to do this kind of work. How much work can you assume that they will have to do per try with the kind of computation power that they will have access to in twenty years?