Using Armorist without Spheres of Power

Having recently come across this question and subsequently being introduced to the Armorist class I had one inkling I can’t shake: Could I finally make a great armor summoner ala Erza?

The mechanics of being able to summon and equip lots of different magical gear is the thing that makes this concept possible. That said, I’d not even looked at Spheres of Power, nor do I really have any desire to ask for it’s use.

Which leads to this question. On it’s head, the armorist allows almost mirror progression to the Fighter (with a few tweaks here and there). So, how much of a disadvantage would it be to simply strip the magic talents and caster level away from the class, leaving it more comparable in vanilla Pathfinder?

The goal, as with any character I try to create, is not immense power or optimization. I simply want a character that fits within the general structure without feeling too strong or too weak.

Frame challenge answers that explore other options for this character that don’t have to use the Armorist class are more than welcome.

Is there an algorithm to check if two spheres are in collision and whether they’re colliding on the x or the x axis?

I was wondering if there was a way to find out whether a spheres is intersecting another sphere on either its x or its z axis. For instance, Planet A is moving along the Z Axis towards Planet B a stationary object and when collision occurs I would like to get a reponse that tells me that they collided on the zAxis. I can find out if a collsion has occured using the code below however I’m not sure on how to impliment the directional aspect of this. Any help would be appreciated.

    enum ECol { x_Axis, z_Axis, none };      // Collision detection between two spheres      distanceX = sphere2XPosition - sphere1XPosition;     distanceZ = sphere2ZPosition - sphere1ZPosition;     distance = sqrt(distanceX * distanceX + distanceZ * distanceZ );      if (distance < (sphere1Radius + sphere2Radius))     { // Collision occurred } 

Can creatures outside of Crystal Spheres dream?

Assumptions: all material from spelljammer, 3.0, 3.5, web/dragon and Pathfinder are available. Everything in this campaign setting is being converted to Pathfinder. All available separate campaign settings are their own crystal spheres. I try to remove as much DM fiat as I can, but some is required to do conversions and a lot is required to implement spelljammer, which this question is based around.

This section will be updated based on clarification request. Please comment to suggest clarifications.

Problem: Inter-planar travel is not possible outside of a crystal sphere. The dimension of dreams / region of dreams exist as kinda sort of part of the ethereal plane. If you can dream, you go to those places as a mental projection and play around in your dream demiplane. Some crystal spheres have more danger here than others depending on local creatures.

If you’re outside of the spheres however Inter-planar spells and abilities don’t work. Can you still enter the Dream world via sleeping? If the answer is yes, can you do so with spells/powers/abilities? Are there Night Hags prowling the spaces between spheres through the dreams of creatures traveling in the phlogiston?

Did the spellplague change the cosmology of other crystal spheres too, or just realmspace?

The spellplague changed the cosmology of Forgotten Realms into the world axis cosmology. Great wheel no more, world tree no more (it seems I missed/skipped this one).

But did the spellplague affected the entire prime material, or just the realmspace crystal sphere. Each campaign setting is inside its own crystal sphere, and the spheres float amidst the phlogiston of the prime material plane. Did the spellplague also affected the cosmology of other crystal spheres / game settings? Like Krynn, Oerth, Mystara, etc?

Can Otiluke’s Freezing Spheres be stockpiled?

In the final paragraph of Otiluke’s freezing sphere it states:

You can refrain from firing the globe after completing the spell, if you wish. A small globe about the size of a sling stone, cool to the touch, appears in your hand. At any time, you or a creature you give the globe to can throw the globe (to a range of 40 feet) or hurl it with a sling (to the sling’s normal range). It shatters on impact, with the same effect as the normal casting of the spell. You can also set the globe down without shattering it. After 1 minute, if the globe hasn’t already shattered, it explodes.

I interpreted this to mean that my players cannot generate a stockpile of spheres. But the wizard at our table made an argument that the last bit merely means that if she left it on the ground it would explode after a minute, like a time bomb, but if she were to store them in a bag (like sling stones) the spheres wouldn’t explode. Am I screwing over my players? What is the correct interpretation?

Gaussian Integrals over Spheres

I’m after a reference for an integral. In particular, I am looking a way to approximate or calculate the following:

$ $ \int \limits_{\| \theta \|_2 = 1} e^{(-(\theta – \mu)^T \Sigma (\theta – \mu))} d\theta $ $ .

I know how to do this when say $ \Sigma$ is the Identity matrix. To see this, $ $ \int \limits_{\| \theta \|_2 = 1} e^{(-(\theta – \mu)^T I (\theta – \mu))} d\theta = \int \limits_{\| \theta \|_2 = 1} e^{- \| \theta – \mu \|_2^2} d\theta = e^{-1} e^{-\|{\mu}\|_2^2} \underbrace{\int \limits_{\| \theta \|_2 = 1} e^{2\|{\mu}\|_2 \theta^T(\frac{\mu}{\|{\mu}\|_2})} d\theta}_{T1} $ $

Now, T1 is essentially the normalization constant for the Von-Mises Fisher Distribution.

How do I do it for general $ \Sigma$ ? Is there some simple trick that I am missing?