3D Arrow path along a surface

I have the following two surfaces, created by the following functions

En1[\[Delta]_,g1_,g2_,k_]:=1/2(-I g1+I g2-Sqrt[-(g1+g2-2k+I \[Delta])(g1+g2+2k+I\[Delta])]) En2[\[Delta]_,g1_,g2_,k_]:=1/2(-I g1+I g2+Sqrt[-(g1+g2-2k+I \[Delta])(g1+g2+2k+I\[Delta])])  g1 = 2;  g2 = -3;  \[Delta]max = 2;  kmax = 1;   a = Plot3D[{Re[En1[\[Delta],g1,g2,k]],Re[En2[\[Delta], g1, g2,k]]},{\[Delta],-\[Delta]max,\[Delta]max}, {k, 0, kmax},AxesLabel->{"\[Delta]", "g"}, PlotStyle->Opacity[0.7],BoxRatios -> {1, 1, 1}];  start = Graphics3D[{Black,Ellipsoid[{-1,0.8,Re[En1[-1,g1,g2,0.8]]},{0.1,0.025,0.075}]}];  end = Graphics3D[{Black,Ellipsoid[{-1,0.8,Re[En2[-1,g1,g2,0.8]]},{0.1,0.025,0.075}]}];   test1=Show[a, start, end, PlotRange -> All] 

enter image description here

Now I would like to make a 3D arrow path by going, along the surface, from one black point to the other one, encircling the origin $ (\delta,k)=(0,0.5)$ .

It seems Mathematica do not have a way to create a path, so I constructed it through a ParametricPlot.

test2 = ParametricPlot3D[{-Cos[t],0.5+kmax Sin[t],Re[En1[-\[Delta]max Cos[t], g1, g2, 0.5 + kmax Sin[t]]]},{t,0,2\[Pi]}];   Show[test1, test2] 

enter image description here

However it seems that this it is not encircling nor being created on the surface. Any thoughts?

Item of Arrow Mind

I am looking to price out an item for one of my players. Basically, they would like an item that grants them continuous use Arrow Mind from the Spell Compendium. It is a 1st level sorcerer/wizard spell with a duration of 1 min/level. So, by standard item creation rules, it would be a 4,000gp item. It would grant them the ability to make attacks of opportunities with a bow and never provoke attacks of opportunity when firing within melee range. 4,000gp seems a bit low, as it provides a ton of versatility in combat. But, I am not sure of a good price point.

Does anyone have any suggestions for how I might evaluate what this is worth? I figure, it is granting a second level ability for a weak class (Order of the Bow Initiate) plus granting the potential for an extra attack per round (by granting attacks of opportunity with a bow). I am thinking the class ability alone is probably worth around 3-4,000gp. Add in the possible extra attack that occurs on average once a combat and you have something similar to a very limited haste effect. Maybe 10,000gp would be more appropriate for the item? Would it make sense for it to take the eyes slot given the fluff for the Arrow Mind spell affecting your vision?

Whats the damage of a colossal non-magical longbow under the effects of shrink item and a medium arrow?

What is the damage of a Colossal non-magical longbow when under the effects of shrink item spell?

Now, your standard medium longbow does 1d8 and weights 3 pounds. Scaling it up 4 size categories means its now does 6d6 according to the damage dice progression chart and should weigh 3x8x8x8x8=12,288 (the x8 is per category larger than medium, and calculated using enlarge person, reduce person, and righteous might). 12k pounds. Under the weapon rules, a large weapon costs 2x as much as a medium weapon, so said colossal longbow should cost 75x2x2x2x2=1200 (found on the weapons page and scrolling down to weapon qualities).

It is also worth mentioning that this weapon MIGHT also have a -8 on attacks roles due to the weapon being sized for a larger creature. Found on the weapons page by scrolling down to Weapon Size.

Inappropriately Sized Weapons: A creature can’t make optimum use of a weapon that isn’t properly sized for it. A cumulative –2 penalty applies on attack rolls for each size category of difference between the size of its intended wielder and the size of its actual wielder. If the creature isn’t proficient with the weapon, a –4 nonproficiency penalty also applies.

Now having shrink spell cast on this colossal longbow now makes it back into a medium sized weapon and weighs 12,288 / 4000 = 3.072. Since shrink spell makes no statements about what damage the weapon would do, we are forced to rely on spells such as enlarge person and reduce person, of which they do not agree on this topic.

Enlarge person

Any enlarged item that leaves an enlarged creature’s possession (including a projectile or thrown weapon) instantly returns to its normal size. This means that thrown and projectile weapons deal their normal damage. Magical properties of enlarged items are not increased by this spell.

Reduce person

Any reduced item that leaves the reduced creature’s possession (including a projectile or thrown weapon) instantly returns to its normal size. This means that thrown weapons deal their normal damage (projectiles deal damage based on the size of the weapon that fired them).

So on one hand, reduce states its the weapon that matters, while enlarge says it does normal damage. So the best examples we have contradict each other for what happens. Since shrink item is more in tune with reduce person as both deal with shrinking, this would imply that a shrink item(colossal longbow) firing a medium arrow should deal 6d6 damage. Are there any rules, errata, FAQs that say otherwise? Crying DMs/GMs do not count.

There are two similar questions, but they ask different things. Shrink Item and the Oversized Starknife is asking about a thrown weapon. How viable is shrink item and massive projectiles? is asking about the projectile and not the launching weapon.

Acid arrow and sneak attack damage

For spells that deal damage over time such as acid arrow, Contagious Flame, or Holy Javelin, how does sneak attack damage work with them? This question assumes the attack hits, and all requirements for sneak attack are fulfilled for the first round. Later rounds the qualifying nature of sneak attack can be discussed.

The first round of AA and HJ I think everyone can agree on that the sneak attack damage would be applied because attack roles were made. The debate starts on the 2nd round of damage. Does the continuing damage benefit from sneak attack?

The first round of CF is just like AA, attack roll(s) was made, so the sneak attack gets applied. Now for the second round bouncing attacks. Would these benefit from the original sneak attack damage boost since the spell fires off a new ray each round, or would it benefit from sneak attack from me, or better would the original damage that includes the sneak be used and then sneak gets applied AGAIN (yes I am dreaming, but it is possible). For any of these do I still have to qualify for the rules of sneak attack such as be invisible, or worse, does the target I hit have to somehow meet the requirements?

Ive tried asking a variant of this question before but it was closed here. So I am limiting it to something more specific than the original.

Do you double the delayed damage for Melf’s Acid Arrow after a critical hit?

The spell Melf’s Acid Arrow does 4d4 on hit and 2d4 next turn (I’m ignoring what happens for a miss). If you roll a 20 for your spell attack roll, you double the 4d4 to 8d4.

What about the 2d4 next turn? Does that get doubled too or does that just stay at 2d4 because it occurs on the next turn?

I know that How does extra damage work for critical hits? covers additional kinds of damage during a critical hit, but this is the same substance that did critical damage, continuing its damage in a later round.

Is an arrow (bolt, bullet) considered a weapon if used as intended?

As stated in the title: is an arrow, bolt, or other object that is generally used as ammunition, count as a weapon when determining bonus effects from other feats/abilities? For example:

Dreadful Strikes – 1d4 psychic damage – TCoE, pg. 58

When you hit a creature with a weapon, you can deal an extra 1d4 psychic damage to the target, which can take this extra damage only once per turn.

It seems clear that hitting a creature with a sword via melee, or even a thrown weapon, like a dart or dagger, would benefit from this feature. But since Arrows and Bolts are “considered” ammunition, they would not (unless used in some other improvised way).

Does an arrow in an invisible creature allow you to see creature for Magic Missle attack?

Dnd 5e Magic Missle requires you to be able to see the target. PHB, pg 257 "Each dart hits a creature of your choice that you can see within range."

Therefore you can’t target an invisible creature even if you know the spot they occupy, since you can’t actually see them.

But what if they had an arrow sticking in them? Or a blanket thrown over them. Does that allow the Wizard to "see" the creature in order to use Magic Missle?

Does a Mundane Arrow Fired From a Magical Bow Count as a Magical Weapon Attack?

I’ve seen this question asked in previous editions, but I want to ask this question specifically for D&D 5e. Apparently there is still some debate about this. If I am a fighter with a +2 bow and I fire a nonmagical, mundane arrow at an enemy (golem, for example) that has resistance to damage from nonmagical weapons, does my attack overcome the damage resistance?

An archer firing through an arrow slit has improved cover. Do his targets have cover?

I’m running a module that features a fort with arrow slits and murder holes, and I’m trying to figure out what the cover rules are for people on each side of them.

Under the Combat rules, the CRB states:

Improved Cover

In some cases, such as attacking a target hiding behind an arrowslit, cover may provide a greater bonus to AC and Reflex saves. In such situations, the normal cover bonuses to AC and Reflex saves can be doubled (to +8 and +4, respectively). A creature with this improved cover effectively gains improved evasion against any attack to which the Reflex save bonus applies. Furthermore, improved cover provides a +10 bonus on Stealth checks.

From this, it seems clear that the defending archers should have improved cover. This is reinforced by this section under Dungeon Environments:

Walls with Arrow Slits

Walls with arrow slits can be made of any durable material but are most commonly masonry, hewn stone, or wood. Such a wall allows defenders to fire arrows or crossbow bolts at intruders from behind the safety of the wall. Archers behind arrow slits have improved cover that gives them a +8 bonus to Armor Class, a +4 bonus on Reflex saves, and the benefits of the improved evasion class feature. (emphasis added)

The words "defenders" and "behind arrow slits" make me think that the cover is at least somewhat directional – the defending archers are meant to be at an advantage over the besiegers (which makes sense). However, the general cover rules seem to suggest that the besiegers might also have some cover:

Cover

To determine whether your target has cover from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target’s square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the target has cover (+4 to AC).

When making a melee attack against an adjacent target, your target has cover if any line from any corner of your square to the target’s square goes through a wall (including a low wall). When making a melee attack against a target that isn’t adjacent to you (such as with a reach weapon), use the rules for determining cover from ranged attacks.

I think that the intent is that arrow slits would be at the corners of grid squares. RAW, I think that would give the besiegers no cover. However, on the map I’m using, the arrow slits are in the middle of the grid squares, which suggests that the besiegers also have at least cover, if not improved cover.

Distinct from this question (although related) in that this is about improved cover like arrow slits, whereas that was more a case of low cover.