Compute Intersection Of Line With Star Shaped Set

Let there be $ k$ planes $ X_i\subseteq\mathbf{R}^3$ , all tangent to the unit sphere, in general position, represented by normal vectors $ v_i$ . Then $ \mathbf{R}^3\setminus\cup_i X_i$ consists of bounded and unbounded segments, let $ S$ denote the closure of the union of all bounded segments and assume that $ \mathbf{0}\in S$ . This should give a star shape w.r.t. $ \mathbf{0}$ , i.e. for all $ s\in S$ , the ‘interval’ $ [\mathbf{0},s]$ lies within $ S$ . Given a unit vector $ w\in R^n$ , in general position to the others, I can compute all scalars $ \lambda_i$ such that $ \lambda_iw$ lies on $ X_i$ . What is the most efficient method to verify which (necessarily unique) positive $ \lambda_i$ lies on the boundary of $ S$ , if I want to apply it to a lot of $ w$ s but the planes stay fixed?

The easiest way I currently see is to compute all intersection points of three planes each, then for every plane $ X_i$ , arrange a list of all triangles on that plane, that means, the three intersection points of $ X_i$ with two out of three other planes. Now, given $ w$ , I first get the largest $ \lambda_i$ , check whether it lies in some of the triangles on $ X_i$ , if not, continue with the second largest $ \lambda_i$ , etc.

Can a Druid Goblin use Nimble Escape while Wild Shaped?

Can a Goblin Druid use its Nimble Escape ability while Wild Shaped?

• Nimble Escape. You can take the Disengage or Hide action as a bonus action on each of your turns.

and, for Wild Shape:

You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.

Are there any conflicts with casting Fire Wings while Wild Shaped?

I have the natural spell feat already. I was curious if there were any rules about layering transmutation spells and the wording of said spells interacting with a druid’s wild shape ability.

Spell in question, with the bit that caught my attention:

Fire Wings (Spell Compendium, p. 93) (Transmutation [Fire]): In a flash of light and a roar of fire, your arms become wings of flame … If you are not flying, you can make up to two attacks each round with the fire wings as if they were natural weapons. A successful attack deals 2d6 points of fire damage.

Because replacing the 2 claws of a wild shape with 2d6 fire damage phoenix wings would be a cool spell interaction. I’m just not sure if there’s a solid rule on layering transmutation spells or if the spell’s specific wording of “arms” would throw the issue.

When a druid reverts to their normal form having wild shaped into a Large beast, can they choose which square they occupy?

When a druid reverts to their normal form they appear where their beast shape was. But if their beast shape was Large and their normal form is Medium, can they choose which of the four squares they reappear in?

For example if a druid wild-shaped into a Polar Bear (occupying 4 squares) and was engaged in melee with several opponents standing in a line, when their beast shape drops to 0 hit points can they choose for their normal form to appear in a square that isn’t adjacent to those opponents?

Depending on the placement of enemies, this allows a druid low on temporary HP to retreat without taking opportunity attacks and take an action on the same turn, rather than spending their action disengaging.

Is it any different if they leave wild shape as a bonus action, or cease to concentrate on a polymorph spell?

Which animal enhancements can a Simic Hybrid druid maintain while Wild Shaped? [on hold]

Which of the animal enhancements can a Simic Hybrid Druid maintain while Wild Shaped? Manta Glide, Nimble Climber, Underwater Adaptation, Grappling Appendages, Carapace, and/or Acid Spit?

Does the type of beast I Wild Shape into determine if I can keep a particular animal enhancement? For instance, if I Wild Shape into a Giant Crab, would I maintain my Grappling Appendages feature? What if I Wild Shape into a Bear?

Can a Druid cast the Flame Blade spell, then use the blade while Wild Shaped?

The Flame Blade spell description says:

You evoke a fiery blade in your free hand. The blade is similar in size and shape to a scimitar, and it lasts for the duration. lf you let go of the blade, it disappears, but you can evoke the blade again as a bonus action.

You can use your action to make a melee spell attack with the fiery blade. On a hit, the target takes 3d6 fire damage.

Assuming you had some means of holding onto the weapon, could a Moon Druid use Flame Blade after it’s cast while Wild Shaped?