Is circular movement treated as moving diagonally or difficult terrain? [closed]

Question

This came up in a discussion in my group about circular movement.

Is circular movement treated as moving diagonally or difficult terrain?

For a situation such as circling a target on a horse shooting arrows at it, we felt it should be treated as difficult terrain.

One situation that was mentioned was where a ranger casts spike growth (which has a 20-foot radius) and wants to completely walk around it. How long would it take? The circumference is about 125 feet, and the ranger's base speed is 30 feet.

Say they cast spike growth and catch someone in the area of effect. If the target tries to move out from it and away from the ranger, can the ranger circle around the AOE faster than the target can move through it?

Running through it counts as difficult terrain, but what about running around it?

We are playing using a grid. The DM prefers to use a square grid over a hex grid.

Answer 1

Something only counts as Difficult Terrain if the terrain itself is... difficult. Whether this is the result of a spell like Spike Growth, or from the terrain being naturally difficult to move through (thick underbrush, etc. See PHB p.190).

When playing on a grid, the DMG (p.251) says: "If an area of effect is circular and covers at least half a square, it affects that square."

A 20 foot radius will look like this:

Use standard movement to move around the outside of the affected area - whether your table uses the standard rule for grid movement (PHB p.192) (diagonals are 5 feet), or the optional rule for diagonals (DMG p.252) (every second diagonal is 10 feet).

Answer 2

It’s a square

By default, D&D 5e isn’t played on a grid, or other mapping—it’s simply played as imagined, the so-called “theater of the mind.” Since there is no mapping or geometric abstraction in play, a circle is simply a circle.

However, 5e does offer a “variant” style in which a grid is used, in which case it uses the same geometry that was used in D&D 4e—moving from one square to any adjacent square, including along diagonals, counts as 5 feet (or 1 square) of movement. It even recommends converting ranges, speeds, and so on to squares (by dividing by 5 feet/square), which is exactly what 4e did when this was the default.

In this geometry—mathematicians know it as Chebyshev distance or chessboard distance—a “circle” (read: the geometric figure formed of the set of points each at some fixed radius away from a central point) looks like a square. A sphere looks like a cube. This is its advantage, even though it looks weird—it’s really easy to calculate. Contrast that with this nonsense for D&D 3.5e, which used a “more accurate” approximation for diagonals by making them cost 1½× horizontal/vertical movement (reality would be \$\sqrt{2}\times \approx 1.414\times\$).

So moving in a “circle” around a target looks (to us) like moving in a square around them. That’s how you maintain a constant distance away from them (presumably outside their range and inside yours). There is no “difficult terrain” involved (only actual difficult terrain, things impeding your ability to move like brambles or water or whatever, should cause that). Diagonals don’t really come up when moving around a circle, but the shape of the circle is certainly dictated by how diagonals work.

Likewise, something with a 20-ft. radius produces a 40-ft × 40-ft square—that’s 160 feet around. Since you’re walking around the squares outside of that, though, it’s actually 180 feet, assuming you cut the corners.

Answer 3

Make the circular movement 'square'

Treat the movement as diagonal.

In the DMG there is an optional diagonal rule that treats diagonal directions as horizontal for quick calculations that wont detract from the game.

"Measuring range on a grid: count every square as 5 feet, even if you’re moving diagonally. Though this is fast in play, it breaks the laws of geometry and is inaccurate over long distances. This optional rule provides more realism, but it requires more effort during combat."

"When measuring range or moving diagonally on a grid, the first diagonal square counts as 5 feet, but the second diagonal square counts as 10 feet. This pattern of 5 feet and then 10 feet continues whenever you’re counting diagonally, even if you move horizontally or vertically between different bits of diagonal movement. For example, a character might move one square diagonally (5 feet), then three squares straight (15 feet), and then another square diagonally (10 feet) for a total movement of 30 feet."

Using this you could circle around something by multiplying the one of the outer diagonals sides (a quarter circle in reqular geometry) by four see how in taxicab geometry spheres become squares.