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The spike growth spell has a range of 150 feet, and its description states:

The ground in a 20-foot radius centered on a point within range twists and sprouts hard spikes and thorns. The area becomes difficult terrain for the duration. When a creature moves into or within the area, it takes 2d4 piercing damage for every 5 feet it travels.

The transformation of the ground is camouflaged to look natural. Any creature that can't see the area at the time the spell is cast must make a Wisdom (Perception) check against your spell save DC to recognize the terrain as hazardous before entering it.

When a creature casts spike growth, do they need to be able to see the center of the circle which spawns the growth? Or can the center or entire growth be behind total cover? Does the area of effect continue around corners, or pass through total cover like a door or thin wall?

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  1. No, you cannot target a point that is blocked by total cover.

From Players Handbook, Spellcasting, subsection "Targets":

To target something, you must have a clear path to it, so it can’t be behind total cover.

If you place an area of effect at a point that you can’t see and an obstruction, such as a wall, is between you and that point, the point of origin comes into being on the near side of that obstruction.

When you cast an area spell, you can place its point of origin on your side of a wall, but not on the opposite side of the wall.

  1. No, area effects normally do not go around corners (unless the spell explicitly says it does).

From Players Handbook, Spellcasting, subsection "Areas of Effect":

A spell’s effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn’t included in the spell’s area. To block one of these imaginary lines, an obstruction must provide total cover.

Lets say you cast Spike Growth and put its point of origin near a wall, at a location that isn't behind total cover. The spell's radius would extend in all directions from its point of origin, but it would stop at the wall. The ground behind the wall would be unaffected.

This is the cast for most spells. However, there are exceptions (such as Fireball) that specifically mention going around corners. In those cases, the spell's text overrides the general rule for other spells, and so that spell's effects will not necessarily stop at a corner.

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    \$\begingroup\$ The first sentence is very misleading. You most certainly can target a point you can't see unless the spell says otherwise, and Spike Growth doesn't say otherwise. The issue is needing an unobstructed line to the point you're targeting, as the Player's Handbook points out. \$\endgroup\$ – Doval Jan 29 '18 at 14:51
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Most of it can be behind total cover, as long as you have line of effect to the center

For example you can cast Spike Growth through a small window to cover a 20 x 20 room.

A spell’s effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn’t included in the spell’s area. To block one of these imaginary lines, an obstruction must provide total cover...

Some parts of the area can be behind total cover from you, if you have line of effect to the center, and the center has line of effect to all parts of the area.

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