Footprint

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{{Lede image|BTD6 footprints.png|Visualization of different tower footprints in ''Bloons TD 6''}}

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== ''Bloons TD 6'' ==

~~{{Incomplete}}~~

[[File:BTD6 tower footprint showcase.png|thumb|Showcase of tower footprints in ''Bloons TD 6'', where the area that the tower actually uses is indicated in green to show correspondence with the in-game model.]]

In [[Bloons TD 6]], the majority of towers have a circular footprint, with a few exceptions, listed on the table below.

In [[Bloons TD 6|''Bloons TD 6'']], the majority of towers, [[Power|powers]] and other items that can be placed on the map have a circular footprint, with a few exceptions, listed on the table below. Despite all towers having an internal "footprint radius" defined (or height and width for rectangular forms), they have separate flags that determine their behavior, as they can block other tower placements, which this is true for the vast majority of towers, however some sub-towers do not have this flag active like [[Sentry Gun (BTD6)|Engineer Sentries]] or Mini-Sun Avatars. This is also true for powers like [[Pontoon (BTD6)|Pontoons]] and [[Portable Lake (BTD6)|Portable Lakes]] and the footprint is used instead to determine the amount of available space for other towers that are placed over them.

Powers and items can also have flags to ignore collisions with towers and/or the capability of be placed at any point of the map, even over obstacles or the Bloons path, examples include the Mega Mine from [[Admiral Brickell (BTD6)|Admiral Brickell]], the totem of [[The Final Harmonic]] or [[Geraldo (BTD6)|Geraldo's]] [[Pet Rabbit|Killer Rabbit]].

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Some maps can have areas where players can place towers where they visually wouldn't fit (e.g. the altar in [[Encrypted]]) and in the other hand, there are also places where towers that can fit are restricted, for example, [[Heli Pilot (BTD6)|Heli Pilots]] cannot be placed in on the top right section of [[Erosion]], but [[Banana Farm (BTD6)|Banana Farms]] can despite having a larger footprint.

Towers and Heroes do not change their footprint when they are upgraded, even if the model is visually larger, which is specially evident on [[Paragon|Paragons]], however, this behavior has one exception, which is when a [[Sun Avatar (BTD6)|Sun Avatar]] is upgraded into a [[Sun Temple (BTD6)|Sun Temple]], in this case the footprint grows from a radius of 8 units to a rectangle with a width of 37 units and a height of 40 units. This usually does not have any interactions with other regular towers as they are sacrificed when the upgrade is purchased, however as the Sun Temple cannot sacrifice Powers or Heroes, if they are placed right next to the Super Monkey before being upgraded, they will end up inside of the Sun Temple's footprint, this interaction does not impact the towers and can bet moved away by using the Redeployment ability of a [[Support Chinook (BTD6)|Support Chinook]],

This behavior can is used used on [[Freeplay]] strategies to save space for [[Tech Bot (BTD6)|Tech Bots]] by placing them around Super Monkeys that are intended to become Sun Temples later in the game. Also, there is a small window of time after purchasing the Sun Temple where after the Monkeys around it are sacrificed but before its footprint grows, this can be exploited by using a Support Chinook to move a tower right next to the Sun Avatar during the transform animation so it ends inside the Temple's footprint.

Optimal placements of towers with the same or different sizes within a certain area is a common problem that is found in recreational mathematics, known as [[wikipedia:Circle packing|circle packing]], and despite the intuition of going for hexagonal or triangular patterns (where the form indicates the arrangement of the center of the circles) are usually not the [[wikipedia:Circle packing in a square|optimal solution]]. Although [https://www.sciencedirect.com/science/article/abs/pii/S0305054812001141 procedures exist] for regular forms, the variety of shapes of open areas in maps in ''BTD6'' makes finding optimal solution it a difficult task that usually can only be solved a brute force trial and error approach.

== ''Bloons Adventure Time TD'' ==

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-{{Stub}}
 {{Lede image|BTD6 footprints.png|Visualization of different tower footprints in ''Bloons TD 6''}}
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 == ''Bloons TD 6'' ==
-{{Incomplete}}
+[[File:BTD6 tower footprint showcase.png|thumb|Showcase of tower footprints in ''Bloons TD 6'', where the area that the tower actually uses is indicated in green to show correspondence with the in-game model.]]
-In [[Bloons TD 6]], the majority of towers have a circular footprint, with a few exceptions, listed on the table below.
+In [[Bloons TD 6|''Bloons TD 6'']], the majority of towers, [[Power|powers]] and other items that can be placed on the map have a circular footprint, with a few exceptions, listed on the table below. Despite all towers having an internal "footprint radius" defined (or height and width for rectangular forms), they have separate flags that determine their behavior, as they can block other tower placements, which this is true for the vast majority of towers, however some sub-towers do not have this flag active like [[Sentry Gun (BTD6)|Engineer Sentries]] or Mini-Sun Avatars. This is also true for powers like [[Pontoon (BTD6)|Pontoons]] and [[Portable Lake (BTD6)|Portable Lakes]] and the footprint is used instead to determine the amount of available space for other towers that are placed over them.
+Powers and items can also have flags to ignore collisions with towers and/or the capability of be placed at any point of the map, even over obstacles or the Bloons path, examples include the Mega Mine from [[Admiral Brickell (BTD6)|Admiral Brickell]], the totem of [[The Final Harmonic]] or [[Geraldo (BTD6)|Geraldo's]] [[Pet Rabbit|Killer Rabbit]].
 {| class="wikitable mw-collapsible mw-collapsed"
 |+
@@ Line 73: / Line 73: @@
 |}
 Some maps can have areas where players can place towers where they visually wouldn't fit (e.g. the altar in [[Encrypted]]) and in the other hand, there are also places where towers that can fit are restricted, for example, [[Heli Pilot (BTD6)|Heli Pilots]] cannot be placed in on the top right section of [[Erosion]], but [[Banana Farm (BTD6)|Banana Farms]] can despite having a larger footprint.
+Towers and Heroes do not change their footprint when they are upgraded, even if the model is visually larger, which is specially evident on [[Paragon|Paragons]], however, this behavior has one exception, which is when a [[Sun Avatar (BTD6)|Sun Avatar]] is upgraded into a [[Sun Temple (BTD6)|Sun Temple]], in this case the footprint grows from a radius of 8 units to a rectangle with a width of 37 units and a height of 40 units. This usually does not have any interactions with other regular towers as they are sacrificed when the upgrade is purchased, however as the Sun Temple cannot sacrifice Powers or Heroes, if they are placed right next to the Super Monkey before being upgraded, they will end up inside of the Sun Temple's footprint, this interaction does not impact the towers and can bet moved away by using the Redeployment ability of a [[Support Chinook (BTD6)|Support Chinook]],
+This behavior can is used used on [[Freeplay]] strategies to save space for [[Tech Bot (BTD6)|Tech Bots]] by placing them around Super Monkeys that are intended to become Sun Temples later in the game. Also, there is a small window of time after purchasing the Sun Temple where after the Monkeys around it are sacrificed but before its footprint grows, this can be exploited by using a Support Chinook to move a tower right next to the Sun Avatar during the transform animation so it ends inside the Temple's footprint.
+Optimal placements of towers with the same or different sizes within a certain area is a common problem that is found in recreational mathematics, known as [[wikipedia:Circle packing|circle packing]], and despite the intuition of going for hexagonal or triangular patterns (where the form indicates the arrangement of the center of the circles) are usually not the [[wikipedia:Circle packing in a square|optimal solution]]. Although [https://www.sciencedirect.com/science/article/abs/pii/S0305054812001141 procedures exist] for regular forms, the variety of shapes of open areas in maps in ''BTD6'' makes finding optimal solution it a difficult task that usually can only be solved a brute force trial and error approach.
 == ''Bloons Adventure Time TD'' ==

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