HeroClix Played on a 3-D Map

[VGA d1sc1pL3]

My friend and I created a very detailed O-Scale map using buildings and objects we bought from rail-road model shops. We have also used O-Scale model cars, etc. HeroClix are O-Scale, so it's a perfect match.

Since the game is being converted from 2-dimensional squares to 3-dimensional cubes, it brings a more comic book feel. It takes longer to scale or fly up to the top of a building based on the height of the building, etc. LOF is also affected in some aspects.

However, there have been some arguments put forth by some of the mathematically challenged regarding adjacency issues.

The cube has 12 sides, 8 vertices and 6 faces.

How do we deduce if vertices, or neighbours, are adjacent? Two vertices u, v∈V of graph G=(V, E) are called adjacent vertices (or neighbours), if uv is an edge of graph G. In other words: if they are the endpoints of the same edge.

Now, take that to a 3-dimensional level: The multiply adjacent vertices are vertices connected with two or more edges.

In HeroClix, on a standard two-dimensional map, a character can move into any adjacent square, including going between two vertices in a diagonal manner.

In regards to HeroClix being played on a map consisting of 3n hybercubes the character would be able to move diagonally as well. But now there are more vertices, sides, and faces a character can move through. A character would be able to move into any of the 12 sides of the cube since the neighbours are adjacent. The only time it would be impossible for a character to move into one of the 12 sides or 6 faces of a cube would be if a cube was filled, i.e. blocking terrain. An example would be out of the 12 sides of a cube, the cube to the direct left is the 3rd, and top, floor of a building. The character would not be able to enter through the left face of the cube or the side of the cube to the bottom-left because it is filled with solid matter. However, he would be able to enter the side diagonally above this filled cube, i.e. the side on top of the building, hence he would be standing on top of the building at this point. This is proven by the fact the vertices are connected by multiple edges, as stated two paragraphs above this one.

If my math is fuzzy, please correct my formula of two vertices u, v∈V of graph G=(V, E) are called adjacent vertices (or neighbours), if uv is an edge of graph G; and the multiply adjacent vertices are vertices connected with two or more edges.

If I am wrong, please reply back with the correct formula.

[Nighthawk]

You are kidding, right?
This is HCRealms, not TrigonomotryRealms

[lancelot]

You are kidding, right?
This is HCRealms, not TrigonomotryRealms

Where's Tony Stark when you need him?

[redskindavyd]

I've done some of the same, getting O scale buildings & gridding the rooftops (so far I have a gas station, apartment bld., a mini-mart and lots of scale items such as cars. It makes the game a lot of fun.

[Harpua]

Um...I think the first mistake here is in believing that the figures are in any way to scale with anything at all. Just look at every Spider-Man side by side and tell me that the figures are to any kind of scale.

[Sheeplover]

If I were you I would just play on those paper things they give you with the starter sets.

[VGA d1sc1pL3]

You are kidding, right?
This is HCRealms, not TrigonomotryRealms

Do I look like the type of guy who would jest? :laugh:

[VGA d1sc1pL3]

Where's Tony Stark when you need him?

He's away from the office right now on official business. He left me in charge. I've ran this through the top of the line Stark micro-computers, and I can find no error in my formula.

[VGA d1sc1pL3]

Um...I think the first mistake here is in believing that the figures are in any way to scale with anything at all. Just look at every Spider-Man side by side and tell me that the figures are to any kind of scale.

Well, they were originally O-scale, but I would say that the designers have taken some liberty with the scale. But in general, they are supposed to be O-Scale.

[VGA d1sc1pL3]

If I were you I would just play on those paper things they give you with the starter sets.

I'm the Christopher Columbus of HeroClix. You see, on those two-dimensional maps, my figures have a tendency to fall off the edge of the world.

On a serious note: Mage Knight had 3-D elements, so why shouldn't HeroClix?

[Gentlegamer]

I think 3D terrain would work fine as long as you keep the same rules of HeroClix in place regarding movement, line of fire, adjacency, etc.

[incredible]

The 200 pt kill and keep that I requested team building help with, was played today on a 3-D map!
I would post pictures but I haven't donated enough.

[JNW7]

I've mainly played on 3d maps since i started. Just pretend it's 2d, look at it top down and set whats hindering, blocking, elevated etc. and then there's no problems.

[Dikarika]

I think the "play 3D just like its 2D" is the simplest answer.

Although, I applaud your intent to fully bring about true 3D gameplay to a flat game. You could compute lines of fire and movement, but I'd think counting squares and multiplying would work pretty well as a simple solution.

Also, I'd recommend getting or making some flight bases for your flyers. It would add to the realism if your flyers could free float within the 3d space as well.

Good luck.

[mr_obvious]

Dude, I'm an Algebra teacher, and my degree took me through Calc III, Discrete math, and a history or mathematics. All I can say is you're making this WAY too hard. If the figures are on the same elevation and in adjacent "squares" (as marked off on the map), then they are adjacent. I'm not really sure what in the world you're having trouble with. Could you please rephrase the question so that anyone could reasonably answer.

I've also played on many different 3-d maps myself. I've got 4 of my own. There are definitely some unique elements to the gameplay, and a lot of fun. But, I've never come across anything that my 9 year old nephew couldn't logically figure out how it should play out.

Final verdict ... I sure hope this thread was a joke.

[redskindavyd]

I think 3D terrain would work fine as long as you keep the same rules of HeroClix in place regarding movement, line of fire, adjacency, etc.



Exactly, that's how we play with our 3-D buildings. Works great!

[VGA d1sc1pL3]

Dude, I'm an Algebra teacher, and my degree took me through Calc III, Discrete math, and a history or mathematics. All I can say is you're making this WAY too hard. If the figures are on the same elevation and in adjacent "squares" (as marked off on the map), then they are adjacent. I'm not really sure what in the world you're having trouble with. Could you please rephrase the question so that anyone could reasonably answer.

I've also played on many different 3-d maps myself. I've got 4 of my own. There are definitely some unique elements to the gameplay, and a lot of fun. But, I've never come across anything that my 9 year old nephew couldn't logically figure out how it should play out.

Final verdict ... I sure hope this thread was a joke.

Since you're a math teacher, this should be easily understandable to you in regards to 3-D cubes.
I, too, have taken advanced math classes, such as geometry, algebra, calculus, trigonometry, ad nauseam.

It sounds like when you play on a 3-D map, you retain the 2-D rules. But if you are going to play on a 3-D map, you can't think in 2-dimensional terms to truly bring it to life.

We play in a truly 3-D environment, with 5 levels of elevation (our tallest building is 4 stories). The lowest elevation is Ground, with the last four levels of elevation being either different levels of buildings, or different arial elevations.

Since it is truly a 3-D environment, it is possible, and does happen, that a grounded character may have multiple fliers directly above him in any of the four elevations above. We have created flight stands, that measure in height in increments of 1.5"; e.g. a character flying at the third level of elevation would be placed on a 3" vertical stand to represent this. He could still have two fliers directly above him, a flier below him, and a grounded character below him.

Another example. Take Spidey with Leap/Climb and a Movement Rate of 8. He starts his movement 5 squares from a 4-story building. He wants to get to the top of the building. He moves 5 squares to the building, he then begins his ascent to the top of the building, but with only 3 movement left, he is only able to reach the side of the building on the 4th floor, one cube away from the top of the building. We have attachments that hook to the side of the buildings for when characters end their movement scaling a wall. Next turn, Spidey can move again to reach and stand on the roof.

We don't use the 2-D adjacency rules, since it is a three dimensional world. We consider a cube adjacent to another cube as adjacency. So a character on the first level of elevation, a.k.a. ground terrain is adjacent to any other character in any adjacent cube, which would be the cube directly above him, or to any side of his cube in the second level of elevation or the first elevation level (grounded).

So no, the final verdict isn't a joke. As a math teacher, I'm sure you can think in 3-dimensional terms, so it should be rather easy for you to understand. I'm not the one having the issues, it's a couple of the other players who can't wrap their two-dimensional minds around a 3-dimensional world.

So, in layman's terms, how many adjacent cubes does any particular cube being occupied by a figure have that said character can move into? I've came up with 18 as the number of adjacent cubes if the character is flying at any elevation level. One guy has said 26 cubes. And yet another guy has stated 10 adjacent cubes. And everyone else agrees with me, with the exception of one guy who really doesn't have a clue.

This is why I asked if my formula that I posted in my original post to deduce if vertices, or neighbours, are adjacent or not is correct.

[jdm61802]

Personally I just use the Heroscape tiles to make 3D maps. Then I apply the Heroscape rules when it comes to adjacent. Each figure is given a height value with 5 being the norm. If a character is standing next to another charcter who is eleveated then they are considered adjacent if the tiles the elevated character are one are no greater than the height of the lower level character. I would think you could apply a similar idea to cubes.

[Darth Sabre]

My head exploded..and I just graduated from college! :confused:

[VisibleNinja5674]

How dare you try to turn a game into homework!

must. kill. more. braincells. with. TV.

[thanoson]

Just got into the 3d aspect myself. It's loads of fun watching Anti-Monitor walking through the city. About to make some new rules for cars and motorcycles as heavy items. Cars are heavies when thrown. They do d6 clix if thrown and on the roll of doubles or a 6 on the damage it explodes like energy explosion. In hth, same rules apply except it's damage +d6. Motorcycles are heavies that just explode on doubles.

I'm using the microtactix buildings and have found them very entertaining. When HoT comes out, my returning players should be very pleased. Gonna have about 30 buildings made by then.

[Dikarika]

So, in layman's terms, how many adjacent cubes does any particular cube being occupied by a figure have that said character can move into? I've came up with 18 as the number of adjacent cubes if the character is flying at any elevation level. One guy has said 26 cubes. And yet another guy has stated 10 adjacent cubes. And everyone else agrees with me, with the exception of one guy who really doesn't have a clue.

This is why I asked if my formula that I posted in my original post to deduce if vertices, or neighbours, are adjacent or not is correct.


Ahhh. Adjacent cubes of usable space, changing from squares to cubes.

Yeah, I'd agree with the guy who said 26.

Why? Look on a standard 2D map. Any character in a square (not on the map edge!) has eight squares adjacent. Ok, next we layer the adjacent squares of the layer above him. This would be an additional eight squares PLUS the open square directly above, making nine. The same would hold true for the layer below. (another adjacent nine squares)

So, assuming a flyer in open space, with no characters or terrain around them, you have 8+9+9 or 26 cubes of adjacent spaces to begin moving into.

I thought your problem was more related to calculating LOF ranges and cubic distance. I'd still recommend my previous post to count the cubes (length and height) and (I incorrectly said to multiply before...) use the Pythagorean Theorem to find your actual used range.

[llyrghmnghyll]

Yeah, huh, I'm lost and it's not because I'm not mathematically inclined, it's because I can't even understand at this point if you are asking a question or making a point.

If we assume a vertice is the requirement for adjacency then there are 9+9+8 adjacent characters to any other character.

However since a 2D vertice of a square stretched into 3 dimensions becomes a line of a cube then you could assume that you are actually only adjacent to other lines, which would give you 5+5+8=18 possible adjacent cubes. Personally this makes more sense to me.

And just count cubes for line of fire.

[Dikarika]

Yeah, huh, I'm lost and it's not because I'm not mathematically inclined, it's because I can't even understand at this point if you are asking a question or making a point.

With VGA, he's doing both.

Its his M.O. to seemingly ask something he already thinks he has figured out.
:squareeye

[VGA d1sc1pL3]

Ahhh. Adjacent cubes of usable space, changing from squares to cubes.

Yeah, I'd agree with the guy who said 26.

Why? Look on a standard 2D map. Any character in a square (not on the map edge!) has eight squares adjacent. Ok, next we layer the adjacent squares of the layer above him. This would be an additional eight squares PLUS the open square directly above, making nine. The same would hold true for the layer below. (another adjacent nine squares)

So, assuming a flyer in open space, with no characters or terrain around them, you have 8+9+9 or 26 cubes of adjacent spaces to begin moving into.

I thought your problem was more related to calculating LOF ranges and cubic distance. I'd still recommend my previous post to count the cubes (length and height) and (I incorrectly said to multiply before...) use the Pythagorean Theorem to find your actual used range.

I can see why it may be 26 adjacent cubes, but wouldn't vertices have to be adjacent? That is why I came up with 18 cubes. Is my thinking wrong on this?

[VGA d1sc1pL3]

However since a 2D vertice of a square stretched into 3 dimensions becomes a line of a cube then you could assume that you are actually only adjacent to other lines, which would give you 5+5+8=18 possible adjacent cubes. Personally this makes more sense to me.

And just count cubes for line of fire.

This is my thoughts exactly, and how I came up with 18 adjacent cubes, instead of 26 adjacent cubes as some would argue.

Again, I agree, we use the cubes for LOF.

[Dikarika]

I AM making vertices adjacent.

You are not (or are somehow not counting some squares...).

Your flyer is in a 3x3x3 cube. It is in the center block of said cube. You have 26 blocks remaining.

26 is the correct number of adjacent 3d squares.

[VGA d1sc1pL3]

With VGA, he's doing both.

Its his M.O. to seemingly ask something he already thinks he has figured out.
:squareeye

So true, you have profiled me correctly. LOL! But so many times I think I have all it all figured out, I'm proven wrong. I always try to do my homework first before posting a question.

[llyrghmnghyll]

I AM making vertices adjacent.

You are not (or are somehow not counting some squares...).

Your flyer is in a 3x3x3 cube. It is in the center block of said cube. You have 26 blocks remaining.

26 is the correct number of adjacent 3d squares.

Possibly, It's up for debate.

on a 2D plane Vertices are counted as adjacent. If we take that literally to 3D then yes 26 is the correct answer. However Mathematically a 2 Dimensional vertice stretched into the 3rd dimension constitutes a line (or line segment for the purpose of a cube). So we can say that because our spaces have gone from 2D to 3D our vertice has gone from 0D to 1D, it has become a line segment. Now our cube is then adjacent by a line segment to 8 adjacent cubes, 5 cubes above, and 5 cubes below.

The mathematics answer is more logical to me, but so long as your play group agrees on which definition your sticking to it really doesn't matter.

[Dikarika]

I don't really see how adjacency can be a debate. The blocks are adjacent to each other, therefore, they are adjacent. It does not matter the connection between them, just that they lie adjacent to one another.

Any other "view" of three dimensional space is not "100% 3D". Its more 2.5D, like the old Duke Nukem game.

I'd love to put up a diagram and get into this further, but its difficult to do with text.

[llyrghmnghyll]

I don't really see how adjacency can be a debate. The blocks are adjacent to each other, therefore, they are adjacent. It does not matter the connection between them, just that they lie adjacent to one another.

Any other "view" of three dimensional space is not "100% 3D". Its more 2.5D, like the old Duke Nukem game.

I'd love to put up a diagram and get into this further, but its difficult to do with text.

Top Layer

T1T2T3
T4T5T6
T7T8T9

Middle Layer

M1M2M3
M4M5M6
M7M8M9

Bottom Layer

B1B2B3
B4B5B6
B7B8B9

Now assume Cap is standing in the middle layer at M5

In 2D space he's considered adjacent to M1-M9 (But not adjacent to M5)

If we go into 3D space and stretch our square to a cube, then our vertices where Cap was adjacent to M1, M3, M7, and M9 are now vertical lines. If the line is what we are now going by we are not adjacent to
T1, T3, T7, T9, B1, B3, B7, or B9, as they are only connected to Cube M5 by a vertice in 3 dimensions.

So the question is what constitutes adjacent in 3D Vertice or line?

[Gentlegamer]

Now add facing rules for even more 3D fun!!11!!11

[Dikarika]

Top Layer

T1T2T3
T4T5T6
T7T8T9

Middle Layer

M1M2M3
M4M5M6
M7M8M9

Bottom Layer

B1B2B3
B4B5B6
B7B8B9

Now assume Cap is standing in the middle layer at M5

In 2D space he's considered adjacent to M1-M9 (But not adjacent to M5)

If we go into 3D space and stretch our square to a cube, then our vertices where Cap was adjacent to M1, M3, M7, and M9 are now vertical lines. If the line is what we are now going by we are not adjacent to
T1, T3, T7, T9, B1, B3, B7, or B9, as they are only connected to Cube M5 by a vertice in 3 dimensions.

So the question is what constitutes adjacent in 3D Vertice or line?

Wait, hold up.

Before you jump to three dimensions, what constitutes adjacency on the standard heroclix map?

Four squares are adjacent by line, and four squares are adjacent by vertex.

So why exactly are we changing the rules when we jump to three dimensions?

You are all over complicating adjacency in three dimensions. If your are next to it, you are adjacent. In a cubic space, it is 26 squares.

No other answer is correct, there is no "optional way" to see it.

You are either using ALL adjacent squares, or you are not using all three dimensions.

[llyrghmnghyll]

Four squares are adjacent by line, and four squares are adjacent by vertex.

So why exactly are we changing the rules when we jump to three dimensions?


We aren't. We are using the exact same rules. If the plane we are considering is height it's 4 by line, 4 by vertex, If the plane we are considering is width it's 4 by line, 4 by vertex, If the plane we are considering is Depth it's still the same.

the only way the other 8 squares are adjacent is if we actually change the rules for 3D. 18 squares are adjacent so long as we consider each dimension according to the planar rules established for the 2D game.

[VGA d1sc1pL3]

Possibly, It's up for debate.

on a 2D plane Vertices are counted as adjacent. If we take that literally to 3D then yes 26 is the correct answer. However Mathematically a 2 Dimensional vertice stretched into the 3rd dimension constitutes a line (or line segment for the purpose of a cube). So we can say that because our spaces have gone from 2D to 3D our vertice has gone from 0D to 1D, it has become a line segment. Now our cube is then adjacent by a line segment to 8 adjacent cubes, 5 cubes above, and 5 cubes below.

The mathematics answer is more logical to me, but so long as your play group agrees on which definition your sticking to it really doesn't matter.

Very sweet. Thanks for the help. 26 adjacent cubes it is.

[VGA d1sc1pL3]

I don't really see how adjacency can be a debate. The blocks are adjacent to each other, therefore, they are adjacent. It does not matter the connection between them, just that they lie adjacent to one another.

Any other "view" of three dimensional space is not "100% 3D". Its more 2.5D, like the old Duke Nukem game.

I'd love to put up a diagram and get into this further, but its difficult to do with text.

With a few of your guys' help, I see my initial 18 is incorrect, and that 26 is correct. Gotta love math! Math is the science of the universe, and God's way of showing us He has sense of humor.