If you are confused, here is how I understand it best:
(Spoilerized for space reasons, if tl;dr then you can skip but not my fault if you don't understand other stuff)
If you're having trouble picturing n-dimensional objects, start by imagining a single geometric point.
A 1D point can be referenced like so: (X)
A 2D point is referenced like this: (X,Y)
While a 3D point is like this: (X,Y,Z)
And a n-D point is like this (a1,a2,a3...an)
Now, imagine seperate each of those numbers.
A 1D point (X) can be represented on a number line.
Next add another number line for Y, this is 2-dimensional.
You can continue the process for n-dimensions
A single n-D point has one position on each of these dimensions.
Now onto solids!
I'm going to spend a little less time on this because I'm starting to confuse myself,
but here it is:
Start with a box. It has length width and height.
If you take the box and cut out one of the dimensions, you have an infinite array of 2D squares.
If you cut a second dimension out, you have an infinite number of line segments.
These are all solids.
Wait a sec? Line segments! Those could go on a -number line-.
3 line segments could represent the box's dimensions in height length and width!
*Drumroll please*
A 3D box can be visualized like this-
0--------[XXXX]-0
0----[XXXX]-----0
0------[XXXX]---0
And you can add infinite dimensions the same way, an n-D point is always a point on each line, a segment on each line is always a solid.
Points A and B in 8 dimensions (when they're in the same position they're shown on top of each other)
0-A--B0 0--B-A0
0-B-A-0 0--A--0
B
0-A---0 0-B-A-0
B
0B-A--0 0-A-B-0
(it might get hard to do with large numbers of objects coinciding on the same position on one line,
but I still think it's better than silly multiple 3D image nonsense)
In game you could have each axis centered on the character
and only show things within a certain distance on each dimension, like the origin on a number line.
That way moving to a position is as easy as sliding along each axis until you're at the same point.
If you run into something then that would be the puzzle part of the game.
2D example and conversion to lines, X is the player, Y is the target, @ is the obstruction
-----
--Y--
--@--
--X--
-----
(V)<=Obstruction
(D1)0--X--0 (D2)0--X@Y0
@
Y
The character would have to be moved on other dimensions until you can get around it.
Reverting to base 2 when doing math with hexadecimal is a similar process.
Higher bases are generally hard to understand, so are higher dimensions.
That means you have to revert to 1D and solve.
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Topic: 5 and nth (spacial)dimensional block based puzzle platformers (Read 3642 times)