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Geek Culture / I made a 4d raycaster! Well... kind of...

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Neuro Fuzzy
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Posted: 3rd Apr 2011 06:14 Edited at: 4th Apr 2011 21:36
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It's not like it's overly-complex, well worked out, detailed, or that reuseable, but it's still kinda cool! I used matrix math/whatevs to project lines from a 3d "screen" further into 4d space. This is the result:



You have to project 4d space into 3d space first. So, each pixel represents about 50 z values. So, for each x and y pixel, and for each z pixel, you project that point into 4d space, and take samples every once in a while. I took 20 samples. This is the same as the "pick screen" command, except having 2 values as the pixels of the screen, you have 3 values representing a point in your 3d screen.

Then, I had a function to determine how close the 4d sample point was to the object. The more iterations, the more accuracy. The .gif shows 10 iterations.

That means that the deepest part of the loop is called 200*200*50*20*10=400,000,000 times.

It actually didn't take all that long to render (10-20 mins for 380 frames), because the deepest part of the loop isn't all that math intensive.

The object that is being shown (on the left) is actually this:
http://www.youtube.com/watch?v=pfLncaQancI

the rightmost object is based on the cosine of the distance of the point from the origin. Imagine a series of concentric circles around the origin. Just in 4d O_O
[edit] and remember, this IS 4d. nothing is changing except your view position.
[edit2] also, I just discovered some really cool shapes. I'm in the process of rendering some more animated gifs
[edit3] added another image.
[edit4] aaaand another (the middle one). It's another julia set, like the lefttmost one, but way higher quality. Its 200*200*50*50*20=2 billion calculations per frame at the deepest part of the loop.

[edit] other 4d pics:


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C0wbox
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Posted: 3rd Apr 2011 06:39
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O(n^4) complexity !



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Cliff Mellangard 3DEGS
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Posted: 3rd Apr 2011 13:01
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Quote: "It's not like it's overly-complex, well worked out, detailed, or that reuseable, but it's still kinda cool! I used matrix math/whatevs to project lines from a 3d "screen" further into 4d space. This is the result:"

Pretty cool

You aint intrested in trying to do some simple snippets of voxel stuff with dbp?
Should be simplier then this stuff for you?
Could be good to learn from someone that actually is good at math

Iam constantly taking short cuts because i suck at math!
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Interplanetary Funk
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Posted: 3rd Apr 2011 13:12
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this confuses me. isn't the 4th dimension time? if so how are you casting a ray through to the future/past? :S

I hate math...

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Quik
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Posted: 3rd Apr 2011 13:45 Edited at: 3rd Apr 2011 13:48
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iam strongly doubting its 4d, iam very sure thats simply a pretty cool 3d effect.

edit:
Quote: "[edit] and remember, this IS 4d. nothing is changing except your view position."
what? so, because my view position is changing, its 4d?
doesnt that mean all games and movies are 4d..?


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bitJericho
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Posted: 3rd Apr 2011 14:23 Edited at: 3rd Apr 2011 14:28
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4d is another plane with right angles to the x,y, and z planes.

For example, 1d is the x axis. 2d is the x and y axis, and those two planes are at right angles to eachother. 3d is the x y and z planes, and all three planes are at right angles to eachother. 4d is the x,y,z, and 4d plane (i think there is a term for it, i forget it though). The 4d plane is at right angles to all the others.

Yes, I realize you can't really envision that, but it's mathematically possible, which is how he came up with those renders.

Interestingly enough, some theories to explain the universe expanding at an accelerating rate go like this. The universe is actually 4d and not 3d (we can only see in 3d). The universe is expanding like a balloon, but in the 4th dimension. If you were to stand on a balloon blowing up and if you look at any other part of the balloon it would look like those points are accelerating away from you. This may be happening to the universe, but in the 4th dimension. So in all directions the universe is expanding away from you no matter where you stand in the universe.

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Interplanetary Funk
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Posted: 3rd Apr 2011 14:30
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so in this sense it's less of a dimensional sense and more of geometrical sense?

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bitJericho
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Posted: 3rd Apr 2011 14:35 Edited at: 3rd Apr 2011 14:44
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It's a 4d render rendered on a 2d plane.

It's like when you view a 2d picture of a cube. The cube is really 3d but it's rendered in 2d.

In this with these renders, it's lines in 4d but rendered in 2d.

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Interplanetary Funk
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Posted: 3rd Apr 2011 16:13
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This is making my brain hurt. So you're rendering the 4th dimension along with 3 others in a 2D format (which isn't so hard to grasp) the thing that's confusing me is that my understanding of the 4th dimension is that it's time so it confuses me that you are rendering time. :S

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budokaiman
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Posted: 3rd Apr 2011 16:21 Edited at: 3rd Apr 2011 16:22
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He's not rendering time, he's rendering the 4th spacial dimension.

Also, that is really cool, I like the first one the most.

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Cliff Mellangard 3DEGS
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Posted: 3rd Apr 2011 16:48
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Why argue ! i want or fuzzy friend to do some voxel stuff in dbp

I never understud how fun it could be to do your own 3d-4d effects until i whas trying to do an simple wolfenstein clone.
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Neuro Fuzzy
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Posted: 3rd Apr 2011 20:09
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Sure! I'll help with some voxel stuff.

The thing is... If AppGameKit is like DBPro is... in DBPro there are a bunch of extra lines for debugging and stuff for each line of code written (or that's what I've heard), and so the time needed for heavily looping stuff like this is a lot longer. This uses matrix multiplications and transformations, which are math-intensive. I could definitely help with a stripped-down version of this kind of math!

Also, 4d is really confusing. With normal rendering you can just be like "Oh yeah, if I rotate it like 80 degrees on the z axis I can see this cool looking part of the object". In 4d... Things are waaaay different spatially. One of the first things you have to account for, is that in 4d rotation isn't defined around an axis, only around a plane. If an object looks like it's morphing, it's really not, it's just rotating and moving in the fourth dimension!

In 3d, if an object is infinitely far away, you can still say "it's in that direction". If you had a 2d screen looking at an infinitely far away point, and rendered that point as a dot on the screen, you could have a dot in the middle of your screen. So then... Say you had one of the left two objects on your 3d screen. If you saw the object shrinking and shrinking until it's just a point, then all it's doing is getting further away from you!

It's creepy seeing the parallels between a 2d object rotating in 3d space, and a 3d object rotating in 4d space. There are some good images here.

Also, that shape I'm drawing in the top two (called a julia set), is defined by iterating the function Z=Z^2+C, where C is constant, Z is a complex number, and the first value for Z is the coordinate in space you're checking. So lets say you start out with some coordinate Q, you get:
Z=Q (iteration 0)
Z=Z^2+C (iteration 1)
Z=(Z^2+C)^2+C (iteration 2)
Z=((Z^2+C)^2+C)^2+C) (iteration 3) etc.

so after a certain number of iterations, if Z's length keeps getting larger and larger, that original point, Q, is NOT part of the julia set. If it stays bounded (IE always close to the origin), then Q IS part of the julia set.

The thing that's really cool is... Well, usually people just use complex numbers as Z=a+bi. With some stretch of the basic principles of math, you can create a 4d "quaternion", Z=a+bi+cj+dk, where i j and k are all imaginary constants. There's also a higher dimensional thing called an "octonion", that has 7 constants. So, you can plug in complex, quaternion, or octonion number equations in the equation, and still get a cool shape! (eerrrrm, there are a bunch of mathematical implications... but all I know it as is a cool shape. derp.)

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TheComet
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Posted: 3rd Apr 2011 20:35
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That's really cool fuzzy! I wonder if you could extend this to the 5th dimension now

TheComet

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Neuro Fuzzy
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Posted: 3rd Apr 2011 20:43
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I kinda want to figure out how this guy made this video:


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PrimalBeans
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Posted: 3rd Apr 2011 22:27 Edited at: 3rd Apr 2011 22:29
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^^ he used magic pixy dust... lol thats neat...
Quote: "He's not rendering time, he's rendering the 4th spacial dimension.

Also, that is really cool, I like the first one the most.

"


I think there may be a tech jargon barrier.... cause the 4th dimension is time... in sceince terms.... when i see some one refur to the 4th dimension this is what i think.

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Indicium
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Posted: 3rd Apr 2011 22:38
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Mathematical Forth Dimension = This
Scientific Forth Dimension = Spacetime.
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PrimalBeans
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Posted: 3rd Apr 2011 23:02
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ah kk lol

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Neuro Fuzzy
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Posted: 4th Apr 2011 00:06 Edited at: 4th Apr 2011 00:07
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O_o

Whenever someone posts something about the fourth dimension, this argument ALWAYS happens! People keep saying "That doesn't make sense because the fourth dimension is time". OK Mr. Smartypants people on that side of the argument: Why is the fourth dimension time? Why can't the first dimension be time? Or the fifth dimension?

Besides, the whole idea of the theory of relativity is that there IS an extra dimension, in which a continuous volume exists (Like if you had a plane warped in the 3rd dimension).

The idea of "space" that most people have is "space" as it is portrayed in video games, where "time" is a given, and all you have to worry about is "space". It's THAT definition (and the same methods of transformation/projection) that is present here.

Also, just saw this:
Quote: "what? so, because my view position is changing, its 4d?
doesnt that mean all games and movies are 4d..?"

I wasn't clear, I meant that... well, take the middle picture for example: It looks like it's morphing and changing and bending, but it's not! It's just rotating in the fourth dimension. (This is "dimension" as defined in video games and math and is the most common definition of dimension! It's not like this is a physical simulation!)

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Quik
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Posted: 4th Apr 2011 00:18
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or maybe its simply rotating in the xyz axis? first is moving in the X and Z axis and the third is only "water" with ripples across the three axises?


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Diggsey
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Posted: 4th Apr 2011 00:50 Edited at: 4th Apr 2011 00:51
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Anything you display on a screen is 2D, so this is just as much 4D as anything you'd classify as 3D on a screen.

[b]
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Neuro Fuzzy
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Posted: 4th Apr 2011 01:03 Edited at: 4th Apr 2011 01:05
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Quote: "or maybe its simply rotating in the xyz axis? first is moving in the X and Z axis and the third is only "water" with ripples across the three axises?"

"the middle picture for example"
the middle picture is rotating in... iunno, the xw or yw or zw plane. one of those. The left one is rotating a *bit* in the w axis, but you can't really see it. The right one is also rotating in the w axis, but the geometry is so... weird that you can't really discern much.
[edit]
it's 4d as much as any video game is 3d.

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Insert Name Here
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Posted: 4th Apr 2011 01:09
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I DON'T UNDERSTAND

Okay, I get the idea that the Y axis is at 90degrees to the X axis, and the Z axis is at 90degrees to the Y, but after that, that's everything used up? There's nowhere for the w axis to go, surely? I can move left and right on the X axis, up and down on the Y axis, and forward and back on Z ... I can't go anywhere else!

"Sticks and stones may break my bones but words will never hurt me." That's a bit like saying Hey bullies! So yeah, this words thing isn't working, but I'll tell you what will
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Neuro Fuzzy
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Posted: 4th Apr 2011 01:17 Edited at: 4th Apr 2011 18:30
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Quote: "Okay, I get the idea that the Y axis is at 90degrees to the X axis, and the Z axis is at 90degrees to the Y, but after that, that's everything used up? There's nowhere for the w axis to go, surely? I can move left and right on the X axis, up and down on the Y axis, and forward and back on Z ... I can't go anywhere else!"


Imagine how a flatlander would feel if it saw a 3d object! "Surely there can't be anything perpendicular to the x and y axis!"
(better yet, lets ask flatlander)

But yeah... the 4th dimension is where there's an axis perpendicular to the x, y, and z axes.

New one. This one is similar to the other sphere-based one. So you have a series of concentric spheres, and you're moving away from it. Due to the near/far clipping planes, what's visible is just "onion" slices of the sphere. Also, the rings you see inside of each major ring are artifacts of the rendering method, because you just render a bunch of slices then add them together.

Aaaaand rendering the same object, in a glitched out way.

(the rows are based on the tangent of a number, but here you can get negative numbers, so besides just adding different slices of the object, you're subtracting :S )
[edit] I also think in that last image, since tangent has no maximum value, that the numbers were wrapping around.

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Quik
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Posted: 4th Apr 2011 02:30
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i still dont see it, as insert name here, all axises is already used up, can you explain to me, which way is the w axis going? up? down? left? right? "into or out of the screen?" thats xzy, now how can w be anything else?


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Interplanetary Funk
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Posted: 4th Apr 2011 02:32
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Maybe some basic maths? (now I understand what's going on)
I find things are easier to understand in maths.

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AndrewT
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Posted: 4th Apr 2011 02:44
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This is some really cool stuff! I love weird math things like this.

Quote: "i still dont see it, as insert name here, all axises is already used up, can you explain to me, which way is the w axis going? up? down? left? right? "into or out of the screen?" thats xzy, now how can w be anything else?"


A fourth spatial dimension doesn't actually exist--it's just an abstract mathematical concept--so you're never going to be able to visualize it.

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Diggsey
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Posted: 4th Apr 2011 02:47
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Quote: "all axises is already used up"


Only if there are 3 axis. In 4D there are 4 axis...

In 3d there's up/down, left/right, forward/backward. In 4d there's also ana/kata. Those last two are obviously not as common because we live in a world with (apparantly) only three spatial dimensions.

If you want to try to imagine it, think of what you get if you take a slice of a cube. You get a 2d square. If you take a slice of a 4d hypercube you get a 3d cube.

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Quik
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Posted: 4th Apr 2011 02:52
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ana/kata said to me.. nothing lol


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Neuro Fuzzy
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Posted: 4th Apr 2011 03:19
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If you try to think of it in the regular spatial terms we're all used to, you're probably never going to understand it, because it isn't what we're used to! It's not up down left right in out over under through around or between, because how everyone thinks of them the words refer to three dimensional geometry!

Quote: "A fourth spatial dimension doesn't actually exist--it's just an abstract mathematical concept--so you're never going to be able to visualize it."

It's not an abstract mathematical concept any more than 3d rendering in video games is an abstract mathematical concept. (not that you were saying otherwise, I'm just sayin' )

@Quick
You're a 2d person claiming the 3rd dimension is some stretched mathematical jargon!

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Neuro Fuzzy
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Posted: 4th Apr 2011 07:51 Edited at: 4th Apr 2011 07:52
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I just had an idea... Would anyone want a primitive 4d model editor? :3

[edit]

you could view an entire animation at once, as a static model!

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bitJericho
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Posted: 4th Apr 2011 12:33 Edited at: 4th Apr 2011 12:37
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Quote: "A fourth spatial dimension doesn't actually exist--it's just an abstract mathematical concept--so you're never going to be able to visualize it."


Um, as I stated in a previous post, the universe may very well have four spacial dimensions which accounts for the universe expanding at an accelerated rate in all directions away from us.

Due to it expanding in the fourth dimension, no matter where you stand the universe looks like it's accelerating away from you.

If you were to stand on a big balloon that's blowing up. And your friend was a few feet away. He would look to you like he was going away from you at an accelerating rate. But really, you're just standing there on your balloon at the same point you were at a moment ago.

The fourth dimension may well be there, we just can't see it because our eyes can only see in 3 dimensions.

If you lived in a 2d plane, where you couldn't see up or down (think like a cell), you would have no concept of up or down, you couldn't point to that direction, and you'd be on a forum saying there is no such thing.

Your limbs don't go into the fourth dimension (at least not that you could tell), so how would you point to it?

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AndrewT
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Posted: 4th Apr 2011 17:03 Edited at: 4th Apr 2011 17:18
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Quote: "Um, as I stated in a previous post, the universe may very well have four spacial dimensions which accounts for the universe expanding at an accelerated rate in all directions away from us."


The most accepted physical model of space has three spatial dimensions and one temporal dimension (Minkowski space). The fourth dimension as it's being used in Neuro Fuzzy's raycaster, however, is just a mathematical generalization of the rules for three dimensions. You could further generalize them and get a fifth dimension, or sixth, or as many as you want.

Though, I won't argue that a fourth spatial dimension certainly could exist.

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bitJericho
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Posted: 4th Apr 2011 18:45
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Perhaps one day we'll know for sure

Then we will have flying cars. Can't wait!

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Neuro Fuzzy
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Posted: 4th Apr 2011 19:03 Edited at: 4th Apr 2011 19:30
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Alright, now I'm determined to make a 4d model editor. I can't tell if it's been done before, however, because everything that says "4d" "5d" or "6d" that I can find on google, is just using the word "dimension" like they use "property", or like cinema 4d or something. Completely lame.
Quote: "he 4D modelshop, Creative Materials Centre is a one stop shop featuring the essential model making tools and materials for all your 3D Design"


I'd better call it "4d hypercube modeler" or something, so that google doesn't bury it under lame results xD

[edit]
There are also things in 4d that I've never even heard speculation about, like volume texturing or w clipping.

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bitJericho
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Posted: 4th Apr 2011 19:09 Edited at: 4th Apr 2011 19:11
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What'd be cool is rendering 4 dimensions in stereoscopic 3d. (In the same way one might render a 3d object in 2 dimensions). That'd be trippy!

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AndrewT
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Posted: 4th Apr 2011 19:21
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Quote: "What'd be cool is rendering 4 dimensions in stereoscopic 3d. (In the same way one might render a 3d object in 2 dimensions). That'd be trippy!"


Kind of like this:

http://www.urticator.net/maze/

Although I never could get it to work for me...

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Neuro Fuzzy
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Posted: 4th Apr 2011 19:44 Edited at: 4th Apr 2011 20:45
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D: Actually, a 4d maze wouldn't be all that hard... it would just look like crap without w clipping...
(I mean, imagine this without z clipping)
I wonder if w clipping would be practical...

*gets out 3d rendering textbook*

[edit]
Bah, it's hard to think what w clipping would even look like! Like (in our 3d screen space), if you had a line going from one point that was visible, to another point that was obscured, there's obviously a point of intersection where the line meets the object it's being obscured by. Does this point of intersection have to lie on a line or a plane??? I'm guessing a plane, but 4d is so unintuitive it's hard to think about it!

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zzz
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Posted: 4th Apr 2011 20:55 Edited at: 4th Apr 2011 20:58
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Quote: "rendering 4 dimensions in stereoscopic 3d."

3d-4d-3d?

Anyway, really nice work! Have you tried rendering hypercubes/spheres? I might have mixed up the names, the 4d cube is called a tesseract, right?


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Neuro Fuzzy
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Posted: 4th Apr 2011 21:34 Edited at: 4th Apr 2011 21:38
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Here's a low-quality rendering of a 4d cube using my current method:


It's not all there, but oh well. I'll definitely be putting up a bunch of cube pics once I get W clipping working.

And yeah, a 4d cube is a tesseract. Those and simplexes are popular 4d shapes

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Insert Name Here
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Posted: 4th Apr 2011 22:11
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It's just a blurry cube
Why don't I understaaaand

I kind of get that I'm never gonna be able to comprehend a fourth axis, and I sort of get the concept, but what purpose does this serve?

"Sticks and stones may break my bones but words will never hurt me." That's a bit like saying Hey bullies! So yeah, this words thing isn't working, but I'll tell you what will
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bitJericho
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Posted: 4th Apr 2011 22:18 Edited at: 4th Apr 2011 22:20
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If there is in fact a 4th dimension, then you could transport a traditional 3d being to any point in space in the universe as simply as taking a step to the left. So there are practical applications... well, if there is a 4th spacial dimension.

At least, that's my understanding of it, I'm not as expert as Neuro on the subject I just know the basics.

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Quik
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Posted: 4th Apr 2011 23:09
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Quote: "It's just a blurry cube
Why don't I understaaaand "


This.
And

Quote: "
I kind of get that I'm never gonna be able to comprehend a fourth axis, and I sort of get the concept, but what purpose does this serve?
"

This.


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Neuro Fuzzy
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Posted: 5th Apr 2011 00:06
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A cube viewed volumetrically would just look like a blurry square half the time O_O

It's this, just filled in, and without drawing the edge lines:


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Posted: 5th Apr 2011 00:15
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This is interesting:
http://4d.shadowpuppet.net/

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Quik
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Posted: 5th Apr 2011 00:19
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Very interesting, however i am still just seeing 3d cubes inside 3d cubes meaning its still 3d


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nackidno
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Posted: 5th Apr 2011 00:36
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By that logic, any "3D-dimensional" pictures you see on your screen is in fact 2D.

I kind of get this 4D thing, you just have to think the "right" way.

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Neuro Fuzzy
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Posted: 5th Apr 2011 01:15
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^^What nackindo said.

You don't see anything in 3d. The best we can get is the faux-3d effect produced by our eyes.

Why is there still debate on that? xD

Also, nackidno, my favorite thing about this raycaster is the 3d screen. So instead of having a 1280x800 monitor, you'd have a 800x800x800 monitor. And then... Well, you know how in 3d, if you point at a pixel on your screen (And you're playing a video game or something), you can project a line into your monitor, and so that single point represents an entire line? Well if you select a point on your 3d screen, that point represents an entire line. X_X

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Slow Programmer
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Posted: 5th Apr 2011 02:53
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For those having trouble with 4th dimensional objects maybe Carl Sagan can help

http://www.youtube.com/watch?v=UnURElCzGc0

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Design Runner
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Posted: 5th Apr 2011 23:39
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This ad appeared at the top of google when I was searching for terrain modeling applications. Turned out be Autodesk Navisworks... I'm a bit confused.

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PrimalBeans
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Posted: 7th Apr 2011 11:14 Edited at: 7th Apr 2011 11:30
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So im kind of lazy so i didnt read everything... but how in the world can you add a spacial 4th dimension... and how is mathamatical and scientific 4th different??? Maybe computer 4th is different... 4th dimensional is slang... So heres my deal.. you only need 3 dimensions to define an object. Period. Adding the forth dimension adds in the possibility for animation... so what else is there... that can be added spatially... When you say that math 4d = this what the hell do you mean exactly... or are you sure you even know... other then its slang for some design that someone developed.. btw... what im looking at is cool but im not sure i understand what is 4d about it other then the time dimension that is displayed in animation... just curious if anyone can defy my stuborn point of view or if there is something im blatently missing..

EDIT: Basically after reading the rest of the posts.. is this is some kind of term for 'optical illusion...' so heres my take on it... you have a very cool design your working on, and a very valid program youve created.... its just the terms are very sh!tily named.. and very missleading... as for who ever says that the difference is the math and science 4d... obviously has no idea what they are talking about. (Sorry... just dont bs ppl if you dont really know...) It would be funny to think that math and science dont coincide.... I could just see our mathmaticians and scientists at conventions together just ready to kill eachother because they cant agree on anything... lol.

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