## INFINITE_PLANE

### INFINITE_PLANE

How exactly is infinity made? Is it actually an infinite plane or does it end eventually? Does it fail to work for anyone else on 0.4?

### Re: INFINITE_PLANE

for anyone who isn't sure what he's talking about:

"Dream as if you'll live forever,

Live as if you'll die today." -James Dean

### Re: INFINITE_PLANE

Way to go, Ratchet.Ratchet wrote:for anyone who isn't sure what he's talking about:

A tragedy is commonplace but in the end they go away.

### Re: INFINITE_PLANE

Derailment: I'm used to other forums where people post memes and cat pics on spoilers so they don't annoy people too much (esp. mods).

It'd actually be pretty cool. And I can say that now cuz he-who-must-not-be-named can't use my vote in his dissertation of why we need spoilers.

P.S. what team would I be on, Z-man?

It'd actually be pretty cool. And I can say that now cuz he-who-must-not-be-named can't use my vote in his dissertation of why we need spoilers.

P.S. what team would I be on, Z-man?

"Dream as if you'll live forever,

Live as if you'll die today." -James Dean

### Re: INFINITE_PLANE

I'd support spoiler tags for that, but have to note there are at least two alternatives available already:

1. Link or attach, don't embed.

2. Don't post them.

On the original topic, yes, it actually is an infinite plane. Well, on hardware where we know it's not supported, only an almost infinite plane. See, OpenGL uses projective geometry (not exactly for the math nerds, but close enough) for its input; points don't just have three coordinates (x,y,z), they have four (x,y,z,w), and four-coorinate-tuples that only differ by a positive factor are considered equivalent. So (x,y,z,w) and (2x, 2y, 2z, 2w) are the same point. And if w is not zero, you can always take the equivalent point (x/w, y/w, z/w, 1) instead. That's the normed form for regular points, and if you give OpenGL a three-vector (x,y,z), it is automatically internally expanded to (x,y,z,1).

And infinite points are just the case where w is 0 and you can't normalize the coordinates to (x', y', z', 1). Look at the limit of the normed form of (x,y,z,w) as you send w to zero: the first three coordinates go to infinity in the direction given by (x,y,z). That's what we use for the infinite plane. For fully functional OpenGL drivers, they should be no problem; the math that maps screen pixel coordinates to texture coordinates is beautiful and simple when expressed in projective geometry. But unfortunately, too many drivers are optimized for the common, boring, normalizable part of projective space because that's what everyone else is using exclusively.

1. Link or attach, don't embed.

2. Don't post them.

I'll have to count your post as half a point for team Evil Empire, it's not exactly not mentioning him. Not removing it because it is unlikely team Terror latches on to it. And if they do, one point for them. Rrrrisky play. Like tickling your sibling.Ratchet wrote:P.S. what team would I be on, Z-man?

On the original topic, yes, it actually is an infinite plane. Well, on hardware where we know it's not supported, only an almost infinite plane. See, OpenGL uses projective geometry (not exactly for the math nerds, but close enough) for its input; points don't just have three coordinates (x,y,z), they have four (x,y,z,w), and four-coorinate-tuples that only differ by a positive factor are considered equivalent. So (x,y,z,w) and (2x, 2y, 2z, 2w) are the same point. And if w is not zero, you can always take the equivalent point (x/w, y/w, z/w, 1) instead. That's the normed form for regular points, and if you give OpenGL a three-vector (x,y,z), it is automatically internally expanded to (x,y,z,1).

And infinite points are just the case where w is 0 and you can't normalize the coordinates to (x', y', z', 1). Look at the limit of the normed form of (x,y,z,w) as you send w to zero: the first three coordinates go to infinity in the direction given by (x,y,z). That's what we use for the infinite plane. For fully functional OpenGL drivers, they should be no problem; the math that maps screen pixel coordinates to texture coordinates is beautiful and simple when expressed in projective geometry. But unfortunately, too many drivers are optimized for the common, boring, normalizable part of projective space because that's what everyone else is using exclusively.

### Re: INFINITE_PLANE

Maybe if I read it a few more times it will make sense. As of now, the only part I get is that as w approaches zero the 3 dimensional vector approaches infinity.

Last edited by Z-Man on Fri Aug 21, 2015 7:48 pm, edited 1 time in total.

**Reason:***She looked really happy and excited about that book.*"Dream as if you'll live forever,

Live as if you'll die today." -James Dean

### Re: INFINITE_PLANE

How do I get on team potato?Z-Man wrote: I'll have to count your post as half a point for team Evil Empire, it's not exactly not mentioning him. Not removing it because it is unlikely team Terror latches on to it. And if they do, one point for them. Rrrrisky play. Like tickling your sibling.

bye

### Re: INFINITE_PLANE

Ratchet wrote:By double-posting! Spamming nooooooob.Magi wrote:How do I get on team potato?Z-Man wrote: I'll have to count your post as half a point for team Evil Empire, it's not exactly not mentioning him. Not removing it because it is unlikely team Terror latches on to it. And if they do, one point for them. Rrrrisky play. Like tickling your sibling.

Dunno how that happened

Last edited by Magi on Thu Aug 20, 2015 10:55 pm, edited 1 time in total.

bye

### Re: INFINITE_PLANE

By double-posting! Spamming nooooooob.Magi wrote:How do I get on team potato?Z-Man wrote: I'll have to count your post as half a point for team Evil Empire, it's not exactly not mentioning him. Not removing it because it is unlikely team Terror latches on to it. And if they do, one point for them. Rrrrisky play. Like tickling your sibling.

"Dream as if you'll live forever,

Live as if you'll die today." -James Dean

- Jonathan
- A Brave Victim
**Posts:**3392**Joined:**Thu Feb 03, 2005 12:50 am**Location:**Not really lurking anymore

### Re: INFINITE_PLANE

OpenGL doesn't/shouldn't care if you goZ-Man wrote:On the original topic, yes, it actually is an infinite plane. Well, on hardware where we know it's not supported, only an almost infinite plane. See, OpenGL uses projective geometry (not exactly for the math nerds, but close enough) for its input; points don't just have three coordinates (x,y,z), they have four (x,y,z,w), and four-coorinate-tuples that only differ by a positive factor are considered equivalent. So (x,y,z,w) and (2x, 2y, 2z, 2w) are the same point. And if w is not zero, you can always take the equivalent point (x/w, y/w, z/w, 1) instead. That's the normed form for regular points, and if you give OpenGL a three-vector (x,y,z), it is automatically internally expanded to (x,y,z,1).

And infinite points are just the case where w is 0 and you can't normalize the coordinates to (x', y', z', 1). Look at the limit of the normed form of (x,y,z,w) as you send w to zero: the first three coordinates go to infinity in the direction given by (x,y,z). That's what we use for the infinite plane. For fully functional OpenGL drivers, they should be no problem; the math that maps screen pixel coordinates to texture coordinates is beautiful and simple when expressed in projective geometry. But unfortunately, too many drivers are optimized for the common, boring, normalizable part of projective space because that's what everyone else is using exclusively.

*beyond*infinity. Such a shame that mere infinity can break some renderers. I wonder what such renderers are doing. I'm not sure if I've ever seen it. I certainly don't have a recollection of it. What does it look like? How would you even 'optimize' this, with the correct process being rather streamlined already?

ˌɑrməˈɡɛˌtrɑn

### Re: INFINITE_PLANE

Well, you can save a couple of multiplications and additions if you assume all point vectors have their projective component set to 1 and all regular transformation matrices have the first row (or column) set to 1,0,0,0. It can also happen that they normalize vectors in between (no, I would not know why) and get division by zero that way. All I know is that it simply does not work properly for some drivers. Drivers and hardware are not, it seems, tested against the specification, but against common clients.

- Jonathan
- A Brave Victim
**Posts:**3392**Joined:**Thu Feb 03, 2005 12:50 am**Location:**Not really lurking anymore

### Re: INFINITE_PLANE

Most of that seems unlikely. Apparently w_o=0.001 is handled correctly when infinity is turned off, suggesting it isn't simply discarded. By the time we get to clip coordinates, we have w_c=-z_e using a standard projection matrix. At that point we have a similar w_c for any kind of perspective rendering, no matter what happened before. Maybe it's normalization for no reason. My carefully considered verdict: whatever.

ˌɑrməˈɡɛˌtrɑn

### Re: INFINITE_PLANE

I agree! But the observed fact was that it did not work properly on some cards/drivers. I think it was back in the day when drivers needed to do all the transformations on the CPU (so saving a mult meant something; today it probably hurts) and there was a greater variety of GPU manufacturers. Today, it seems even the worst offender that's still around (Intel) gets it right.Jonathan wrote:Most of that seems unlikely.

- Jonathan
- A Brave Victim
**Posts:**3392**Joined:**Thu Feb 03, 2005 12:50 am**Location:**Not really lurking anymore

### Re: INFINITE_PLANE

I'm thinking of so many possible reasons, and I don't even know what it looks like. I should just stop. I guess I'll vanish again.

ˌɑrməˈɡɛˌtrɑn

### Re: INFINITE_PLANE

Wait, what?

Z-man, what does your edit even mean?

"She looked really happy and excited about that book."

I don't think there was anything in the original post that required censorship.. lol? Wut?

Z-man, what does your edit even mean?

"She looked really happy and excited about that book."

I don't think there was anything in the original post that required censorship.. lol? Wut?

"Dream as if you'll live forever,

Live as if you'll die today." -James Dean