> It's news to me that POV supports splines in the first place.

It does bezier patches which are the closest you are going to get to 
describing "any curved surface" mathematically.

> Only if you have the original curve to hand.

What if you designed the curve by seeing how it turned out after 
sub-divison?  Blender works like this, you can edit the vertices of a very 
rough triangle mesh and see how the perfectly smooth surface reacts in real 
time.  You are then defining the "original curve" by the crude mesh.

> If you *insist* on using triangles, you're going to need a hell of a lot 
> of them to fake the appearence of a good curve. That means you either need 
> a triangle mesh of absurd dimensions, or you need to generate the 
> triangles on the fly.

Exactly.  This is what all film-quality renderers do.

> What all known computer games do is use a static, very low resolution 
> triangle mesh and then smother it with lashes of low-level trickery to 
> give a vague semblance of curvature.

Of course, because that method gets the highest quality output in realtime. 
And it's very easy to have two (or more) versions of a mesh at different 
resolutions, eg for stills rendering, close-up real-time rendering, far away 
rendering etc.  When you have a mathematical surface rendered directly it's 
very difficult to speed it up!

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scott wrote:
>>> Imagine how long that would take to render in POV, media, DOF, 
>>> refraction! And I don't think the result would be *that* different 
>>> (maybe the refraction would look slightly different, but a normal 
>>> person probably couldn't tell which one was correct, especially 
>>> during animation).
>>
>> It wouldn't have all those glitches that games have though. (Like 
>> grass that rotates as you run past it, or "mist" that has sharp edges 
>> where it intersects things.)
> 
> I don't think modern games have those glitches anymore, the grass is 
> true 3D geometry not just billboards, and the mist billboards usually 
> compare depths of existing pixels to avoid the hard edges with 
> geometry.  Some games even have true 3D volume textures and rendering 
> for smoke and mist, I don't know if Crysis uses this or just cheats with 
> multiple billboards.  Maybe the glitches you mention are on a game from 
> 5 years ago or on a very badly written modern one.

HalfLife 2: Episode 2 has mist in one section. Looks really 
impressive... until it intersects something.

Mind you, POV-Ray has the exact same problem, until you turn the 
settings up so high that it takes 82+ hours to render a single frame...

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Ever heard of subdivision surfaces, Andrew?  You can get a perfectly 
round sphere out of a plain cube cage by specifying up to 5 iterations. 
  This is the norm in the industry, and there's also NURBS.

Pixar got its own gig with REYES in Renderman, basically an automatic 
triangulator breaking down every geometry on screen into triangles until 
they are less than one pixel wide in the final resolution.  It probably 
breaks them down by subdivision as well, since one of the well-known 
algorithms has the name of one of Pixar founding fathers...

No one designs multibillion triangle meshes by carefully moving them one 
by one.

BTW:
http://www.3d-coat.com/v3_voxel_sculpting.html

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nemesis wrote:
> Ever heard of subdivision surfaces, Andrew?  You can get a perfectly 
> round sphere out of a plain cube cage by specifying up to 5 iterations. 

Yes. But the resulting surface can only be controlled by the 8 original 
cube corners. That's not much control.

> No one designs multibillion triangle meshes by carefully moving them one 
> by one.

And yet, in all known editors, moving triangle corners around one at a 
time is the only available editing operation...

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Invisible wrote:
> nemesis wrote:
>> Ever heard of subdivision surfaces, Andrew?  You can get a perfectly 
>> round sphere out of a plain cube cage by specifying up to 5 iterations. 
> 
> Yes. But the resulting surface can only be controlled by the 8 original 
> cube corners. That's not much control.

If you need refinement, you do loop cuts over the control cage and extrude.

>> No one designs multibillion triangle meshes by carefully moving them 
>> one by one.
> 
> And yet, in all known editors, moving triangle corners around one at a 
> time is the only available editing operation...

You have your head in the 80's.  Do you ever click on the links I provide?

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>>> No one designs multibillion triangle meshes by carefully moving them 
>>> one by one.
>>
>> And yet, in all known editors, moving triangle corners around one at a 
>> time is the only available editing operation...
> 
> You have your head in the 80's.  Do you ever click on the links I provide?

Really?

Everybody says that Wings3D is the best editor going, but all it does is 
manipulate triangle meshes, one point at a time. Last time I checked, it 
didn't exist in the 80s.

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Invisible wrote:
>>>> No one designs multibillion triangle meshes by carefully moving them 
>>>> one by one.
>>>
>>> And yet, in all known editors, moving triangle corners around one at 
>>> a time is the only available editing operation...
>>
>> You have your head in the 80's.  Do you ever click on the links I 
>> provide?
> 
> Really?
> 
> Everybody says that Wings3D is the best editor going, but all it does is 
> manipulate triangle meshes, one point at a time. Last time I checked, it 
> didn't exist in the 80s.

I'm used to Blender, not Wings, but I'm pretty sure they share the same 
operations and that means extruding and controlling and selecting 
friggin' amounts of vertices at the same time by mean of vertex loops 
and rings.  Let alone by sculpting like in the link I provided.

Not knowing how to use such operations doesn't mean they don't exist. 
Almost never I've had to move a single vertex alone.

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Invisible wrote:
> scott wrote:
> 
>> I don't understand the fascination with perfect mathematically 
>> described surfaces, they are inflexible and slow to render.
> 
> Really? I was under the impression that splines can describe any 
> possible surface. Triangles, on the other hand, can only give a crude 
> approximation to curves.

This is not true.  Just like triangles splines can only approximate most 
curves, they just give a different approximation.


Back to the initial topic -- the main reason why I like the ability to 
support arbitrary surfaces is that isosufraces are such a useful 
modeling tool.  Sure you could always tessilate them to triangles, but I 
don't think that doing so correctly, quickly, and automatically is that 
easy of a problem -- particularly if you want to treat the normals 
correctly.

Of course if you have a really nice modeler the added value of 
isosurfaces is less, so it makes sense to go with a pure-triangle 
approach.  For a text-based editor like Povray, however, I think having 
a larger vocabulary of surfaces is extremely handy.

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scott wrote:
> I don't understand the fascination with perfect mathematically described 
> surfaces, they are inflexible and slow to render.  If you use 
> sub-divided triangle meshes you can make the output perfectly smooth all 
> the time and of course do whatever transformations you like very easily 
> by just transforming every vertex.

True, as long as you dynamically adjust the subdivision level so that 
triangles aren't too large.  Unfortunately, nobody actually does that. 
In reality, everyone pre-subdivides the meshes.

Mathematically described surfaces don't have to be subdivided, because 
they're rendered at the pixel level.

...Chambers

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>> Ever heard of subdivision surfaces, Andrew?  You can get a perfectly 
>> round sphere out of a plain cube cage by specifying up to 5 iterations.
>
> Yes. But the resulting surface can only be controlled by the 8 original 
> cube corners. That's not much control.

It's very simple to add in more control points, every time you want more 
control you simple add in another point, this leaves you free to have 
certain areas with very few control points, and other areas with lots of 
control points, yet the result will be perfectly smooth.  For example when 
modelling a car the large flat roof might only need a handful of control 
points, but something around the wheel-arch might need many more to get the 
curvature correct.

Another benefit is that you can instantly switch between the level of 
subdivision, so you can have a 10 million triangle mesh for perfectly smooth 
rendering, or a 100k mesh for use in a game, both coming from exactly the 
same control points.

Watch this for a demo of it working (in BLender);

http://www.youtube.com/watch?v=ckOTl2GcS-E

around 0:47 you can see him editing the control points and the perfectly 
smooth surface is following.  This is how you design smooth triangle meshes, 
not point by point of the individual triangles!

> And yet, in all known editors, moving triangle corners around one at a 
> time is the only available editing operation...

Haha, do you *really* think that people haven't thought of a better way to 
edit triangle meshes? LOL

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