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Bilinear interpolation on a quadrilateral using Barycentric coordinates

gpuopen.com

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Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#11

Post by spookie »

GolDDranks wrote: post #5

I am definitely not an expert in 3D graphics... but this looks such an astonishingly simple and effective method, it makes me to question why this wasn't already thought of and picked up? I get that with fixed-pipeline GPUs you do what the hardware and driver make you do, but with the advent of programmable pipelines, you'd though improving stuff like this would be the first things people do? Anyway, gotta run and im…

Because there is no reason to not use triangles.

Look at prideout's reply in the thread, the argument about having just one normal vector and the fact they can only describe one plane is huge. Unless you want more edge cases to deal with (hehe, pun intended), you're better off sticking to tris.

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#12

Post by hnuser123456 »

prideout wrote: post #7
hnuser123456 wrote: post #3

This is one of those things that feels like a broken/half-assed/oversimplified implementation got completely proliferated into the world a long time ago and it took several years for the right person to do a full-depth mathematical analysis to reveal what we should've been doing all along. Similar to antialiasing and sharpening, texture filtering, color spaces and gamma correction, etc. It reminded me of this article…

The fact that triangles have proliferated is not due to half-assery. Hardware can rasterize them very quickly, and a triangle can have only one normal vector. Quads can be non-planar. It's true that quads are nice for humans and artists though! As an aside, Catmull-Clark subdivision has been around since 1978, which, as a first step, breaks an arbitrary polyhedron into a mesh of quadrilaterals.

It's not so much that triangles are the primitive, as much as our logic for combining multiple triangles into a mesh and texturing, lighting, and deforming them in continuous ways clearly has some gaps. It's definitely not an easy problem and it's a fun exercise to see how various silicon innovations unlocked increasingly accurate solutions, and what corners needed to be cut to hit 30fps back in the day.

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#13

Post by AlienRobot »

hnuser123456 wrote: post #3

This is one of those things that feels like a broken/half-assed/oversimplified implementation got completely proliferated into the world a long time ago and it took several years for the right person to do a full-depth mathematical analysis to reveal what we should've been doing all along. Similar to antialiasing and sharpening, texture filtering, color spaces and gamma correction, etc. It reminded me of this article…

This seems to happen really often! I think I remember there was another one being about color blending being done on the wrong gamma space on GPUs?

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#14

Post by GolDDranks »

spookie wrote: post #11
GolDDranks wrote: post #5

I am definitely not an expert in 3D graphics... but this looks such an astonishingly simple and effective method, it makes me to question why this wasn't already thought of and picked up? I get that with fixed-pipeline GPUs you do what the hardware and driver make you do, but with the advent of programmable pipelines, you'd though improving stuff like this would be the first things people do? Anyway, gotta run and im…

Because there is no reason to not use triangles. Look at prideout's reply in the thread, the argument about having just one normal vector and the fact they can only describe one plane is huge. Unless you want more edge cases to deal with (hehe, pun intended), you're better off sticking to tris.

I know about the advantages and uniqueness properties of triangles. However, if the article is correct about that artists prefer using quads when editing (I know absolutely nothing about 3D editing, and didn't know that, I thought triangles are universal these days), something is clearly missing from the pipeline if a neatly mapping textures to quads, then converted to triangles ends up messing the interpolation.

Maybe we can continue to describe the geometry in triangles, but could use an additional "virtual fourth handle point" data (maybe expressed in barycentric coords of the other three, so everything is automatically planar) for stretching the interpolation in the expected way.

Anyway, I'm just getting started with Metal, and this provided for a nice theme for experimentation.

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#15

Post by badsectoracula »

pixelesque wrote: post #8
idbehold wrote: post #6

Earlier quoted context omitted.

It's quite astonishing how complicated it is to draw lines in 3D graphics. As a novice it was a little unbelievable that the primitives for drawing lines was effectively limited to a solid screen-space pixel wide line. Want to draw a 2 pixel wide line? Do it yourself with triangles.

Ironically, back in the OpenGL 2.0 days, it was a lot easier to do things like this.

Well, technically the API is still available pretty much everywhere (be it directly or via a wrapper library) and most hardware still has support for drawing lines, so it is still easy in current days to do things like this too :-P.

I'm using it all the time when i want to draw lines in 3D.

(though as far as lines and OpenGL is concerned i remember reading ages ago that not even SGI's implementation had full support for everything OpenGL was supposedly able to do)

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#16

Post by badsectoracula »

GolDDranks wrote: post #14
spookie wrote: post #11

Earlier quoted context omitted.

Because there is no reason to not use triangles. Look at prideout's reply in the thread, the argument about having just one normal vector and the fact they can only describe one plane is huge. Unless you want more edge cases to deal with (hehe, pun intended), you're better off sticking to tris.

I know about the advantages and uniqueness properties of triangles. However, if the article is correct about that artists prefer using quads when editing (I know absolutely nothing about 3D editing, and didn't know that, I thought triangles are universal these days), something is clearly missing from the pipeline if a neatly mapping textures to quads, then converted to triangles ends up messing the interpolation. May…

Modern GPUs - and really GPUs for about 10 years - are stupidly fast when it comes to rasterizing triangles, so artists simply work with quads (and polygons of more than four vertices - when Blender added "n-gons" back in the day many artists rejoiced) and they just subdivide them if they want neater looking interpolation before triangulating them. But a lot of detail nowadays come from geometry anyway.

This could have been nice ~15 years ago when using much fewer poly counts and relying a lot more on textures for detail was more common. But at the same time, GPUs were also much slower so this approach would be slower too.

So in practice this is really a niche approach for when you want to have a large quad that isn't "perfectly" mapped to an underlying texture and you can't subdivide the quad. Nowadays such use cases are more likely to come from more procedural sides (or perhaps effects) of the engine than artists making assets for the game.

It might be useful for an artist wanting to use a modern engine running on a modern PC to make a low-poly retro-styled game though.

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#17

Post by meindnoch »

hnuser123456 wrote: post #3

This is one of those things that feels like a broken/half-assed/oversimplified implementation got completely proliferated into the world a long time ago and it took several years for the right person to do a full-depth mathematical analysis to reveal what we should've been doing all along. Similar to antialiasing and sharpening, texture filtering, color spaces and gamma correction, etc. It reminded me of this article…

For most workflows this is a non-issue. When texturing a triangle mesh, the distortions are baked into the texture map, so no seams are visible at the quad diagonals.

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#18

Post by GolDDranks »

badsectoracula wrote: post #16
GolDDranks wrote: post #14

Earlier quoted context omitted.

I know about the advantages and uniqueness properties of triangles. However, if the article is correct about that artists prefer using quads when editing (I know absolutely nothing about 3D editing, and didn't know that, I thought triangles are universal these days), something is clearly missing from the pipeline if a neatly mapping textures to quads, then converted to triangles ends up messing the interpolation. May…

Modern GPUs - and really GPUs for about 10 years - are stupidly fast when it comes to rasterizing triangles, so artists simply work with quads (and polygons of more than four vertices - when Blender added "n-gons" back in the day many artists rejoiced) and they just subdivide them if they want neater looking interpolation before triangulating them. But a lot of detail nowadays come from geometry anyway. This could ha…

Interesting - low-poly (and 2D) are exactly where my interests are.

Btw. wouldn't it be possible in modern pipelines to remap or "disfigure" the texture when converting to triangles, so that it counters the bias accordingly? Ah, but that bakes in the shape of the quad, so it can't be modified runtime or it will get distorted again, right.

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#19

Post by somethingsome »

GolDDranks wrote: post #5

I am definitely not an expert in 3D graphics... but this looks such an astonishingly simple and effective method, it makes me to question why this wasn't already thought of and picked up? I get that with fixed-pipeline GPUs you do what the hardware and driver make you do, but with the advent of programmable pipelines, you'd though improving stuff like this would be the first things people do? Anyway, gotta run and im…

You want triangles in general, they behave way better, think for example computing intersections.

Also, debugging colors on a 3D surface is not an easy task (debugging in general in 3D is not easy). So if the rendering is nice and seems correct, you tend to think it is.

And if it was not, and you didn't encounter something that bothers you, it doesn't matter that much, after all, what is important is the final rendering style, not that everything is perfectly accurate.

Re: Bilinear interpolation on a quadrilateral using Barycentric coordinates

#20

Post by meindnoch »

GolDDranks wrote: post #5

I am definitely not an expert in 3D graphics... but this looks such an astonishingly simple and effective method, it makes me to question why this wasn't already thought of and picked up? I get that with fixed-pipeline GPUs you do what the hardware and driver make you do, but with the advent of programmable pipelines, you'd though improving stuff like this would be the first things people do? Anyway, gotta run and im…

Because when working with a textured asset, these seam distortions simply don't occur. The inverse of the distortion is baked into the texture map of the asset. So the distortion between a triangle's world-space size vs. its texture-space size cancels out exactly, and everything looks correct.
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