glDrawElements - Tetrahedron

[MakKlaski]

Hello!
We have functionality to draw points (1 vertex), lines (2 vertices), triangles (3 vertices).
Why don't we have a possibility to draw tetrahedron (4 vertices)?

4 vertices can be projected to screen as usual. And then in the zone inside of them (in screen space) the device can check if _the existing values in depth buffer_ are located inside tetrahedron (in 3D). If they are inside -> the fragment shader will run. With interpolated values from tetrahedron vertices (volume interpolation).

This will add possibility to approximate 3D functions with vertices (not in regular grid). Now we have 3D textures for that.

For example, we can create volumetric light sources and dimming sources, which interact with existing geometry via depth buffer. We can take a mesh and create extruded faces using normals, this crust can be filled with tetrahedrons (base mesh and extruded mesh). Then some values can be interpolated based on distance from the surface of the mesh (light intensity for example).

[V-man]

It sounds like you are asking for a special case to be implemented in hardware : if the depth value from the depth buffer is inside the tetrahedron, then run the fragment shader. If it is not inside, then don't run the fragment shader.

Therefore, the GPU needs to evaluate 2 points on the tetrahedron and then compare if the value from the depth buffer is inside.

Also, why is this suggestion limited to a terahedron? Light volumes aren't always tetrahedrons : I have used cylinders.

Your suggestion doesn't fit with the rest of the graphics pipeline and it is limited to a tetrahedron.

[MakKlaski]

Yes, the depth test for volumetric object can be INSIDE, not only LESS or GREATER. Or even OUTSIDE, if it is needed.

You can create any shape with tetrahedrons by putting them together just like the surface is formed with triangles. Tetrahedron is a simplex which supports interpolation with barycentric coordinates just like triangle.
I'm just moving to the next dimension and not taking shapes like cylinder.

[Alfonse Reinheart]

Why don't we have a possibility to draw tetrahedron (4 vertices)?

We use triangles because they're fast to rasterize. They are fast to rasterize because they're flat objects. They're guaranteed planar, and they require nothing more than 4D homogenous math and well-known rasterization algorithms.

Rasterizing a tetrahedron requires a lot more work.

[MakKlaski]

I don't think that it requires a lot of work as it is a convex shape. It's just a rasterization of back and front sides at the same time and getting depths.

[The Little Body]

The idea seem fine


I see another problem about the selection of the back and front sides, since a tetrahedron has 4 faces, not only one as triangles or planar quads

But this can perhaps to be handled via the use of two temporally depth buffers that can store the back sides on the first depth buffer and the front sides on the second depth buffer ?
(and at a second pass, we can use the content of the "back sides" and "front sides" depth buffers for to see if the current voxel is inside or outside this volume)

Note that this can too add anothers volumetric effects such as things like clouds and smoke or a fast emulation of semi-transparents glass windows between the eye and drawed objects for example (but without reflexions and refractions effects of course)

Something, this can to be see such as something more or less near to the inverse of dual paraboloid maps, no ?

[aqnuep]

Why you don't do that already?

You could use a geometry shader to generate the tetrahedron slices and output gl_Layer so that your fragment shader outputs go to the appropriate slice of the 3D texture.

This may not be exactly what you want to do as I didn't 100% understand your original request but I'm pretty sure you can achieve what you want using the existing toolset. The only question may be performance.

[MakKlaski]

Why you don't do that already?

You could use a geometry shader to generate the tetrahedron slices and output gl_Layer so that your fragment shader outputs go to the appropriate slice of the 3D texture.

This may not be exactly what you want to do as I didn't 100% understand your original request but I'm pretty sure you can achieve what you want using the existing toolset. The only question may be performance.

No, I'm not talking about rendering to 3D texture.
My idea is more similar to rendering lights in deferred shading.
When the scene is drawn we have a depth buffer to work with.
So for each pixel we have a 3d position. We can do lookup in 3d texture, which stores some value distributed in volume.
Or we can lookup in a mesh of tetrahedrons -> far more efficient approach without a regular grid of 3d texture.

[MakKlaski]

For example the point light can be done like this: we take a polygonal sphere and fill it with tetrahedrons - all sharing the vertex in the center of the sphere. Other 3 vertices of tetrahedrons are faces of the sphere. The center vertex can have color value 1 and surface vertices can have value 0. So when we render this mesh of tetrahedrons existing depth buffer will get interpolated value based on position from center to surface.
But we can model any light source shape this way.
Of course the traditional way of doing point light in DS (by passing center position and drawing sphere triangles) is better.

We can also render a transparent mesh which gets opaque in the middle (made of colored glass, liquid, etc.). We must get the distance between front side and back side of tetrahedrons. Or front side and depth buffer - if depth value is inside tetrahedron. We get the density based on this distance and determine the color.

There are lots of things we can do

[V-man]

Of course the traditional way of doing point light in DS (by passing center position and drawing sphere triangles) is better.

Then shouldn't your suggestion actually be "glDrawElements should support GL_SPHERE"?

Anyway, the depth test stage is designed to test the depth value of an incoming fragment with the depth value of the depth buffer.
In your case, you want it to have 2 fragments from different faces of your tetrahedron to be the incoming fragments. How exactly is that suppose to happen?
Imagine this, you have a fragment from face 1 with position XYZ.
Which fragment is behind that face? Which face is behind that face? Is there even a face behind that face?
Is it face 2 or face 3 or face 4?
The GPU would have to go into a series of calculations to figure out what that second fragment is. It would actually need access to the primitive assembly stage information.

And the final question. Is that going to be faster than a 2 pass approach?