[skye-adaire]

>Why are SDFs useful at all?

Meshes and bezier patches are boundary representations with no information of the volume they enclose. Imagine you'd like to cut an object out of smoke or clouds. SDFs enable you to cut out arbitrary volumes from any material. This is more realistic than skinning a mesh object with textures, especially with translucent objects.

> So why do we need neural nets to represent them?

You don't. I didn't notice render times, but "interactive frame rates" would be lacking.

Most SDF primitives and their compositions are not analytic (from use of abs, fract, etc). Differentiation by finite differences is most common. Few are using automatic differentiation. I don't quite follow how back prop would produce the surface gradient, but I doubt it would be faster than these methods.

[dartmoose]

> Meshes and bezier patches are boundary representations with no information of the volume they enclose

Pedantic on my part, but SDF is still just a surface/boundary representation at the end of the day. It may have additional benefits that you point out such as quickly computing if you're inside/outside or being able to more easily deform the shape (through any number of procedures including slicing), but you'd probably use a density grid instead of a SDF if you're dealing with anything volumetric, such as clouds or smoke.

> You don't. I didn't notice render times, but "interactive frame rates" would be lacking.

Yeah definitely, poor wording on my part.

> Most SDF primitives and their compositions are not analytic (from use of abs, fract, etc). Differentiation by finite differences is most common. Few are using automatic differentiation. I don't quite follow how back prop would produce the surface gradient, but I doubt it would be faster than these methods.

I don't think we're talking about the same thing, I'm not referring to the surface gradient when I say differentiable rendering.

Both differentiable rendering with an SDF (i.e. SDFDiff https://arxiv.org/pdf/1912.07109.pdf) and with a neural SDF(DIST http://b1ueber2y.me/projects/DIST-Renderer/) use automatic differentiation to compute the gradient of the rendering/image-generating process. Section 3.4 in the DIST paper discusses where back prop comes into all of this. Basically your surface is defined by the weights of some neural net (i.e. a neural SDF) and you need to know the gradient of your image with respect to those weights.

For a variety of reasons, these surface representations are easier to handle than triangle meshes which break certain desirable properties for differentiation and require extra care as a result (see edge sampling https://people.csail.mit.edu/tzumao/diffrt/ for an early example of the challenges of doing differentiable rendering with a triangle mesh).

[skye-adaire]

>SDF is still just a surface/boundary representation

Meshes and Bezier patches are parametric representations (defined over R^2, evaluated with vec2, output vec3). Implicit functions are volumetric representations of surfaces (defined over R^3, evaluated with vec3, output float). This is a key difference between parametric modelers like AutoCad and implicit modelers like nTopology.

>density grid instead of a SDF if you're dealing with anything volumetric, such as clouds or smoke.

These functions of time change every frame. In the implicit paradigm, it's not necessary to evaluate the smoke ahead of time since sphere tracing can reduce to marching adaptively when we are within smoke. Image quality will not be bound to any resource resolution other than the screen (a low res smoke grid would appear blocky).

I agree with you that the current triangle-based RT implementations have faster alternatives that accomplish similar things on the surface.

Thanks for the links!

[dartmoose]

Thanks again for the insights here and in the other thread!

> In the implicit paradigm, it's not necessary to evaluate the smoke ahead of time since sphere tracing can reduce to marching adaptively when we are within smoke.

Makes sense. The SDF is separate from the density grid for the cloud/smoke. We need both, one to detect the boundary (SDF) and another to actually render the volume (density grid).

In offline rendering we usually just have some primitive (sphere, cube etc) that acts as the boundary but that obviously isn't as adaptive and doesn't let you easily reveal arbitrary slices of a volume.

[skye-adaire]

>In offline rendering we usually just have some primitive (sphere, cube etc) that acts as the boundary

Right, using a SDF as a boundary condition is to discretely check it as an indicator function (if negative do x else do y). You can use basically any SDF to bound your procedural medium, including a procedural boundary (via domain distortion).

You can also apply a continuous blend instead of the discrete check (smooth step the level curve). This is preferred since discrete checks will often result in popping.

[tovacinni]

Render times are listed on table 3 of the paper- interactive, but perhaps not high-performance!