#### Arbitrary derivatives

Bo Schwarzstein <bo.schw...@...>

Hello,

I'm clear now. The OSL as an independent shading language do not care
about how the user implement this feature on Raytracer (Arnold ?),
REYES renderer or GPU.

I will take a look at the AD, seems interesting.

On Jan 19, 11:24 pm, Larry Gritz <l...@...> wrote:
On Jan 19, 2010, at 12:52 AM, Bo Schwarzstein wrote:

Hello folks,
In specification, it sais "Arbitrary derivatives without grids or
extra shading points.", but I really confused how it works without
explicit grid. Does it like the GPU, compute the derivatives on screen
space ?
Thanks.
Let's separate the language specification, from the implementation in this library, from what a renderer is expected to do when using the OSL library.

The language spec just requires that an implementation can take derivatives of any quantity with respect to "x" and "y".  The definitions of x,y are purposely undefined, they are allowed to be anything convenient to the renderer as long as they are roughly perpendicular and that x and/or y change by approximately 1 from pixel to pixel (so derivatives can be used to estimate filter sizes).  Also, the language itself doesn't really care how Dx() and Dy() are implemented.

In the implementation of the OSL runtime library, we really wanted derivatives to work just as well for ray tracers that shade in arbitrary locations than for Reyes-like renderers that have grids.  We chose to use a kind of "automatic differentiation" based on dual arithmetic that tracks the differentials correctly for every calculation (read Dan Piponi's paper from JGT 2004 for a good introduction), so then the implementation of Dx() and Dy() is simply looking up the x and y partials of the variable in question.  The bottom line is that it does not require grids or extra shading points.

At SPI, our renderer is a pure ray tracer, so for us x and y are pixel coordinates and we use ray differentials when setting up shading batches (you need to pass things like dP/dx and dP/dy into OSL, then it handles all the rest).

If a Reyes-like renderer (shading on grids) wanted to use our OSL implementation, there's no reason why a shading batch couldn't be arranged in a rectilinear grid, and if they wanted their derivatives to be aligned to the grids, they could still pass the initial values using x==u*du and y==v*dv and mimic what would usually happen for Reyes (even though our library would not actually be differencing grid points to find the derivatives).

Similarly, a pure GPU-based implementation of OSL would be allowed to have x,y aligned to screen space and use the funny/awful "alternating forward and backward differences" that GPUs do naturally.

Does that all make sense?

(Aside: at this moment, we use the dual arithmetic for everything, leading to quite a bit of wasted math.  Among other optimizations I'm currently working on is to use the dual arithmetic only for the subset of calculations that lead to expressions whose derivatives are actually used, this should eliminate most of the extra math, since so few derivatives are taken.  I've done some experiments that indicate that we can save somewhere near 30% when this is done.)

-- lg

--
Larry Gritz
l...@...

Bo Schwarzstein <bo.schw...@...>

Hello,

Yes, it's amazing, I did not hear the Automatic Differentiation
before, it seems like an ideal math method to handle this.

On Jan 19, 11:09 pm, Henri <henr...@...> wrote:
On 19 jan, 09:52, Bo Schwarzstein <bo.sc...@...> wrote:

Hello folks,
In specification, it sais "Arbitrary derivatives without grids or
extra shading points.", but I really confused how it works without
explicit grid. Does it like the GPU, compute the derivatives on screen
space ?
No, it does automatic differentiation.

The overall idea is that if your inputs know their derivatives ( for
instance, when raytracing a primitive, computing P, dP/dx and dP/dy is
easy )
you are able to maintain derivatives quantities while shading.

Look athttp://jgt.akpeters.com/papers/Piponi04/for a complete
reference.

Hopes this helps

Henri

Thanks.

Larry Gritz <l...@...>

Well put, a very concise explanation of the basic idea.

-- lg

On Jan 19, 2010, at 7:09 AM, Henri wrote:

No, it does automatic differentiation.

The overall idea is that if your inputs know their derivatives ( for
instance, when raytracing a primitive, computing P, dP/dx and dP/dy is
easy )
you are able to maintain derivatives quantities while shading.

Look at http://jgt.akpeters.com/papers/Piponi04/ for a complete
reference.

Hopes this helps

Henri
--
Larry Gritz
l...@...

Larry Gritz <l...@...>

On Jan 19, 2010, at 12:52 AM, Bo Schwarzstein wrote:

Hello folks,

In specification, it sais "Arbitrary derivatives without grids or
extra shading points.", but I really confused how it works without
explicit grid. Does it like the GPU, compute the derivatives on screen
space ?

Thanks.

Let's separate the language specification, from the implementation in this library, from what a renderer is expected to do when using the OSL library.

The language spec just requires that an implementation can take derivatives of any quantity with respect to "x" and "y". The definitions of x,y are purposely undefined, they are allowed to be anything convenient to the renderer as long as they are roughly perpendicular and that x and/or y change by approximately 1 from pixel to pixel (so derivatives can be used to estimate filter sizes). Also, the language itself doesn't really care how Dx() and Dy() are implemented.

In the implementation of the OSL runtime library, we really wanted derivatives to work just as well for ray tracers that shade in arbitrary locations than for Reyes-like renderers that have grids. We chose to use a kind of "automatic differentiation" based on dual arithmetic that tracks the differentials correctly for every calculation (read Dan Piponi's paper from JGT 2004 for a good introduction), so then the implementation of Dx() and Dy() is simply looking up the x and y partials of the variable in question. The bottom line is that it does not require grids or extra shading points.

At SPI, our renderer is a pure ray tracer, so for us x and y are pixel coordinates and we use ray differentials when setting up shading batches (you need to pass things like dP/dx and dP/dy into OSL, then it handles all the rest).

If a Reyes-like renderer (shading on grids) wanted to use our OSL implementation, there's no reason why a shading batch couldn't be arranged in a rectilinear grid, and if they wanted their derivatives to be aligned to the grids, they could still pass the initial values using x==u*du and y==v*dv and mimic what would usually happen for Reyes (even though our library would not actually be differencing grid points to find the derivatives).

Similarly, a pure GPU-based implementation of OSL would be allowed to have x,y aligned to screen space and use the funny/awful "alternating forward and backward differences" that GPUs do naturally.

Does that all make sense?

(Aside: at this moment, we use the dual arithmetic for everything, leading to quite a bit of wasted math. Among other optimizations I'm currently working on is to use the dual arithmetic only for the subset of calculations that lead to expressions whose derivatives are actually used, this should eliminate most of the extra math, since so few derivatives are taken. I've done some experiments that indicate that we can save somewhere near 30% when this is done.)

-- lg

--
Larry Gritz
l...@...

Henri <henri...@...>

On 19 jan, 09:52, Bo Schwarzstein <bo.sc...@...> wrote:
Hello folks,

In specification, it sais "Arbitrary derivatives without grids or
extra shading points.", but I really confused how it works without
explicit grid. Does it like the GPU, compute the derivatives on screen
space ?
No, it does automatic differentiation.

The overall idea is that if your inputs know their derivatives ( for
instance, when raytracing a primitive, computing P, dP/dx and dP/dy is
easy )
you are able to maintain derivatives quantities while shading.

Look at http://jgt.akpeters.com/papers/Piponi04/ for a complete
reference.

Hopes this helps

Henri

Thanks.

Bo Schwarzstein <bo.schw...@...>

Hello folks,

In specification, it sais "Arbitrary derivatives without grids or
extra shading points.", but I really confused how it works without
explicit grid. Does it like the GPU, compute the derivatives on screen
space ?

Thanks.

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