Everything I Always Wanted to Know About Derivatives (But Was Afraid to Ask)

[Etienne Sandré-Chardonnal]

Hi,

When we write, for instance, the following shader:

float uvscale = 1;

float s = u*uvscale;

float t = 1.0-v*uvscale;

float a = 7.68;

float b = 0.165;

float height = a*exp(-((s-0.5)*(s-0.5)+(t-0.5)*(t-0.5))/b); //Gaussian

float dHdX = Dx(height);

float dHdY = Dy(height);

It works!

I'm curious, is that numerical derivation (ie the OSL compiled code does recompute height with slightly offset u and v values obtained from dudx, etc... derivatives), or are math functions such as exp analytically derivative-aware?

Thanks!

[Olivier Paquet]

Short answer is option B. See:

https://github.com/imageworks/OpenShadingLanguage/blob/ffc5303dcfd63cf395d3a1b6fbf6ca3894b44d5e/src/include/OSL/dual.h#L1120

https://en.wikipedia.org/wiki/Automatic_differentiation#Automatic_differentiation_using_dual_numbers

Olivier