reflect(I, N) functions returns inverted vector

[Secrop]

I notice today, that the reflect function of the VectorMath node, uses the Normal as if it was a surface Tangent.
In mathematical terms, the reflected vector is supposed to be R = 2*dot(I, N) - I;;

But I quickly discovered that the fuctions reflect_v3_v3v3()(blenlib/intern/math_vector.c), reflect()(cycles/util/util_math_float3.c) and reflect()(cycles/kernel/shaders/stdosl.h), they all output R = I - 2*dot(I, N);

In math_vector.c, it was even added an ascii graphic and a note that for “bouncing” we should negate the result…

Going further, since stdosl.h should be very similar to the one from ImageWorks, I found out that they did the same thing (and also a clarification in the specs).

I wonder why this choice? Is there any reason to output the inverted vector (instead of the real ‘reflected’ one)?

[brecht]

It depends what you mean by reflection exactly.
http://mathworld.wolfram.com/Reflection.html

The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror).
…
The term reflection can also refer to the reflection of a ball, ray of light, etc. off a flat surface.

[Secrop]

That example from Wolfram is what I’d expect…

The question still is what do we mean by Normal in our functions?

[brecht]

See formula (3) on the Wolfram page and the image above it, the direction of v (and so I) is reversed, like an incoming ray direction.

[Secrop]

But is there a reason to do it like this?
I find it a bit strange to use vectors that don’t start in the origin… Formula (3) explicitly says X1' - X0.

[brecht]

It just the convention in shading languages and graphics math libraries. It doesn’t seem strange to me to work with ray direction vectors.

[Secrop]

Ok… Thanks for the answer.
I can keep using -I (or -reflect(I, N)) for calling the function, thought it seems that is just one extra step to get a more usefull vector.