Can anyone do anything with this.

Atero here is the proof:
Lets take the x,y<->d,r formula as a prooved fact:
We will start from
d=sqrt(x1*x1+y1*y1);r=atan2(x1,y1)+t;
x2=sin(r)*d;y2=cos(r)*d;
and
x2=x1*sin(t)+y1*cos(t);y2=y1*sin(t)-x1*cos(t);

this means that
sin(r)*d=x1*sin(t)+y1*cos(t);
cos(r)*d=y1*sin(t)-x1*cos(t);

rise this to the power of 2 and you will get:
sin^2(r)*d^2=x1^2*sin^2(t)+2*x1*y1*sin(t)*cos(t)+y1^2*cos^2(t);
cos^2(r)*d^2=x1^2*cos^2(t)-2*x1*y1*sin(t)*cos(t)+y1^2*sin^2(t);

now add one equalation to the other
d^2(sin^2(r)+cos^2(r))=x1^2(sin^2(t)+cos^2(t))+y1^2(sin^2(t)+cos^2(t))

now becouse of the sin^2(alpha)+cos^2(alpha)=1 its proven that
d^2=x1^2+y1^2
and since d=sqrt(x1^2+y1^2) you can write this as
x1^2+y1^2=x1^2+y1^2
or
0=0
what is true and that means that
x2=x1*sin(t)+y1*cos(t);y2=y1*sin(t)-x1*cos(t);
is true too

yeah, but that's like saying "since x=x, x must equal x."

It mathematicly proofes that rottation matrix works.
Isnt this what you asked for?

Hehe...
Well yea...
OK...
I got nothing to say... (because I got now TOO many things to ask, say, tell...).
🙁

Jack, that post was completely useless. Nixa was proving that the 3-D rotation equations are true. And Atero, I think Nixa did answer your question. If you want personal proof, just sit down and try to figure it out yourself. This is what I did and although I did it wrong I was easily able to figure out how they actually do work by looking at the equations in you're primer and elsewhere.

the reason it doesn't work is because you're assuming it's true before you prove it, then using the matrix to prove itself. you can do the same thing with any arbitrary formula.

So all proofes made by mathematical induction are wrong then?

No, all proofs using that which is to be proven to prove them are only using circular logic. However, looking back at your post I don't think you did this.

Actually it's in between.

The only things nixa proved is that if we know that cos^2+sin^2 = 1, then the formula for rotation doesn't modify a point's distance to the origin, which means it was either rotated around the origin, or not moved at all.
However he didn't prove that a point was rotated around the specified angle 😉.

I believe Jheriko will post the actual proof soon in the "AVS Primer - now hiring" thread. I'd post it if I'd remember it from high school 😉. In that same thread I've already explained how you go from the rotational formula to a matrix btw.

aww damn...you learn that in the trig course i never finished, don't you? 😉

Atero,are there actually any more ways to rotate a superscope then the way described in the AVS Primer? If you want you could
remove rotation from the AVS Primer but it would be a good idea to leave 3D-2D tranlation in it.