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Im looking for the paper: Coordinate Rotation Digital Computer by Jack E. Volder (1959).
If anyone knows where to find it please let me know, or provide an link.
Thanks.

According to this blog, you can find it in here. Be aware though, those are two books, i don't know which one it is in.

If you're good to read something else than the original paper, you could download this fine PDF, as it seems to cover all the related topics.

Ah thanks HellMood. I see it's a different title of the paper: "The COORDIC Trigonometric Computing Technique".
I found it here, but I wonder if its the whole paper.

or look here: https://scholar.google.nl/scholar?q="JE+Volder"

Doing FPGA stuff? :)

Not quite. I want to find a way to do 3D-rotations with the smallest amount of instructions/opcode and data.

Thus see if one can find any building-clocks for generating the trigonometric-functions plus doing multiply (for rotation around the three axises) in a discrete manner with just simple discrete logic.

Of course that's possible, but it will be hard to beat a clever FPU setup with stack adressing ;)

Hehe.
I know one can use log/exp tables for multiplications, and i will look into that as well. But the problem is tables take space (or they have to me generated with the smallest amount of code). sin and cos are instructions available, also multiply (which are slow in some cases). (Here we're talking about x86). The only thing I can see is some form of Cellular Automata that with the appropriate rules. But that logic is impossible to find without the proper/simple arithmetic framework one can reverse engineer.

How accurate do you need sin/cos to be? and do you have a MUL instruction?

CORDIC is good if you don't have a MUL+memory, but the iterative nature makes it relatively slow.

Funny, that CORDIC system is actually similar to interpolating per-pixel normals.
You interpolate them linearly in 3d-space, which gives the proper rotation, they just get denormalized because the length varies. So you renormalize them (or use some approximation function to adjust length).

trc_wm: the precision is probably 8-10 bits or such in that region. i have mul, but the fewer the better. the same goes with precision.

To be precise, this works okay-ish for normals in the most use cases, but try interpolating between (1,0,0) and (-1,0,0) with that method. You will need a proper slerp there.

Not quite sure what you want to do. But if you want to learn how to do vector math with very limited resources, you should check all the 3D vector tutorials for the C64. There are some very clever and very fast vector/matrix multiplication routines out there.

Just noticed you are working on X86. All that bit fiddling will get you nowhere there, I guess...

yeh. I currently use FPU-instructions.

"an" is only used if a VOCAL is the first letter of the next word! :p
for "frenchies" it is in almost every next word! ;)
[/hitler]

about your problem:
to get rid of the MULs: just bitshift as we always did! have a frame of 256*256 and just shift your bytes! ;)
Fastest Rotations in a Matrix would be what i found in the Raymarchers Thread:
#define W(p,a) cos(a)*p+sin(a)*float2(-p.y,p.x);
it´s only on 2 axis, but you can redefine it easily to handle all 3 of them! ;)
p.xy = W(p.xy, time); //do this 3 times vs rewrite W ;)

I looked for a paper from 1847 written by J. B. Listing called "Introductory Studies in Topology". Vandenheockund Represcht, Gottingen (1847)
Original title: "Vorstudien zur Topologie"

Preferable in .pdf format and english translation.

Anyone got it?

I do not have the paper, but I'm curious.
You seem to be looking for older and older papers. Who knows what will be next :)
Jokes aside, I don't really understand what your problem, constraints and objectives are, and I am not an expert, but I have spent some time over quite some years thinking about how to build (and have implemented to some extent) a 3d engine using only integer math (not even fixed point, even if the distinction can be a matter of interpretation) and understanding precision and error accumulation through the whole system. My goal was not absolute performance on a given hardware but performance with a set of rules I set to myself, as well as understanding and implementing everything from scratch starting with only add shift (optionally mul div), with no desire to implement things "the way everyone does it" in the usual matrix pipeline fashion. I know it's not very clear but that's how I would describe it right now.
Maybe you could describe what your problem, constraints and objectives are in a way I could better understand, I know you already gave information on that but I do not see it clearly.
Have a nice night.

sure, it'll be: "i'm looking for this paper "Elements" by Euclid... around ~300BC. Preferable in .pdf and translated to english. Anyone got it?!?!?!?"

Search string: ""Vorstudien zur Topologie" Johann Benedict PDF" - first google hit:
https://archive.org/details/vorstudienzurto00listgoog/page/n11

Yes it's in german, but you can download a PDF. So that's 1/2 of what you want. Doesn't look really super interesting content wise.

I thought I was doing some underground scene algorithm until I found Euclid’s paper and found it was all done 2319 years ago. The papers in this thread have a nice alchemy vibe to the print. It looks like some declassified ufo shit