From 5340592791276710425 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f78e5,94e9c2bbb0060b48 X-Google-Attributes: gidf78e5,public X-Google-ArrivalTime: 2002-08-14 14:29:04 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!kibo.news.demon.net!news.demon.co.uk!demon!mail2news.demon.co.uk!not-for-mail From: ros0230@iperbole.bologna.it (Natale Fietta) Newsgroups: comp.std.c++ Subject: Re: Proposals for small vectors? Date: Wed, 14 Aug 2002 21:28:36 GMT Organization: NETTuno Approved: Fergus Henderson , moderator of comp.std.c++ Message-ID: <3d5a1dd2.2181932@news.iperbole.bologna.it> References: <87wurryywb.fsf@grue.ucsd.edu> <87hei3zkxb.fsf@grue.ucsd.edu> Reply-To: ros0230@iperbole.bologna.it X-Trace: mail2news.demon.co.uk 1029360522 mail2news:14215 mail2news mail2news.demon.co.uk X-Complaints-To: abuse@demon.net X-Mail2News-Path: news.demon.net!mulga.cs.mu.oz.au X-Authentication-Warning: mulga.cs.mu.OZ.AU: fjh set sender to devnull@stump.algebra.com using -f X-Robomod: STUMP, ichudov@algebra.com (Igor Chudov) Delivered-To: std-c++@ncar.ucar.edu NNTP-Posting-Date: 14 Aug 2002 09:22:37 GMT X-Newsreader: Forte Free Agent 1.21/32.243 Lines: 187 Xref: archiver1.google.com comp.std.c++:13254 On Sat, 10 Aug 2002 11:46:39 GMT, Walter Landry wrote: >Natale Fietta wrote: >> Please, define "simple equation". > >What I meant is do your equations tend to look like > > A=B*C; > D=A+E*F; > >or is it more like > > A=(B*C + D*F)/(B*E - D*B) + B*B - F*C; With matrixes i usually write long expression breaked in little token to get rid of unnecessary temporaries, so i can be happy if the library can automagically eliminate temporary for me :-) My expressions often are not a simple sequence of arithmetic operators, but are intermixed with various function calls, this way: A=Normalize( CrossProduct((A - B), (C - B)) ); a=DotProduct( Vector(A.z, A.y, -A.x), Normalize(B - A) ); It is very infrequent for me to mix matrixes and vectors in the same expression, i usually have strong separation betwen them, instead i do often mix float in the same expression, this way: //in this example lower-case are floats, upper-case are vectors or matrixes A=(u*B + v*C) / t; The only very frequent case i mix vector and matrixes is vector*matrix multiplications, usually they are in the simplest form: U=V*M; or also V*=M; Note: for some API matrixes are transposed, so i must use M*V instead of V*M. because using the wrong multiplication order can be a difficult bug to find (and also a pain to write if the same program must be compiled for both conventions) i usually define both V*M and M*V to be equivalent to the only geometrically correct multiplication for the currently selected API. (i can hear mathematicians cry out with horror ;-) This is very different form what a general purpose library can reasonably do... >Let me get this straight. You have matrices of the form > > A00 A01 A02 A03 >A= A10 A11 A12 A13 > A20 A21 A22 A23 > 0 0 0 1 > >and you want to be able to multiply it by a vector > > B=(B0 B1 B2 B3) >to get C=A*B without actually doing any multiplies for the last >element of C. Not only, i also want to multiply two matrixes of this form using the minimal needed number of operations, like as C00 = A00*B00 + A01*B10 + A02*B20 instead of C00 = A00*B00 + A01*B10 + A02*B20 + A03*B30 > B=(B0 B1 B2 B3) It is worth noting that i prefer traditional names (with a geometrical meaning) for vectors components, i do not access them using B[0] B[1] B[2] but instead i use B.x, B.y B.z; this is far more readable for me because i do think in terms of xyz, i am not interested in a vector class without the ability to access components with a .x or .x() or GetX() syntax or similar (the .x is my favourite). > What I could do is something >like > > Index<'i',3> i; > Index<'j',4> j; > > C(i)=A(i,j)*B(j); > C(3)=B(3); > >Where the template parameter '3' for Index 'i' is so that only the >first three elements of C are computed. I've had a quick look at FTensor library, tensor concept is very interesting (it is new to me) but for my work it is an unneeded complexity; i am very happy with unrelated vector and matrix classes, i do use them in very different modes and do not have any need to generalize them in a tensorial way... Also note that often videogames console do not have very standard conforming C++ compilers, so a library that do not work even on MSVC++6 in out of my range of usefulness. i strongly hope in a near future all C++ compilers can be standard conforming, but i must work with current compilers :-( >For matrix*matrix operations, if you're using 3x4 matrices, you could >do something like The strange thing is that being 3x4 (widely used in past, but less often now) a space optimized form of 4x4, i do want to be able to multiply them, i mean multiply a 3x4 matrix for a 3x4 matrix obtaining as result another 3x4 matrix (another cry from mathematicians ;-) > Index<'i',3> i; > Index<'j',4> j; > Index<'k',3> k; > > D(i,j)=A(i,k)*B(k,j); > >and it would do the minimum number of multiplies. In addition, this >D(i,j) would still work with the vector*matrix example above. Sorry, this tensorial formalism only confuse me... :-( >> Also we often use 3-vector to represent normalized 4-vector in >> homogeneous coordinates, so we can multiply a 3-vector by a 4x4 >> matrix and obtain another 3-vector as result. (i suppose this sound >> very odd to mathematicians). > >I think you want to be able to multiply > > A00 A01 A02 A03 B0 > A10 A11 A12 A13 * B1 > A20 A21 A22 A23 B2 > 0 0 0 1 1 > >without storing that last B3=1. Instead of simply > C=A*B Yes, but i do also use (less often) this: A00 A01 A02 A03 B0 A10 A11 A12 A13 * B1 A20 A21 A22 A23 B2 A30 A31 A32 A33 1 performing the full multiplication and returning as result: Vector(C.x/C.w, C.y/C.w, C.z/C.w) //C.w is C3 >Well, it seems like you can do most of what you need with a general >tool. I will admit that it is not quite as simple as a specialized >library. In cases where this matters, though, it shouldn't be >difficult to define your own inline functions. It will at least free >you from having to construct the basic operations. For me it is *far* more easy to construct all the basic operations than to understand and use a tensor library... >If, as John Nagle says, the algebra3 library is considered useful, >then a more powerful and flexible interface with equivalent >optimizations should work fine for most people. As i said in my first post in this thread, i am talking only about my personal experience and needs; i am not surprised John Neagle has slightly (or also not so slightly) different needs than me; we do work in differents niche of the geometric community. I dislike some of algebra3 design, in particular the missing x y z names for vector components, and various missing optimizations. >I've also rooted around the Quake II source code a little, and it >seems like that code in particular could benefit greatly from a >standard vector and matrix toolkit. Well, first of all this particular code is not a good example of C++ programming, because it is written in C... In any case i must make my position more clear: i think a good quality standard vector/matrix library can be a great benefit for the graphic community, but i do think the needs are too peculiar and specific to include a similar library in the C++ standard or boost libraries. The library i do dream of has some peculiarity (for example the mentioned V*M==M*V) that can be only cause of unexpected bugs for more general purpose applications... Regards, Natale Fietta --- [ comp.std.c++ is moderated. To submit articles, try just posting with ] [ your news-reader. If that fails, use mailto:std-c++@ncar.ucar.edu ] [ --- Please see the FAQ before posting. --- ] [ FAQ: http://www.jamesd.demon.co.uk/csc/faq.html ]