From -3171245195890368311 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f78e5,94e9c2bbb0060b48 X-Google-Attributes: gidf78e5,public X-Google-ArrivalTime: 2002-08-19 12:39:04 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!logbridge.uoregon.edu!kibo.news.demon.net!news.demon.co.uk!demon!mail2news.demon.co.uk!not-for-mail From: Walter Landry Newsgroups: comp.std.c++ Subject: Proposals for small vectors? Date: Mon, 19 Aug 2002 19:37:58 GMT Organization: Univ of Calif San Diego Approved: Fergus Henderson , moderator of comp.std.c++ Message-ID: <87bs7yps0l.fsf_-_@grue.ucsd.edu> X-Trace: mail2news.demon.co.uk 1029785883 mail2news:13147 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 Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii NNTP-Posting-Date: Mon, 19 Aug 2002 19:28:42 +0000 (UTC) User-Agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.2 Lines: 149 Xref: archiver1.google.com comp.std.c++:13308 Natale Fietta wrote: > 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... Well, this is where I think the tensor notation will help you. V*M would be something like V(i)*M(i,j), or equivalently as M(i,j)*V(i). Similarly, M*V -> M(j,i)*V(i) or V(i)*M(j,i). The indices keep things in order. > >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 Well, you could do Index<'i',3> i; Index<'j',3> j; Index<'k',3> k; C(i,k)=A(i,j)*B(j,k); C(i,3)+=A(i,3); > 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). I'm sure that you can add a non-member function of your own named GetX() that does the right thing. This would be, for the const and non-const cases template double GetX(const T &t) { return t(0); } template double & GetX(T &t) { return t(0); } The member functions are probably not amenable to standardization, though. Some people use x,y,z, some use x,y,z,t, some use t,x,y,z, some use r,theta,phi, and still others use U,V, etc. > 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 :-( I'm sure that the library could be made to have the same interface and still work with broken compilers. It just wouldn't use expression templates, removing some of its nice aspects. > > 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... :-( Wherever you see an index (i.e. i, j, or k), substitute a loop. So the previous example would be equivavlent to for(int i=0;i<3;++i) for(int j=0;j<4;++j) { D(i,j)=0; for(int k=0;k<3;++k) D(i,j)=A(i,k)*B(k,j); } On my website, I have a paper that talks about the library. You only have to read the introduction (about 2 pages) to understand tensor notation. > 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 In that case, you can write Index<'i',3> i; Index<'j',3> j; C(i)=(A(i,j)*B(j) + A(i,3)) / (A(3,j)*B(j) + A(3,3)); And it will use the minimum number of operations (Really!). Tensor notation is really a powerful tool. > 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... Well, this is one thing that Tensor notation clears up. Also, relating to POD's, for a non-constant vector C, &(C(0)) would give you a pointer to the beginning of the vector. Regards, Walter Landry wlandry@ucsd.edu --- [ comp.std.c++ is moderated. 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