On 14 Aug 2009, at 22:27, DE wrote:
on 15.08.2009 at 1:12 Edward Grace wrote :
it's terribly wrong to overload '^' in such a way Why? The precedence rules? Fair enough - sometimes what's tempting is bad for you, but you still want to try it anyway! because '^' is associated with bitwise xor operator and there is no such operation on vectors it is semantically wrong
Err - surely the point of overloading is to assign meaningful context specific behaviour to the same operator, so. unsigned a,b,c; c = a ^ b; // ^ => XOR makes sense. pseudovector<3> c; vector<3> a,b; c = a ^ b; // ^ => Wedge product makes sense XOR does not. It seems reasonable - at least at first sight. I can understand the objection vis-a-vis operator precedence and associativity constraints though - e.g. pseudoscalar<double> s; vector<3> a,b,c; s = a ^ b ^ c; // Equivalent to scalar triple product. What's first (a ^ b) ^ c, a ^ (b ^ c) it shouldn't matter - I don't recall the implicit associativity , precedence of the XOR operator.... Anyhow, wedge(a,b) --- much less potential for trouble ! ;-) One thing to bare in mind, type trouble! Sticking with ^, since it's easier to write. If each entity is a vector of length 3, a ^ b ^ c | | +---+---+ | directed area a.k.a. bivector [a pseudovector] | | +--------+---------+ | directed volume a.k.a. trivector [a pseudovector] If, for example, b and c were pseudovectors then s would be a (true) scalar and could be assigned to the concrete type double. This is where carrying along some (meta) information concerning the transformation rules of these different entities would be both tricky and crucial.
w = wedge(u,v); w = cross_product(u,v) please :p Err, that's only true in 3D (vectors of length 3). There's no such thing as a cross product between (say) vectors of length 2,4 or indeed anything else. The cross product is, in effect, a restricted version of the exterior (wedge) product which exists for higher dimensions. if i get the point right consider wedge_product(u,v) or exterior_product(u,v)
Yes indeed. Or, if the vector has exactly 3 elements you can say... vector<3> u,v; cross_product(u,v); but only then. -ed P.S. Anyone wondering what the heck a pseudo-vector/scalar is: http://en.wikipedia.org/wiki/Triple_product just when you thought the distinction between vectors / covectors was confusing enough!