Changes between Version 3 and Version 4 of BoundingRegionTransformation

10/01/10 04:52:30 (5 years ago)
byorgey (IP:

add notes on computing orthonormal bases


  • BoundingRegionTransformation

    v3 v4  
    6868  2. Work out the details of step (4).  Does it really work? 
     70For step (4), perhaps see [–Schmidt_process Gram-Schmidt process], and also this exchange from the [ #haskell IRC channel on 30 Sep 2010]: 
     7318:18:27 <byorgey> given a vector v in an inner product space, how might I go about computing a basis for the hyperplane orthogonal to v? 
     7418:18:45 <Veinor> ask #math? :D 
     7518:19:02 --- join: dnolen ( joined #haskell 
     7618:19:09 * byorgey shudders 
     7718:19:11 <ddarius> byorgey: for all basis vectors b, keep b if b ^ v /= 0 
     7818:20:00 --- join: c_wraith (~c_wraith@ joined #haskell 
     7918:20:01 <byorgey> ddarius: ^ is inner product? 
     8018:20:10 <Cale> byorgey: Well, pick random vectors and subtract off the orthogonal projection onto the subspace spanned by v 
     8118:20:11 <benmachine> isn't ^ usually used for cross product 
     8218:20:11 <ddarius> byorgey: Wedge product. 
     8318:20:13 <benmachine> or is that v 
     8418:20:24 * benmachine always just used, you know, cross 
     8518:20:30 <ddarius> Of course, the dual of v will be a blade that represents the hyperplane orthogonal to it already... 
     8618:20:50 <aristid> so google found IOSpec for me 
     8718:20:53 <ddarius> b ^ v = b . dual(v) 
     8818:21:08 <byorgey> ddarius: where can I read about this? 
     8918:21:28 <Veinor> byorgey: for each basis vector b, compute b - proj_v b 
     9018:21:36 <byorgey> can I apply affine transformations to such duals? 
     9118:21:47 <Veinor> (I don't know anything about vector spaces besides R^n) 
     9218:22:42 <ddarius>  (mathematical/physics), (physics), (computer science) 
     9318:22:47 <ddarius> byorgey: ^ 
     9418:23:36 <benmachine> haskell-src-exts' fixity resolution is super-brokwn 
     9518:23:39 <benmachine> *broken 
     9618:23:45 <benmachine> well, fairly broken anyway 
     9718:24:12 <ddarius> byorgey: I recommend starting here: and here: 
     9818:25:14 <ddarius> byorgey: This deceptively named paper is rather useful a bit later on: 
    70101== Inverse transpose ==