Re: [Algorithms] SQRT vs. SIN and COS

[Alex M. <Am...@Bw...>]

    P.S. I realize that y/d and x/d is an identity for cos and sin, I am =
more interested in whether or not this is used in hand optimizing matrix =
routines rather than the infamous FCOS and FSIN

  ----- Original Message -----=20
  From: Alex Morano=20
  To: gda...@li...=20
  Sent: Wednesday, December 20, 2000 11:48 AM
  Subject: [Algorithms] SQRT vs. SIN and COS


      I was wondering if anyone has run across this method of dealing =
with affine transformations, just found it, in of all things, a VB WIN =
API graphics programming book (don't ask), they use the following idea:

      Instead of the regular=20

     =20
                  C  S  0  0
                  -S C  0  0
                  0  0   1  0
                  0  0   0  1

      for rotation about the Z axis, they make it a 2-dimensional =
transformation:

              Distance of X and Y (d)  =3D Sqrt(X ^ 2 + Y ^ 2)

                  x/d  -y/d  0  0
                  y/d   x/d  0  0
                  0       0   1  0
                  0       0   0  1

      Now, I tried some quick benchmarks, changed the divs into =
multiplies (1/d) and sure enough, I get a 16% increase on my =
transformations. And the accuracy is exactly the same.  Is this =
something I have missed that is a known trick, or is it an accepted algo =
to use the cos/sin, or even lookup tables? My only gripe about lookups =
is that they can never be accurate enough without the sarifice of a huge =
swat of memory.

      So I am curious if this is a used standard?
             =20