
Re: How can I get better solution for this...?
Posted:
Jul 7, 2011 6:48 AM


Hi Bobby, The P matrix and D are constants, the values of which I will know at the time of the evaluation. Maybe the mistake I made was in not "somehow" specifying that the elements of P and D itself are constants? How is this fact specified in Mathematica? i.e, for a given P and D, solve for sx, sy, gx and gy..... In light of this, maybe, new information, would you be kind enough to reevaluate the problem? Or if you can let me know, I can try it myself.... Thanks again for all your help, and time #
On Wed, Jul 6, 2011 at 11:18 AM, DrMajorBob <btreat1@austin.rr.com> wrote:
> Someone else may have more insight into "the decomposition of an Affine > transformation matrix into scale (sx sy) and shear (gx gy) components", but > there IS no alternative way to solve that system of equations, nor any > system equivalent to it, with d and the p parameters variable. > > Bobby > > > On Wed, 06 Jul 2011 13:05:39 0500, Siddharth Srivastava <siddys@gmail.com> > wrote: > > Hi Bobby, >> Thanks for the quick reply. What I am trying to do is to get an >> analytical form for >> the decomposition of an Affine transformation matrix into scale (sx sy) >> and >> shear >> (gx gy) components. Maybe if you have an alternative way to get this, that >> would >> be helpful too... >> Thanks, >> # >> >> On Wed, Jul 6, 2011 at 10:36 AM, DrMajorBob <btreat1@austin.rr.com> >> wrote: >> >> Ah yes... I misread your post in the heat of the moment. >>> >>> The first three equations determine sy, gx, and gy in terms of p00, p01, >>> p11, and sx: >>> >>> soln = Quiet@ >>> >>> Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00, >>> sx sy gx (1 + gx gy) + sx sy gy == p01, >>> sy^2 (1 + gx^2) == p11}, {sx, sy, gx, gy}]; >>> soln[[All, All, 1]] >>> >>> {{sy, gx, gy}, {sy, gx, gy}, {sy, gx, gy}, {sy, gx, gy}} >>> >>> giving four solutions. If the fourth equation is also true, each of these >>> solutions determines a value for d: >>> >>> Solve[sx sy == d, d] /. soln >>> >>> (four solutions) >>> >>> Hence, your four equations have no solution with d free to vary. >>> >>> >>> Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00, >>> sx sy gx (1 + gx gy) + sx sy gy == p01, sy^2 (1 + gx^2) == p11, >>> sx sy == d}, {gx}] >>> >>> {} >>> >>> Bobby >>> >>> >>> On Wed, 06 Jul 2011 11:50:17 0500, Siddharth Srivastava < >>> siddys@gmail.com> >>> wrote: >>> >>> Hi Bobby, >>> >>>> Thanks. I actually wanted sx, sy, gx and gy in terms of the P coeff. >>>> The >>>> solution >>>> you gave is just the equation that I wanted to solve! >>>> # >>>> >>>> On Wed, Jul 6, 2011 at 9:18 AM, DrMajorBob <btreat1@austin.rr.com> >>>> wrote: >>>> >>>> Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00, >>>> >>>>> sx sy gx (1 + gx gy) + sx sy gy == p01, sy^2 (1 + gx^2) == p11, >>>>> sx sy == d}, {p00, p01, p11, d}] >>>>> >>>>> {{p00 > sx^2 + 2 gx gy sx^2 + gy^2 sx^2 + gx^2 gy^2 sx^2, >>>>> p01 > gx sx sy + gy sx sy + gx^2 gy sx sy, p11 > (1 + gx^2) sy^2, >>>>> d > sx sy}} >>>>> >>>>> Bobby >>>>> >>>>> On Wed, 06 Jul 2011 04:39:55 0500, sid <siddys@gmail.com> wrote: >>>>> >>>>> Hi all, >>>>> >>>>> I am trying to solve the following for {sx,sy,gx,gy} >>>>>> >>>>>> sx^2 (1 + gx gy)^2 + sx^2 gy^2 = P00 ........(1) >>>>>> sx sy gx (1 + gx gy) + sx sy gy = P01 .......(2) >>>>>> sy^2 ( 1 + gx^2) = P11 ..............................******.(3) >>>>>> sx sy = D ..............................** >>>>>> ****..................(4) >>>>>> >>>>>> in terms of P00,P01,P11, and D. >>>>>> >>>>>> When I use Solve[] , I get a huge output containing the P terms up >>>>>> till the order of 16 (i.e P00^16 etc..), which >>>>>> I know is not correct. I do not think I am specifying the problem >>>>>> correctly, and being a nonexpert in Mathematica, would appreciate >>>>>> some help. Specifically >>>>>> 1) should I specify the simultaneous equation using && operator? I >>>>>> have tried it, and I get different (but huge) output >>>>>> 2) can I break the problem into parts? how? >>>>>> Thanks, >>>>>> s. >>>>>> >>>>>> >>>>>> >>>>>>  >>>>> DrMajorBob@yahoo.com >>>>> >>>>> >>>>> >>>  >>> DrMajorBob@yahoo.com >>> >>> > >  > DrMajorBob@yahoo.com >

