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homogenization question
Author
This is a math question.
For example ,
x'' = x*c1/z
y'' = y*c2/z
z'' = c3z
how to get the matrix M .
V'' = M * V
| x'' |
V'' = | y'' |
| z'' |
and
| x |
V = | y |
| z |
quote: Original post by davidadams
This is a math question.
Post it to the Math and Physics forum.
quote:
For example ,
x'' = x*c1/z
y'' = y*c2/z
z'' = c3z
how to get the matrix M .
V'' = M * V
| x'' |
V'' = | y'' |
| z'' |
and
| x |
V = | y |
| z |
Your notation is a little unclear, but I gather that you want to construct the transformation matrix M. Given that
|m11 m12 m13|M = |m21 m22 m23| |m31 m32 m33| and
|m11*x + m12*y + m13*z|M * V = |m21*x + m22*y + m23*z| |m31*x + m32*y + m33*z|(column-major multiplication) your desired matrix is:
|c1/z 0 0 |M = |0 c2/z 0 | |0 0 c3| This can be tricky to construct since the matrix is dependent upon the multiplicand.
Then you logically have no solution. You could multiply by another matrix which did the z division for you, but there''s no way a single matrix M will yield the desired result if it cannot contain z. Sorry.
People who can''t do shit, talk.
-Dwight Yorke
People who can''t do shit, talk.
-Dwight Yorke
quote: Original post by davidadams
This is a math question.
For example ,
x'' = x*c1/z
y'' = y*c2/z
z'' = c3z
how to get the matrix M .
V'' = M * V
| x'' |
V'' = | y'' |
| z'' |
and
| x |
V = | y |
| z |
Of course this doesn''t belong in this particular
forum, right....?
Ferretman
ferretman@gameai.com
www.gameai.com
From the High Mountains of Colorado
Since I cannot move this thread (being a roving moderator) then all I can do is reply with some questions to try and assist with solving the problem.
Firstly, is this transformation from (x,y,z) to (x'',y'',z'') intended to be a coordinate transformation or a time update?
That is, if it were a time update then it might look something like
x(t+1) = x(t) + c1/z(t)
y(t+1) = y(t) + c2/z(t)
z(t+1) = c3z(t)
Either way of course, for your set of equations there is no constant matrix such that
V'' = M*V
where V = [x y z]T
because your variables form nonlinear functions of each other
Perhaps you could elaborate on the context of the problem so that we could help a little more?
Cheers,
Tim
Firstly, is this transformation from (x,y,z) to (x'',y'',z'') intended to be a coordinate transformation or a time update?
That is, if it were a time update then it might look something like
x(t+1) = x(t) + c1/z(t)
y(t+1) = y(t) + c2/z(t)
z(t+1) = c3z(t)
Either way of course, for your set of equations there is no constant matrix such that
V'' = M*V
where V = [x y z]T
because your variables form nonlinear functions of each other
Perhaps you could elaborate on the context of the problem so that we could help a little more?
Cheers,
Tim
This topic is closed to new replies.
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