I think I'm onto something:
If I replace the ...e-017 values in the original matrix (before the
inversion) the result is correct!
{ { 0.0 -1.0 0.0 0.5 } { 1.0 0.0 0.0 0.5 } { 0.0 0.0 1.0 0.0 } { 0.0
0.0 0.0 1.0 } } inverse
results in
{ { 0.0 1.0 0.0 -0.5 } { -1.0 0.0 0.0 0.5 } { 0.0 0.0 1.0 0.0 } { 0.0
0.0 0.0 1.0 } }
So the problem seems related to some sort of over/underflow.
Randy
On Thu, Dec 16, 2010 at 5:03 AM, Joe Groff <[email protected]> wrote:
> On Dec 15, 2010, at 7:51 PM, Randy Voet wrote:
>
> Hi,
>
> I'm looking for matrix (4x4) inversion. I've found
> math.matrices.elimination, but I've come across a problem:
>
> { 0.5 0.5 0.0 } translation-matrix4
> { 0.0 0.0 1.0 } pi 0.5 * rotation-matrix4 m.
> dup inverse m.
>
> This results in
>
> { { 1.0 0.0 0.0 0.0 }
> { 0.0 1.0 0.0 -0.4... }
> { 0.0 0.0 1.0 0.0 }
> { 0.0 0.0 0.0 1.0 } }
>
> instead of the identity matrix (though the difference is small, just one
> cell).
>
> Hi Randy. It looks like the "inverse" function is indeed wrong. Here's the
> result of "inverse":
> ( scratchpad ) { 0.5 0.5 0.0 } translation-matrix4
> ( scratchpad ) { 0.0 0.0 1.0 } pi 0.5 * rotation-matrix4 m.
> ( scratchpad ) inverse .
> {
> { 0.0 1.0 0.0 -0.9065658975290974 }
> { -1.0 6.123233995736766e-17 0.0 0.4999999999999999 }
> { 0.0 0.0 1.0 0.0 }
> { 0.0 0.0 0.0 1.0 }
> }
> Compared against manually inverting the components:
> ( scratchpad ) { 0.0 0.0 -1.0 } pi 0.5 * rotation-matrix4
> ( scratchpad ) { -0.5 -0.5 0.0 } translation-matrix4 m. .
> {
> { 6.123233995736766e-17 1.0 0.0 -0.5 }
> { -1.0 6.123233995736766e-17 0.0 0.4999999999999999 }
> { 0.0 0.0 1.0 0.0 }
> { 0.0 0.0 0.0 1.0 }
> }
> Aside from numerical error, the 3x3 submatrix looks correct; however, the
> fourth column of the "inverse" result is off by { -0.4 0 0 }.
> -Joe
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