Awesome! Hey, Roban, are you willing to release that under the PDL
license? (currently the disjunction of Artistic and GPL, if I remember
right)? If so, I'd like to do some tweaks and paste it into compose()...
Cheers,
Craig
On Apr 30, 2008, at 9:09 AM, Roban Kramer wrote:
> A while ago I wrote code to mathematically compose linear
> transformations. I make no guarantee of its correctness or robustness,
> but it might be useful to someone:
>
> =head2 t_compose_linear
>
> Mathematically compose transformations and combine the C<pre> and
> C<post> translations into a single C<post> translation. The
> C<t_compose> function just does the transformations in order, while
> this function creates a single mathematical transformation.
>
> =cut
>
> sub t_compose_linear{
> my (@t_in) = @_;
>
> # set up the initial output matrix and post translation
> my $out_matrix = identity($t_in[-1]->{'params'}->{'matrix'});
> my $out_post = zeroes($out_matrix->dim(-1));
>
> foreach my $in (reverse @t_in) {
> # check to make sure we have the right type of transformation
> unless(UNIVERSAL::isa($in,'PDL::Transform::Linear')) {
> Carp::cluck( "PDL::Transform::t_inverse_linear: ".
> "got a transform that is not linear.\n"
> );
> return undef;
> }
> unless(defined $in->{params}->{inverse}) {
> Carp::cluck( "PDL::Transform::t_inverse_linear: ".
> "got a transform with no inverse.\n"
> );
> return undef;
> }
>
> my $in_matrix = $in->{'params'}->{'matrix'};
>
> # get the post and pre translations of the input xform
> my $in_post = topdl($in->{'params'}->{'post'});
> my $in_pre = topdl($in->{'params'}->{'pre'});
> $in_post = $in_post->copy();
> $in_pre = $in_pre->copy();
>
> # if they're single element piddles, make them vectors
> $in_post = $in_post * ones($in_matrix->dim(1))
> if ($in_post->nelem() < $in_matrix->dim(1));
> $in_pre = $in_pre * ones($in_matrix->dim(1))
> if ($in_pre->nelem() < $in_matrix->dim(1));
>
> # now combine the pre and post translations into a single post
> $in_post = $in_post + ($in_pre x $in_matrix);
>
> # and convert that into the combined post translation
> $out_post = $in_post + matmult($out_post,$in_matrix);
> $out_matrix = $out_matrix x $in_matrix;
> }
>
>
> On Wed, Apr 30, 2008 at 8:52 AM, Craig DeForest
> <[EMAIL PROTECTED]> wrote:
>>
>> That would be the part in NOTES where it says
>>
>>
>> Composition works OK but should probably be done in a more
>> sophisticated
>> way so that, for example, linear transformations are combined at
>> the
>> matrix level instead of just strung together pixel-to-pixel.
>>
>> For 100-10,000 coordinates you shouldn't worry. That will fit
>> entirely in
>> the CPU cache for most modern machines, so the performance hit
>> isn't bad.
>> When I say build your own rotation matrix, I mean as a PDL using
>> elementwise
>> calculation or matrix multiplication.
>>
>> The comment in the notes, and the point I made, is that if you have
>> three
>> linear operators to string together, it is much faster (54
>> multiplications)
>> to multiply your three 3x3 matrices together, than to apply each
>> matrix in
>> order with the data (27 times 3N multiplications). But with only
>> (say) 1000
>> points, that means each operation will take under 9000
>> multiplications, or
>> about 30-100 microseconds if you're using a recent machine and the
>> data are
>> in CPU cache.
>>
>> My suggestion: try it using the Transform composition; if it is too
>> slow,
>> you can make it faster by applying your composition Transform to the
>> identity matrix, and then pass the resulting matrix into t_linear
>> to make a
>> single transform.
>>
>> Cheers,
>> Craig
>>
>> On Apr 30, 2008, at 6:31 AM, Sina Türeli wrote:
>>
>> Okay this part seems important. Where in the documentation does it
>> write
>> that? So if to rotate around an arbitrary axis, I compose three
>> rotation
>> matrices T^-1.R.T<v>, where T takes the arbitrary axis to x axis, R
>> does the
>> rotation around x axis and T^-1 maps the arbitrary axis back to its
>> original
>> direction how much of an inefficiency are we talking about. This is
>> likely
>> to operate on a data set of anywhere between 100 to 10000
>> coordinates. These
>> T and R operators are all t_linear rotation operator in PDL. When
>> saying
>> build your own rotation matrix do you mean from scratch and by just
>> using
>> multplication and inverse operations defined in PDL and not any
>> t_linear
>> opeartions...
>>
>> Thanks alot for your help
>>
>> On Tue, Apr 29, 2008 at 11:23 PM, Craig DeForest <[EMAIL PROTECTED]
>> >
>> wrote:
>>
>>>
>>>
>>> You can compose transformations to get to the axis you want, but
>>> as you
>> will have seen in the documentation it is inefficient because the
>> code just
>> strings the transformations together. If your data are big then you
>> will
>> want instead to build your own rotation matrix (or extract the one
>> in the
>> transform) to minimize the number of passes. You can still use
>> Transform to
>> encapsulate the operations, which is good in case you later want to
>> generalize. t_linear will accept a matrix if you want.
>>>
>>>
>>>
>>>
>>> On Apr 29, 2008, at 1:26 PM, "Sina Türeli" <[EMAIL PROTECTED]>
>>> wrote:
>>>
>>>
>>>
>>>
>>> Thanks for the answers. One more question, is there any build in
>>> function
>> for rotationa around an arbitrary axis of the object? If there isnt
>> I am
>> planning to first rotate all the object so that the arbitrary axis
>> concides
>> with say x axis, rotate the object around the x axis and apply the
>> inverse
>> of the first transformation to put the arbirtrary axis back in its
>> place.
>> But somehow this seems computationally really inefficient. I am
>> might also
>> think of a way to transform rotations around an arbitrary axis to
>> their
>> correspoding transformation angles around x,y,z axis that also is I
>> assume
>> possible...
>>>
>>>
>>> On Tue, Apr 29, 2008 at 7:37 PM, Sina Türeli
>>> <[EMAIL PROTECTED]> wrote:
>>>
>>>>
>>>>
>>>> Ok, for a certain program I am writing (protein folding), I need
>>>> to be
>> able perform rotations. I was first planning to do it manually by
>> defining
>> rotation matrices and change of basis matrices etc but I think pdl
>> might
>> save me time. However I am not sure how to use its use
>> PDL::Transform to do
>> so. Here is a piece of code that I was using to experiment with pdl
>> use PDL;
>>>> use PDL::Transform;
>>>>
>>>> @a = [[1,0,0],[0,1,0],[0,0,1]];
>>>>
>>>> $c= pdl @a;
>>>>
>>>> $e = t_rot(45,45,45);
>>>>
>>>> $c = $e * $c
>>>>
>>>> print $c;
>>>>
>>>> I was hoping this would rotate my 1,1,1 vector in all directions
>>>> by 45
>> degrees but it gives the error. "Hash given as a pdl - but not
>> {PDL} key!".
>> I am not able to understand what this error is for? Also I have
>> seen no
>> tutorial where these rotationa matrices are explained so I would
>> appreciate
>> any help, thanks.
>>>>
>>>> --
>>>> "Vectors have never been of the slightest use to any creature.
>> Quaternions came from Hamilton after his really good work had been
>> done; and
>> though beautifully ingenious, have been an unmixed evil to those
>> who have
>> touched them in any way, including Maxwell." - Lord Kelvin
>>>>
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>> --
>>> "Vectors have never been of the slightest use to any creature.
>>> Quaternions
>> came from Hamilton after his really good work had been done; and
>> though
>> beautifully ingenious, have been an unmixed evil to those who have
>> touched
>> them in any way, including Maxwell." - Lord Kelvin
>>>
>>> _______________________________________________
>>>
>>> Perldl mailing list
>>> Perldl@jach.hawaii.edu
>>> http://mailman.jach.hawaii.edu/mailman/listinfo/perldl
>>>
>>
>>
>>
>> --
>> "Vectors have never been of the slightest use to any creature.
>> Quaternions
>> came from Hamilton after his really good work had been done; and
>> though
>> beautifully ingenious, have been an unmixed evil to those who have
>> touched
>> them in any way, including Maxwell." - Lord Kelvin
>>
>> _______________________________________________
>> Perldl mailing list
>> Perldl@jach.hawaii.edu
>> http://mailman.jach.hawaii.edu/mailman/listinfo/perldl
>>
>>
>
_______________________________________________
Perldl mailing list
Perldl@jach.hawaii.edu
http://mailman.jach.hawaii.edu/mailman/listinfo/perldl
