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two-dimensional coordinate transformation

by dimar (Curate)
on Nov 02, 2005 at 21:44 UTC ( #505119=perlquestion: print w/ replies, xml ) Need Help??
dimar has asked for the wisdom of the Perl Monks concerning the following question:

### Problem: Q has a very simple representation of 2d geometric shape coordinates, and he wants to pass them into some functions to do very basic transformations. This is just for a quick number-crunching throwaway script to generate sample data.

### Question: A quick search on CPAN doesn't seem to reveal anything that directly addresses this simple need, and PDL looks like extreme overkill. Can anyone suggest some very straightfoward and basic code to do coordinate transformations indicated below (i.e., does it already exist or is this a 'write it yourself' problem).

### init $aCoords = [0,0 10,0 10,10 0,10]; ### a square $bCoords = rotate($aCoords,45); ### a diamond $cCoords = scale($aCoords,2.00); ### a bigger square $dCoords = skew(...); ### etc. $eCoords = translate(...);

The goal is simply to get a handful of small functions like that to enable quick output of the new coordinates to generate sample data. This isn't math homework, and Q is not a whiz with matrix multiplications, hence the inquiry.


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Re: two-dimensional coordinate transformation
by thor (Priest) on Nov 02, 2005 at 22:17 UTC
    It's too bad that Q isn't a whiz with linear algebra (or matrix multiplications as you put it). Rotations and scaling are linear transformations. For the following examples, assume that A is a 2xn matrix (that is 2 columns and n rows; n is the number of points that you're dealing with).
    Rotation by an angle t: A' = A * [ [cos t, -sin t][sin t, cos t] ]; Scaling by a factor of x: A' = A * [ [x, 0][0, x] ]; Translation by dx in the x direction and dy in the y direction (not actually linear transform, but easily accomplished with matricies +): A' = A + [ [dx, dy] ]; ( add dx to each value in the first column and +dy to each in the second column)
    I would help you with skew, but I don't know *how* you want to accomplish this. In colloquial terms, I'd imagine a stretch of some description, but I don't know what kind of parameters you've got.


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Re: two-dimensional coordinate transformation
by Roy Johnson (Monsignor) on Nov 02, 2005 at 22:06 UTC
    Each of them would be a map, except you want it to take them two-by-two. Scale is the easiest, since you don't have to worry about that:
    sub scale { my ($coords, $factor} map { $_ * $factor } @$coords }
    But a more properly-formed structure would be
    $a_coords = [ [0,0], [0,10], [10,10], [10,0] ]; # a square
    which would be amenable to mapping for all transformations. I think this is a do-it-yourself project, but wouldn't be too surprised to be surprised. :-) Check out Math::Polygon for something in the right ballpark.

    Caution: Contents may have been coded under pressure.

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