php function to transpose a matrix of (x,y) coordinate around a pivot point

Question

I have a matrix of [ n x m ] elements where center may not be on coordinate(x,y) 0,0:

<?php
$matrix_yx = array(
     21 => array(10,11,12),
     22 => array(10,11,12),
     23 => array(10,11,12),
     24 => array(10,11,12)
);
$origin_yx = array(23,11);
?>

I'm trying to write a function to pass as input

the matrix
pivot coordinate to be used as fulcrum
eventually the rotation in degree (that can be only 90, 180 or 270)

So, considering a representation of matrix (x,y) elements:

y
^
| 10,24   11,24   12,24
| 10,23  >11,23<  12,23
| 10,22   11,22   12,22
| 10,21   11,21   12,21
+-----------------------> x

I need to rotate it of 90' degree clockwise around point (11,23) basically obtaining a new matrix like this:

y
^
| 09,24   10,24   11,24   12,24
| 09,23   10,23  >11,23<  12,23
| 09,22   10,22   11,22   12,23
+-------------------------------> x

I'm a little bit confused as if the (x,y) origin would be on coordinate (0,0) then it would be simple as

(x,y) = (11,23)

translate of 90' around (0) i would obtain

function Rotate($matrix) {
    list($x,y) = array($y,-$x);
    (x,y) = (23,-11);
}

but then what I have to consider if I want to pass a different pivot coordinate?

function Rotate($matrix, $pivot_x, $pivot_y) {
    //-- (...)
}

In case I would have to transpose the matrix of 180 or 270 degree (instead of 90) then function will be called 2 or 3 times... unless obviously there's a smarter approach (that I'm sure exists but - at the moment - not in my mind).

you dont need do worries about your pivote, translate your matrix to pivot (0,0) this mean if you have your point (x,y) = (11,23) and your pivote (x_p,y_p) = (1,1) your point in (0,0) = (x-x_p, y-y_p) and can apply your function. And about your called function, remeber you are in a circle, divide your grade with 90 and do mod 4, example 450:90 = 5 , 5 mod 4 = 1 => 1 time you need call your function and max time = 3, 3 mod 4 = 3 — Laurentiu

Stefano Radaelli Stefano Radaelli · Accepted Answer · 2015-11-13T08:59:22

Following the @Laurentiu suggestion this is the function that should reply to my question:

$matrix = array(
     21 => array(10,11,12),
     22 => array(10,11,12),
     23 => array(10,11,12),
     24 => array(10,11,12)
);

function Rotate($matrix, $pivot_x, $pivot_y) {
        $output = array();
        krsort($matrix);
        while (list($y) = each($matrix)) {
                reset($matrix[$y]);
                while (list(,$x) = each($matrix[$y])) {
                        list($offset_x,$offset_y) = array(
                                ($pivot_y - $y),
                                -1 * ($pivot_x - $x)
                        );
                        list($newx,$newy) = array($pivot_x - $offset_x , $pivot_y - $offset_y);

                        $output[$newy][] = $newx;
                }
        }
        return($output);
}

So, starting from a matrix like this...

10,24    11,24    12,24
10,23   >11,23<   12,23
10,22    11,22    12,22
10,21    11,21    12,21

If I rotate on pivot (x,y) (11,23)..

$output  = Rotate($matrix, 11, 23);

9,24    10,24    11,24    12,24
9,23    10,23   >11,23<   12,23
9,22    10,22    11,22    12,22

Whereas if I rotate on pivot (0,0):

$output = Rotate($matrix, 0, 0);

21,-10    22,-10    23,-10    24,-10
21,-11    22,-11    23,-11    24,-11
21,-12    22,-12    23,-12    24,-12

Obviously, any error correction is more than appreciated!

php function to transpose a matrix of (x,y) coordinate around a pivot point

1 Answers