アフィン変換行列を求めるのに必要な連立方程式をphpで解く

結構めんどくさいんですが、一度書いてやれば使いまわせます。

$pointには0～2までx1→x2、y1→y2という座標点の対応を入れる前提です。

	// アフィン変換の未知数
	$a = '';
	$b = '';
	$c = '';
	$d = '';
	$l = '';
	$m = '';
	// 連立方程式を解く
	$a = ($point[0]['x2'] * $point[1]['y1'] + $point[1]['x2'] * $point[2]['y1'] + $point[2]['x2'] * $point[0]['y1'] - $point[0]['x2'] * $point[2]['y1'] - $point[1]['x2'] * $point[0]['y1'] - $point[2]['x2'] * $point[1]['y1']) / ($point[0]['x1'] * $point[1]['y1'] + $point[1]['x1'] * $point[2]['y1'] + $point[2]['x1'] * $point[0]['y1'] - $point[0]['x1'] * $point[2]['y1'] - $point[1]['x1'] * $point[0]['y1'] - $point[2]['x1'] * $point[1]['y1']);
	$b = ($point[0]['x1'] * $point[1]['x2'] + $point[1]['x1'] * $point[2]['x2'] + $point[2]['x1'] * $point[0]['x2'] - $point[0]['x1'] * $point[2]['x2'] - $point[1]['x1'] * $point[0]['x2'] - $point[2]['x1'] * $point[1]['x2']) / ($point[0]['x1'] * $point[1]['y1'] + $point[1]['x1'] * $point[2]['y1'] + $point[2]['x1'] * $point[0]['y1'] - $point[0]['x1'] * $point[2]['y1'] - $point[1]['x1'] * $point[0]['y1'] - $point[2]['x1'] * $point[1]['y1']);
	$l = ($point[0]['x1'] * $point[1]['y1'] * $point[2]['x2'] + $point[1]['x1'] * $point[2]['y1'] * $point[0]['x2'] + $point[2]['x1'] * $point[0]['y1'] * $point[1]['x2'] - $point[0]['x1'] * $point[2]['y1'] * $point[1]['x2'] - $point[1]['x1'] * $point[0]['y1'] * $point[2]['x2'] - $point[2]['x1'] * $point[1]['y1'] * $point[0]['x2']) / ($point[0]['x1'] * $point[1]['y1'] + $point[1]['x1'] * $point[2]['y1'] + $point[2]['x1'] * $point[0]['y1'] - $point[0]['x1'] * $point[2]['y1'] - $point[1]['x1'] * $point[0]['y1'] - $point[2]['x1'] * $point[1]['y1']);
	$c = ($point[0]['y2'] * $point[1]['y1'] + $point[1]['y2'] * $point[2]['y1'] + $point[2]['y2'] * $point[0]['y1'] - $point[0]['y2'] * $point[2]['y1'] - $point[1]['y2'] * $point[0]['y1'] - $point[2]['y2'] * $point[1]['y1']) / ($point[0]['x1'] * $point[1]['y1'] + $point[1]['x1'] * $point[2]['y1'] + $point[2]['x1'] * $point[0]['y1'] - $point[0]['x1'] * $point[2]['y1'] - $point[1]['x1'] * $point[0]['y1'] - $point[2]['x1'] * $point[1]['y1']);
	$d = ($point[0]['x1'] * $point[1]['y2'] + $point[1]['x1'] * $point[2]['y2'] + $point[2]['x1'] * $point[0]['y2'] - $point[0]['x1'] * $point[2]['y2'] - $point[1]['x1'] * $point[0]['y2'] - $point[2]['x1'] * $point[1]['y2']) / ($point[0]['x1'] * $point[1]['y1'] + $point[1]['x1'] * $point[2]['y1'] + $point[2]['x1'] * $point[0]['y1'] - $point[0]['x1'] * $point[2]['y1'] - $point[1]['x1'] * $point[0]['y1'] - $point[2]['x1'] * $point[1]['y1']);
	$m = ($point[0]['x1'] * $point[1]['y1'] * $point[2]['y2'] + $point[1]['x1'] * $point[2]['y1'] * $point[0]['y2'] + $point[2]['x1'] * $point[0]['y1'] * $point[1]['y2'] - $point[0]['x1'] * $point[2]['y1'] * $point[1]['y2'] - $point[1]['x1'] * $point[0]['y1'] * $point[2]['y2'] - $point[2]['x1'] * $point[1]['y1'] * $point[0]['y2']) / ($point[0]['x1'] * $point[1]['y1'] + $point[1]['x1'] * $point[2]['y1'] + $point[2]['x1'] * $point[0]['y1'] - $point[0]['x1'] * $point[2]['y1'] - $point[1]['x1'] * $point[0]['y1'] - $point[2]['x1'] * $point[1]['y1']);

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