<?

/**
 * 3D Captcha
 * (C) 2006 by Marc S. Ressl
 */
 
// Get captcha text
session_start();
$captchaText = $_SESSION['3DCaptchaText'];

// Functions
function addVector($a, $b) {
	return array($a[0] + $b[0], $a[1] + $b[1], $a[2] + $b[2]);
}

function scalarProduct($vector, $scalar) {
	return array($vector[0] * $scalar, $vector[1] * $scalar, $vector[2] * $scalar);
}

function dotProduct($a, $b) {
	return ($a[0] * $b[0] + $a[1] * $b[1] + $a[2] * $b[2]);
}

function norm($vector) {
	return sqrt(dotProduct($vector, $vector));
}

function normalize($vector) {
	return scalarProduct($vector, 1 / norm($vector));
}

// http://en.wikipedia.org/wiki/Cross_product
function crossProduct($a, $b) {
	return array(
		($a[1] * $b[2] - $a[2] * $b[1]),
		($a[2] * $b[0] - $a[0] * $b[2]),
		($a[0] * $b[1] - $a[1] * $b[0])
		);
}

function vectorProductIndexed($v, $m, $i) {
	return array(
		$v[$i + 0] * $m[0] + $v[$i + 1] * $m[4] + $v[$i + 2] * $m[8] + $v[$i + 3] * $m[12],
		$v[$i + 0] * $m[1] + $v[$i + 1] * $m[5] + $v[$i + 2] * $m[9] + $v[$i + 3] * $m[13],
		$v[$i + 0] * $m[2] + $v[$i + 1] * $m[6] + $v[$i + 2] * $m[10]+ $v[$i + 3] * $m[14],
		$v[$i + 0] * $m[3] + $v[$i + 1] * $m[7] + $v[$i + 2] * $m[11]+ $v[$i + 3] * $m[15]
		);
}

function vectorProduct($v, $m) {
	return vectorProductIndexed($v, $m, 0);
}

function matrixProduct($a, $b) {
	$o1 = vectorProductIndexed($a, $b, 0);
	$o2 = vectorProductIndexed($a, $b, 4);
	$o3 = vectorProductIndexed($a, $b, 8);
	$o4 = vectorProductIndexed($a, $b, 12);

	return array(
		$o1[0], $o1[1], $o1[2], $o1[3],
		$o2[0], $o2[1], $o2[2], $o2[3],
		$o3[0], $o3[1], $o3[2], $o3[3],
		$o4[0], $o4[1], $o4[2], $o4[3]
		);
}

// http://graphics.idav.ucdavis.edu/education/GraphicsNotes/Camera-Transform/Camera-Transform.html
function cameraTransform($C, $A) {
	$w = normalize(addVector($C, scalarProduct($A, -1)));
	$y = array(0, 1, 0);
	$u = normalize(crossProduct($y, $w));
	$v = crossProduct($w, $u);
	$t = scalarProduct($C, -1);
	
	return array(
		$u[0], $v[0], $w[0], 0,
		$u[1], $v[1], $w[1], 0,
		$u[2], $v[2], $w[2], 0,
		dotProduct($u, $t), dotProduct($v, $t), dotProduct($w, $t), 1
		);
}

// http://graphics.idav.ucdavis.edu/education/GraphicsNotes/Viewing-Transformation/Viewing-Transformation.html
function viewingTransform($fov, $n, $f) {
	$fov *= (M_PI / 180);
	$cot = 1 / tan($fov / 2);

	return array(
		$cot,	0,		0,		0,
		0,		$cot,	0,		0, 
		0,		0,		($f + $n) / ($f - $n),		-1,
		0,		0,		2 * $f * $n / ($f - $n),	0
		);
}
// 3dcha parameters
$fontsize = 24;
$fontfile = 'fonts/3dcaptcha.ttf';

$details = imagettfbbox($fontsize, 0, $fontfile, $captchaText);
$image2d_x = $details[4] + 7;
$image2d_y = $fontsize * 1.3;

$bevel = 3;

// Create 2d image
$image2d = imagecreatetruecolor($image2d_x, $image2d_y);
$black = imagecolorallocate($image2d, 0, 0, 0);
$white = imagecolorallocate($image2d, 255, 255, 255);

// Paint 2d image
imagefill($image2d, 0, 0, $black);
imagettftext($image2d, $fontsize, 0, 2, $fontsize, $white, $fontfile, $captchaText);

// Calculate projection matrix
$T = cameraTransform(
		array(rand(-90, 90), -200, rand(150, 250)),
		array(0, 0, 0)
	);
$T = matrixProduct(
		$T,
		viewingTransform(60, 300, 3000)
	);

// Calculate coordinates
$coord = array($image2d_x * $image2d_y);
$count = 0;
for ($y = 0; $y < $image2d_y; $y+=2) {
	for ($x = 0; $x < $image2d_x; $x++) {
		// calculate x1, y1, x2, y2
		$xc = $x - $image2d_x / 2;
		$zc = $y - $image2d_y / 2;
		$yc = -(imagecolorat($image2d, $x, $y) & 0xff) / 256 * $bevel;
		$xyz = array($xc, $yc, $zc, 1);
		$xyz = vectorProduct($xyz, $T);

		$coord[$count] = $xyz;
		$count++;
	}
}

// Create 3d image
$image3d_x = 256;
//$image3d_y = $image3d_x / 1.618;
$image3d_y = $image3d_x * 9 / 16;
$image3d = imagecreatetruecolor($image3d_x, $image3d_y);
$fgcolor = imagecolorallocate($image3d, 100, 100, 100);
$bgcolor = imagecolorallocate($image3d, 248, 248, 248);
imageantialias($image3d, true);
imagefill($image3d, 0, 0, $bgcolor);
$count = 0;
$scale = 1.75 - $image2d_x/400;
for ($y = 0; $y < $image2d_y; $y++) {
	for ($x = 0; $x < $image2d_x; $x++) {
		if ($x > 0) {
			$x0 = $coord[$count - 1][0] * $scale + $image3d_x / 2;
			$y0 = $coord[$count - 1][1] * $scale + $image3d_y / 2;
			$x1 = $coord[$count][0] * $scale + $image3d_x / 2;
			$y1 = $coord[$count][1] * $scale + $image3d_y / 2;
			imageline($image3d, $x0, $y0, $x1, $y1, $fgcolor);
		}
		$count++;
	}
}

header("Content-type: image/jpeg");
header("Cache-Control: no-cache, must-revalidate"); // HTTP/1.1
header("Expires: Mon, 03 Apr 1977 11:05:00 GMT"); // Date in the very past, guess what it is
imagejpeg($image3d);

?>