3DCaptcha for .net

/*
* 3DCaptcha for .net
*
* http://www-personal.umich.edu/~mressl/3dcaptcha/ (php)
* http://code.google.com/p/3dcaptcha/ (php)
*
* Translate : Aimeast
* Blog : http://www.cnblogs.com/Aimeast/
*/

using System;
using System.Drawing;

namespace WebApplication1
{
public static class Captcha3D
{
private static double[] addVector(double[] a, double[] b)
{
return new double[] { a[0] + b[0], a[1] + b[1], a[2] + b[2] };
}

private static double[] scalarProduct(double[] vector, double scalar)
{
return new double[] { vector[0] * scalar, vector[1] * scalar, vector[2] * scalar };
}

private static double dotProduct(double[] a, double[] b)
{
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}

private static double norm(double[] vector)
{
return Math.Sqrt(dotProduct(vector, vector));
}

private static double[] normalize(double[] vector)
{
return scalarProduct(vector, 1.0 / norm(vector));
}

// http://en.wikipedia.org/wiki/Cross_product
private static double[] crossProduct(double[] a, double[] b)
{
return new double[] {
(a[1] * b[2] - a[2] * b[1]),
(a[2] * b[0] - a[0] * b[2]),
(a[0] * b[1] - a[1] * b[0])
};
}

private static double[] vectorProductIndexed(double[] v, double[] m, int i)
{
return new double[]{
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]
};
}

private static double[] vectorProduct(double[] v, double[] m)
{
return vectorProductIndexed(v, m, 0);
}

private static double[] matrixProduct(double[] a, double[] b)
{
double[] o1 = vectorProductIndexed(a, b, 0);
double[] o2 = vectorProductIndexed(a, b, 4);
double[] o3 = vectorProductIndexed(a, b, 8);
double[] o4 = vectorProductIndexed(a, b, 12);

return new double[]{
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
private static double[] cameraTransform(double[] C, double[] A)
{
double[] w = normalize(addVector(C, scalarProduct(A, -1)));
double[] y = new double[] { 0, 1, 0 };
double[] u = normalize(crossProduct(y, w));
double[] v = crossProduct(w, u);
double[] t = scalarProduct(C, -1);

return new double[]{
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
private static double[] viewingTransform(double fov, double n, double f)
{
fov *= (Math.PI / 180);
double cot = 1.0 / Math.Tan(fov / 2);

return new double[]{
cot, 0, 0, 0,
0, cot, 0, 0,
0, 0, (f + n) / (f - n), -1,
0, 0, 2 * f * n / (f - n), 0
};
}

public static Image Generate(string captchaText)
{
Random rnd = new Random();

// 3dcha parameters
int fontsize = 24;
Font font = new Font("Arial", fontsize);

SizeF sizeF;
using (Graphics g = Graphics.FromImage(new Bitmap(1, 1)))
{
sizeF = g.MeasureString(captchaText, font, 0, StringFormat.GenericDefault);
}

int image2d_x = (int)sizeF.Width;
int image2d_y = (int)(fontsize * 1.3);

double bevel = 4;

// Create 2d image
Bitmap image2d = new Bitmap(image2d_x, image2d_y);
Color black = Color.Black;
Color white = Color.White;

// Paint 2d image
using (Graphics g = Graphics.FromImage(image2d))
{
g.Clear(black);
g.DrawString(captchaText, font, Brushes.White, 0, 0);
}
// Calculate projection matrix
double[] T = cameraTransform(
new double[] { rnd.Next(-90, 90), -200, rnd.Next(150, 250) },
new double[] { 0, 0, 0 }
);
T = matrixProduct(
T,
viewingTransform(60, 300, 3000)
);

// Calculate coordinates
double[][] coord = new double[image2d_x * image2d_y][];

int count = 0;
for (int y = 0; y < image2d_y; y += 2)
{
for (int x = 0; x < image2d_x; x++)
{
// calculate x1, y1, x2, y2
int xc = x - image2d_x / 2;
int zc = y - image2d_y / 2;
double yc = -(double)(image2d.GetPixel(x, y).ToArgb() & 0xff) / 256 * bevel;
double[] xyz = new double[] { xc, yc, zc, 1 };
xyz = vectorProduct(xyz, T);

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

// Create 3d image
int image3d_x = 256;
//$image3d_y = $image3d_x / 1.618;
int image3d_y = image3d_x * 9 / 16;
Bitmap image3d = new Bitmap(image3d_x, image3d_y);
Color fgcolor = Color.White;
Color bgcolor = Color.Black;
using (Graphics g = Graphics.FromImage(image3d))
{
g.Clear(bgcolor);
count = 0;
double scale = 1.75 - (double)image2d_x / 400;
for (int y = 0; y < image2d_y; y += 2)
{
for (int x = 0; x < image2d_x; x++)
{
if (x > 0)
{
double x0 = coord[count - 1][0] * scale + image3d_x / 2;
double y0 = coord[count - 1][1] * scale + image3d_y / 2;
double x1 = coord[count][0] * scale + image3d_x / 2;
double y1 = coord[count][1] * scale + image3d_y / 2;
g.DrawLine(new Pen(fgcolor), (float)x0, (float)y0, (float)x1, (float)y1);
}
count++;
}
}
}
return image3d;
}
}
}