Captcha.cs

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using System;
using System.Drawing;

public static class Captcha
{
    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));
    }

    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);