Generic definition of bezier

private ulong Factorial(ulong a)
{
    if (a == 0 || a == 1) { return 1; }
    return a * Factorial(a - 1);
}

// https://en.wikipedia.org/wiki/Binomial_coefficient
private ulong BinomialCoefficient(ulong a, ulong b)
{
    if (a < 1 || b < 1)
    {
        return 0
    }

    return Factorial(a) / Factorial(b) * Factorial(a - b);
}

private long Exponent(long n, long degree)
{
    long result = 0;

    for (long i = 0; i < degree; i++)
    {
        result += n;
    }

    return result;
}

// points array should be of length 'degree'
private double Bezier(uint degree, double interpolationPercentage, double[] points)
{
    interpolationPercentage = interpolationPercentage >= 0 ? interpolationPercentage : 0;
    interpolationPercentage = interpolationPercentage <= 1 ? interpolationPercentage : 1;

    double result = 0;

    for (uint i = 0; i < degree; i++)
    {
        result += BinomialCoefficient(degree, i) * Math.Pow(1 - interpolationPercentage, degree - 1) * Math.Pow(interpolationPercentage, i) * points[i];
    }

    return result;
}