Drawing a clothoid spline

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This is a rather strange question but here goes anyway, I need an algorithm that interpolate values given that there is a straigth line between A and B, and the point C that is either to the left or right of the line between A and B. The algorithm I want to implement is often called a G2 interpolation, using an Euler spiral.

I found an article that outlines the algorithm that I want to use:
http://www.ams.org/journals/mcom/1992-59-199/S0025-5718-1992-1134736-8/home.html[^]

However it seems to be extremely complicated to implement. My question is simply, does anybody know if there either exists a more elaborate (or for dummies if you'd like) explination of this (or possibly some code) that could explain what to actually do. Do I have to choose some of the values or is it a unique implementation?

So far I have just found an algorithm for the Fresnel integrals:

''' <summary>
       ''' Source code is converted from Michael Moser given in "Engineering Acoustics - An introduction to noise control" pages 342 - 343, 10.11 Appendix: Matlab program for Fresnel integrals
       ''' </summary>
       ''' <param name="xarg">The x argument of the Sin and Cos functions inside the Fresnl integrals</param>
       ''' <returns>A Double(2), were Double(0) is the Cos_Fresnel and Double(1) is the Sin_Fresnel integrals</returns>
       ''' <remarks></remarks>
       Public Function FresnelIntegral(ByVal xarg As Double) As Double()
           Dim result(2) As Double
           Dim x, arg, s, c, cfrenl, sfrenl As Double

           x = Math.Abs(xarg) / Math.Sqrt(Math.PI / 2)
           arg = Math.PI * (x ^ 2) / 2

           s = Math.Sin(arg)
           c = Math.Cos(arg)

           If x > 4.4 Then
               Dim x4, x3, x2, x1 As Double
               x4 = x ^ 4
               x3 = x ^ 3
               x2 = 0.10132 - 0.154 / x4
               x1 = 0.3183099 - 0.0968 / x4

               cfrenl = 0.5 + x1 * s / x - x2 * c / x3
               sfrenl = 0.5 - x1 * c / x - x2 * s / x3

               If xarg < 0 Then
                   cfrenl *= -1
                   sfrenl *= -1
               End If

           Else
               Dim a0, sum, xmul, an, nend, xnenn, an1 As Double
               a0 = x
               sum = x
               xmul = -((Math.PI / 2) ^ 2) * (x ^ 4)
               an = a0
               nend = (x + 1) * 20

               For n As Integer = 0 To nend
                   xnenn = (2 * n + 1) * (2 * n + 2) * (4 * n + 5)
                   an1 = an * (4 * n + 1) * xmul / xnenn
                   sum += an1
                   an = an1
               Next


               cfrenl = sum
               a0 = (Math.PI / 6) * x ^ 3
               sum = a0
               an = a0
               nend = (x + 1) * 20

               For n As Integer = 0 To nend
                   xnenn = (2 * n + 2) * (2 * n + 3) * (4 * n + 7)
                   an1 = an * (4 * n + 3) * xmul / xnenn
                   sum += an1
                   an = an1
               Next

               sfrenl = sum

               If xarg < 0 Then
                   cfrenl *= -1
                   sfrenl *= -1

               End If

           End If

           result(0) = cfrenl
           result(1) = sfrenl

           Return result
       End Function