Re: Curve Driving Generator
@Ether: The example in the .pdf was more deliberate than unfortunate. I chose a tangent line slope that would exagerate the effect and help high school students to make connections to their work in schools. (I am an educator, not an engineer.)
I included the .pdf more to show what a Mathcad worksheet looks like. I think it is more transparent than either Excel or Maxima because Mathcad uses standard math notation. The .pdf was not meant to be the primary contribution.
The Mathcad worksheet is a computational document, so it is possible to change the parameters. The worksheet is therefore a general method for calculating a cubic polynomial given the endpoints and tangent slopes. As you observed in your post, there are some examples where the solution is efficient, others where it is not. With the Mathcad worksheet, it is possible to quickly derive and plot a path and determine whether or not it is a solution worth implementing.
It is certainly possible to build a Mathcad worksheet to generate the Bezier Curve. I will add this to my "Want to Do" list and post it to the Thread when I cross it off. Thanks for the suggestion and the Excel worksheet. I'll probably convert your Excel spreadsheet to Mathcad.