I don't understand. With cubic splines, all of your data points ARE on the lines. You take a bunch of cubic polynomials and paste them together in such a way that all your data points are on at least one cubic, and the polynomials are continuous and differentiable everywhere.
The set up is similar to a cubic spline, but the points are actually ON the line.
I don't understand what determines the lengths of your tangent lines. Theoretically, tangent lines are infinitely long. By what criterion are you chopping them off into segments?
...you'll notice that in the image the tangent line from point 'a' is significantly longer than the tangent line from point 'b'.
This sentence makes no sense.
(yes I know that line wouldn't work unless 140 degrees were flipped by 180.)
Percentage of what divided by what? What are you comparing to what?
If I were to check the first point based on percentage,...
Distance from what to what?
...the distance would not be the same as if I were to check the distance from point 'b' with the same percentage.
What would be all "that extra processing"? An alternative algorithm?
This was far easier to handle than doing all that extra processing.
Of course? I have no idea why you're doing what you're doing.
...and of course the list of tangent angles...
A general comment: I accept your apology for not being able to communicate clearly, but don't you think you should work on improving your abilities? The way you write is incredibly confusing. In answering one of my questions, it almost seems like you raise two more questions just in your answers! I haven't the faintest idea what the original problem is (it might be good to state that!).
I work as an engineer, and I work in research and development. You can take it from me that the most important skills in the workplace are the communication skills. All the technical problem-solving abilities, as valuable as they can be, are no good to anyone if you can't talk with people in a way that they can understand. This is why it is so incredibly important for technical people to read good books and take humanities courses. As an example, the Challenger blew up partially as the result of bad communication on the part of the engineers. They knew there was a problem with the o-rings, and they wanted to delay the launch. However, they didn't realize they were up against political pressure not to delay yet again. In addition, the PowerPoint slide that contained the critical data was far too dense to convey the intended important piece of data. As a result, they didn't convince their superiors, and the launch went ahead. You know what happened.
So you see, good communication is essential. It's not enough to have the truth - you must be able to convince others of it.