Smooth Path Generator for RoboRio 2015

[faust1706]

Ether posted a math quiz on here a little while ago that basically required someone to lay out the mathematics of how to calculate the left and right path trajectory of a robot given it's route.

http://www.chiefdelphi.com/forums/sh...d.php?t=126639

How I solved the problem was some simple calculus. I download a symbolic-numeric library that allowed me to take the derivative of my original function (the path), and then I found the function that at point x gives the slope of the normal line of my derivative function. Then I solve a system of linear equations. I want to "march out" n units from my original function, so I have the equation of the normal line and a circle around my point x (x^2 + y^2 = n^2). Then I solve the system. I do that for every point, then compile the points and fit a function to it. I feel as though there is a much better way of doing this though. (This method has proven to be quick enough for it's purpose. It takes about 10ms to go through a function with precision of 1,000 points to solve for) Could either of you explain your mathematics?