Piecewise Cubic Spline

Trajectory planning for robotic locomotion by stitching two cubic polynomials

Simple code that uses the following initial and final conditions to generate the x and y co-ordinate trajectory.
t(s) x(m) y(m)
0.0 0.1 0.0
0.5 0.3 0.1
1.0 0.5 0.0

Two solve for two cubic polynomials (polynomial 0/1 or p0/p1) look at time intervals t 0.0 to 0.5 and t 0.5 to 1.0. This requires eight bits (4 each) of independent information to solve for each coefficient.

This is denoted in the eight by eight matrix. The coefficients are evaluated and cubic spline plotted against time.