2- Spline toolpath planning and interpolation: Write a MATLAB program to plan and interpolate the toolpath shown in Figure 2, using cubic spline interpolation. The toolpath intermediate points (i.e. knots) are provided in a MATLAB file on LEARN. The spline interpolation program should call the feed planning function, written in Part 1, in order to generate the feed profile with the following parameters: 1,-1,-0 [mm/sec], F=100 [mm/sec). A=-D=1000 [mm/sec]. J=30000 [mm/sec], 7, -1 [msec] Implement the spline interpolation using: (a) Natural Interpolation: u = (1/S)-s (b) 1 Order Taylor Series Interpolation: -+- x2 (1) + x(x-1) Show the results obtained with both interpolation techniques on the same graph using different line styles, or preferably color. Provide graphs for: Toolpath geometry and spline knots (i.e. given points): y vs. x Position profiles in time (1): x vs. z. y vs. ! - Numerically differentiated x and y axis velocity profiles and estimated feed (/) profile: (i vs. 1. vs. 1. / ==+ vs. 1), Zoom into the feed graph and make a comparison between the two interpolation techniques Numerically differentiated x, y axis and resultant acceleration profiles: ( vs. . vs. 1. + vs. 1) 62 12 V 40 YAxs [mm] 40 3 -40 0 x Axis [mm] Figure 2: Fan-shaped spline toolpath. 40