4. James Carver, a dentist, is now the main suspect for the murder of Robert Durst, but po- lice are still watching Samatha Brundi carefully. More solid evidence is needed to convict someone of the murder of Robert Durst. The police would like to know the unlock pattern so they can access Mr. Carver's phone while he is in the shower at the gym. The phone is guarded by a lock screen that unlocks via a pattern that the user draws on a 4x4 grid of circles. The user begins at a circle and drags their finger across four other circles in one continuous motion, as illustrated in the figure. 13 14 0 878 1424 1969 2737 import numpy as np O # Display grid of 16 circles def DrawGrid(): 15 Figure 2: Example of an unlock pattern, 9-11-2-4-6 The police have managed to intercept some data packets sent from Mr. Carver's cell phone. The packets, collected by Gooble (the company that manufactures the phone), convey usage data in a logfile, including some screen digitizer data. Luckily, some of the logfile data pertains to his unlock pattern. The logfile includes the position of the finger at 5 different times, listed in the table below: Time (milliseconds) x position (mm) y position (mm) DrawGrid() Ⓒ 16 1 60 32 29 44 Ⓒ The coordinates in the table are with respect to a lock-screen coordinate system in which the bottom left circle (labelled "1") is the origin, (0, 0). Each subsequent circle in the x-axis direction increments the x-position by 20 mm, and each subsequent circle in the y-axis direction likewise increments the y-position by 20 mm. For example, in figure 2, the pattern starts at (0,40) and goes to (40, 40), (20, 0), (60,0) before ending at (20, 20). The notebook includes a function called DrawGrid () that draws the unlock grid. As a specialist working for the police department, your job is to interpolate the data given in the logfile to determine the unlock pattern of the dentist's phone. You may assume that the dentist's finger is stationary for the first and last points. 59 24 22 42 62 (a) Edit the notebook so that it creates a parametric cubic spline that interpolates the points from the logfile. You may assume that the suspect's finger was at rest at the beginning and end of the swipe pattern (i.e. velocity was zero). (b) Create a plot of the path of the parametric spline on top of the unlock-grid. Include this plot in your assignment. (c) What do you think is the unlock pattern? List the five circles in order. What's in the "notebook" for Part(a), also for Part(b) and Part(c). Basically just code to begin with: plt.figure(figsize=(6,6)) [gx, gy] = np.meshgrid([0, 20, 40, 60], [0, 20, 40, 60]) plt.plot(gx, gy, 'o', color="lightgray', markersize=10); plt.axis ('square');