(10) A particle moving in R2 is animated so that its position B(t) at time t is given by a degree three Bzier curve with control points P0,P1,P2,P3. At time t= 0 , the particle is at (0,0) and has velocity (6,0). At time t=1, the particle is at (0,4) and has velocity (12,0). a. What are the control points P0,P1,P2, and P3 equal to? b. Draw on the graph, the four control points, and the control polygon. c. Calculate B(1/2), the position at time t=1/2. Show your work on the same graph. d. Sketch the Bzier curve for 0t1 on the same graph. Be sure to show the starting and ending slopes (tangencies) clearly. e. Consider the second half of the path of the particle, namely the path traced out when 21t1. This is also a degree three Bezier curve. What are its control points? (10) A particle moving in R2 is animated so that its position B(t) at time t is given by a degree three Bzier curve with control points P0,P1,P2,P3. At time t= 0 , the particle is at (0,0) and has velocity (6,0). At time t=1, the particle is at (0,4) and has velocity (12,0). a. What are the control points P0,P1,P2, and P3 equal to? b. Draw on the graph, the four control points, and the control polygon. c. Calculate B(1/2), the position at time t=1/2. Show your work on the same graph. d. Sketch the Bzier curve for 0t1 on the same graph. Be sure to show the starting and ending slopes (tangencies) clearly. e. Consider the second half of the path of the particle, namely the path traced out when 21t1. This is also a degree three Bezier curve. What are its control points