Q15. In practice the LEDs are positioned using a string of length 50 fixed at the...

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Q15. In practice the LEDs are positioned using a string of length 50" fixed at the image origin and rotated in 60 degree steps. Starting at the right and proceeding anti-clockwise, label the LEDs A, B, C, D, E and F, and express their positions as vectors using polar coordinates. [6 marks] Q16. Explain the relationship between polar and Cartesian coordinates, and the role of the trigonometric functions in that relationship. [4 marks] Q17. Convert the positions of the LEDs to Cartesian coordinates (rounding to the nearest integer). [6 marks] Q18. For a 200" diagonal image and with the display set to 1024 x 768 pixels, where should the points be located on the LCD screen (in screen coordinates)? [10 marks] Q19. In a particular setup, the screen PC generated points are located at positions: A' = (113, -40) B' = (72,32) C=(-12,32) D = (-53,-40) E = (-12, -112) F1 = (72,-112) Plot these points on a graph. [6 marks] Q20. What scaling and offset adjustment is required so that these points coincide with the LED positions in Figure 4? [4 marks] End of Assessment inches LED Location 200 150 100 50 O 0- -200 -150- -100 50 0 50 +8 100 150 200 -50 -100 -150 -200 inches Figure 4. Placement of LEDs on the wall. Part 4: LED Positions It is important that the position of the projector is accurate so that the LCD pixels used to activate the sensors are accurately projected onto the sensors. Initially the set-up is to be done manually but the operator will be provided with some assistance to enable the set-up to be accurate. The proposal is that six light emitting diodes (LEDs) in the shape of a hexagon are embedded in the wall and lit during set-up. The PC generates a corresponding screen of six red Q15. In practice the LEDs are positioned using a string of length 50" fixed at the image origin and rotated in 60 degree steps. Starting at the right and proceeding anti-clockwise, label the LEDs A, B, C, D, E and F, and express their positions as vectors using polar coordinates. [6 marks] Q16. Explain the relationship between polar and Cartesian coordinates, and the role of the trigonometric functions in that relationship. [4 marks] Q17. Convert the positions of the LEDs to Cartesian coordinates (rounding to the nearest integer). [6 marks] Q18. For a 200" diagonal image and with the display set to 1024 x 768 pixels, where should the points be located on the LCD screen (in screen coordinates)? [10 marks] Q19. In a particular setup, the screen PC generated points are located at positions: A' = (113, -40) B' = (72,32) C=(-12,32) D = (-53,-40) E = (-12, -112) F1 = (72,-112) Plot these points on a graph. [6 marks] Q20. What scaling and offset adjustment is required so that these points coincide with the LED positions in Figure 4? [4 marks] End of Assessment inches LED Location 200 150 100 50 O 0- -200 -150- -100 50 0 50 +8 100 150 200 -50 -100 -150 -200 inches Figure 4. Placement of LEDs on the wall. Part 4: LED Positions It is important that the position of the projector is accurate so that the LCD pixels used to activate the sensors are accurately projected onto the sensors. Initially the set-up is to be done manually but the operator will be provided with some assistance to enable the set-up to be accurate. The proposal is that six light emitting diodes (LEDs) in the shape of a hexagon are embedded in the wall and lit during set-up. The PC generates a corresponding screen of six red