Derive the homogenous matrices to represent the following transformation

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Translation - Rotation about the origin – Scaling

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Bijay Satyal

Bijay Satyal

Oct 22, 2021

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1. Magnify the triangle with vertices A (0, 0), B (1, 1) and C (5, 2) to twice its size while keeping C (5, 2) fixed.

2. Consider the square A (1, 0), B (0, 0), C (0, 1), D (1, 1). Rotate the square ABCD by 45 degree clockwise about A (1, 0).

3. Find the transformation matrix that transforms the square ABCD whose center is at (2, 2) is reduced to half of its size, with center still remaining at (2, 2). The coordinate of square ABCD are A (0, 0), B (0, 4), C (4, 4) and D (4, 0). Find the co-ordinate of new square.

4. Perform a 45o rotation of a triangle A(0,0, B(1,1), C(5,2) a. About the origin. b. About the point p(-1,-1)

5. Translate the square ABCD whose co-ordinate are A(0,0), b(3,0), C(3,3), D(0,3) by 2 units in both direction and then scale it by 1.5 units in x direction and 0.5 units in y direction.

6. A triangle is defined by Find the transformed coordinates after the following transformation a. 90o rotation about origin. b. Reflection about line y = -x.

7. The process of drawing circle using Brute force method can be enhanced by taking greater advantage of the symmetry in a circle. Write the complete algorithm used to apply this enhancement.

8. Implement the DDA algorithm to draw a line from (0,0) to (6,6). M=(6-0)/(6-0)=6/6 =1 XK+1=Xk+1 YK+1=Yk+m = Yk+1 Xk=0 Yk=0

9. Digitize a line with end points (20, 10) and (30, 18) using DDA line drawing Algorithm.

10. Using the DDA algorithm digitize a line with end points (10,15) and (15,30).

11. Write the algorithm of the line drawing algorithm using Digital Differential Analyzer (DDA).

12. Digitize a line with end points (20, 10) and (30, 18).

13. Using the Brute force algorithm to digitize a line with end points (20, 10) and (26, 14).

14. Write pseudo code for applying the algorithm

15. For the brute force line drawing algorithm:

16. Describe what is performed by the following functions:

17. How can an application program actually draw something on screen?

18. Suppose an RGB raster system is to be designed using an 8-inch by 10-inch screen with a resolution of 100 pixels per inch in each direction. If we want to store 6 bits per pixel in the frame buffer, how much storage bytes do we need for the frame buffer?

19. How long would it take to load a 640-by-480 frame buffer with 12 bits per pixel, if 105 bits can be transferred per second? How long would it take to load a 24-bit-per- pixel frame buffer with a resolution of 1280 by 1024 using this same transfer rate?

20. Suppose we have a video monitor with a display area with 12 inches width and 9.6 inches high. If the resolution is 1280 X 1024 and the aspect ratio is 1, what are the width and the height of each point on the screen?

21. How much time is spent in scanning across each row of pixels during screen refresh on a raster system with a resolution of 1280 by 1024 and refresh rate of 60 frames per second?

22. How long does it take to load a 640-by-480 frame buffer with 12 bits per pixel, if 105 bits can be transferred per second?

23. Consider three different raster systems with resolutions of 640 by 480, 1280 by 1024, and 2560 by 2048. What size frame buffer (in bytes) is needed for each of these systems to store 12 bits per pixel? How much storage is required for each system if 24 bits per pixel are to be stored?

24. Find out the aspect ratio of the raster system using 8 x 10 inches screen and 100 pixel/inch.

25. Suppose RGB raster system is to be designed using on 8 inch X 10 inch screen with a resolution of 100 pixels per inch in each direction. If we want to store 6 bits per pixel in the frame buffer, how much storage (in bytes) do we need for frame buffer?

26. How much time is spent scanning across each row of pixels during screen refresh on a raster system with resolution of 1280 X 1024 and a refresh rate of 60 frames per second?

27. How Many k bytes does a frame buffer needs in a 600 x 400 pixel?

28. Consider a raster system with the resolution of 1024 x 768 pixels and the color palette calls for 65,536 colors. What is the minimum amount of video RAM that the computer must have to support the above-mentioned resolution and number of colors?

29. Consider two raster systems with the resolutions of 640 x 480 and 1280 x 1024.

30. Consider three different raster systems with resolutions of 640 x 480, 1280 x 1024, and 2560 x 2048.

31. What are the popular image storage formats?

32. What are the different types of Flat-Screens, and what is the difference between them?

33. Define shadow masking.

34. What is a Beam penetration method?

35. What do you mean by interlacing?

36. What do you mean by retracing? Define horizontal as well as vertical retracing.

37. What are the different types of Flat-Screens, and what is the difference between them?

38. What are the different properties of phosphorus?

39. What do you mean by an aspect ratio?

40. Define resolution.

41. Define persistence in terms of CRT Phosphorous.

42. List the operating characteristics for the video display systems based on the CRT technology?

43. What is the difference between raster storage image and vector storage image?

44. Differentiate between raster and random scan displays.

45. Describe the Basic Components of computer graphics system?

46. Give an example of memory mapping for 5 X 5 resolution color display device?

47. Memory mapping

48. What do you mean by scan conversion?

49. Define Graphics controller /Display controller/Display processor.

50. What is the role of a video controller?

51. Define bitmap.

52. Define Pixel.

53. Define refresh buffer/Frame buffer?

54. What does it mean by RGB?

55. What do you mean by GUI?

56. Computer Graphics API

57. How can the computer graphics used in solving problems?

58. What can the programmer do in computer graphics?

59. What are the applications of computer graphics?

60. What do you mean by computer graphics?

61. Describe the steps to be followed in Digital Differential Analyzer scan conversion algorithm

62. Describe the Implementation of Midpoint Circle Algorithm

63. Explain Ellipse generating Algorithm?

64. Explain the Midpoint Circle Algorithm?

65. Explain Bresenhams Line Drawing Algorithm?

66. Explain DDA (Digital Differential Analyzer) Scan Conversion Algorithm?

67. What is reflection?

68. What is shearing?

69. What is scaling in computer graphic?

70. What is rotation in computer graphic?

71. What is translation in computer graphic?

72. Write short notes on active and passive transformations?

73. What is Transformation in Computer Graphic?

74. What is point in the computer graphics system?

75. What is an output primitive?

76. Consider a raster system with the resolution of 1024 x 768 pixels and the color palette calls for 65,536 colors.

77. What is the access time per pixel in each system?

78. Use the Cohen Sutherland algorithm to clip line P1 (70,20) and p2(100,10) against a window lower left hand corner (50,10) and upper right hand corner (80,40).

79. Prove that simultaneous shearing in both direction (X & y direction) is not equal to the composition of pure shear along x-axis followed by pure shear along y-axis.

80. Show that the 2 X 2 matrix represents pure rotation.

81. A unit square is transformed by 2 x 2 transformation matrix. what is the transformation matrix?

82. Suppose RGB raster system is to be designed using on 8 inch X 10 inch screen with a resolution of 100 pixels per inch in each direction.

83. How much time is spent scanning across each row of pixels during screen refresh on a raster system with resolution of 1280 X 1024 and a refresh rate of 60 frames per second?

84. Find out the aspect ratio of the raster system using 8 x 10 inches screen and 100 pixel/inch.

85. How Many k bytes does a frame buffer needs in a 600 x 400 pixel ?

86. What is the minimum amount of video RAM that the computer must have to support the above-mentioned resolution and number of colors?

87. Consider two raster systems with the resolutions of 640 x 480 and 1280 x 1024.

88. Consider three different raster systems with resolutions of 640 x 480, 1280 x 1024, and 2560 x 2048

89. What is the advantages of electrostatic plotters?

90. What are the advantages of laser printers?

91. What is the features of Inkjet printers?

92. What is the difference between impact and non-impact printers?

93. Explain the merits and demerits of Plasma panel display.

94. Explain the merits and demerits of DVST.

95. Explain the merits and demerits of Penetration techniques.

96. What do you mean by scan conversion?

97. Define Graphics controller /Display controller/Display processor.

98. What is the role of a video controller?

99. List some 3D viewing devices.

100. Differentiate emissive and non emissive displays.

101. What are advantages of DVST over CRT? Also list some disadvantages of DVST

102. What are composite monitors?

103. Define shadow masking

104. What is a Beam penetration method?

105. What do you mean by interlacing?

106. What do you mean by retracing? Define horizontal as well as vertical retracing

107. Define Bitmap

108. Define Pixel

109. Define Refresh buffer/Frame buffer?

110. Differentiate raster and random scan displays

111. What are the different properties of phosphorus?

112. What do you mean by an aspect ratio?

113. Define resolution

114. Define persistence in terms of CRT Phosphorous

115. Define VDU?

116. What does it mean by RGB?

117. What do you mean by GUI?

118. What do you mean by interactive computer Graphics?

119. What are the applications of computer graphics?

120. What do you mean by computer graphics?

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