1. Computer Graphics Panos Trahanias e-mail: trahania@csd.uoc.gr ΗΥ358 Spring 2009

2. Panos Trahanias: Computer Graphics Ιστορική Αναδρομή Architecture of a Vector Display

3. Panos Trahanias: Computer Graphics Ιστορική Αναδρομή Architecture of a Raster Display

4. Panos Trahanias: Computer Graphics Ιστορική Αναδρομή Random scan versus raster scan

5. Panos Trahanias: Computer Graphics Conceptual Framework of CG

6. Panos Trahanias: Computer Graphics Line Drawing – Midpoint Algorithm

7. Panos Trahanias: Computer Graphics Line Drawing – Midpoint Algorithm

8. Panos Trahanias: Computer Graphics Line Drawing – Midpoint Algorithm

9. Panos Trahanias: Computer Graphics Line Drawing – Midpoint Algorithm

10. Panos Trahanias: Computer Graphics Line Drawing – Midpoint Algorithm

11. Panos Trahanias: Computer Graphics Line Drawing – Midpoint Algorithm

12. Panos Trahanias: Computer Graphics Line Drawing – Midpoint Algorithm

13. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm

14. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm

15. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm Eight-way symmetry

16. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm

17. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm

18. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm

19. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm

20. Panos Trahanias: Computer Graphics Circle Drawing – Midpoint Algorithm

21. Panos Trahanias: Computer Graphics Ellipse Drawing – Midpoint Algorithm

22. Panos Trahanias: Computer Graphics Ellipse Drawing – Midpoint Algorithm

23. Panos Trahanias: Computer Graphics Ellipse Drawing – Midpoint Algorithm

24. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm Increasing Resolution

25. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm Unweighted Area Sampling

26. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm Properties of Unweighted Area Sampling: Intensity of a pixel intersected by a line decreases as the distance between the pixel center and the edge increases. A primitive (e.g. line) does not influence a pixel at all if they are not intersected. Equal areas contribute equal intensity, regardless of the distance between the pixel’s center and the area.

27. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm Unweighted Area Sampling: Box Filter

28. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm Weighted Area Sampling: Cone Filter

29. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm Dramatic Effects of the cone filter.

30. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm

31. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm

32. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm

33. Panos Trahanias: Computer Graphics Antialiasing – Midpoint Line Algorithm

34. Panos Trahanias: Computer Graphics Polygon Filling

35. Panos Trahanias: Computer Graphics Polygon Filling

36. Panos Trahanias: Computer Graphics Polygon Filling Calculation of Span Extrema

37. Panos Trahanias: Computer Graphics Polygon Filling

38. Panos Trahanias: Computer Graphics Polygon Filling

39. Panos Trahanias: Computer Graphics Polygon Filling

40. Panos Trahanias: Computer Graphics Polygon Filling

41. Panos Trahanias: Computer Graphics Polygon Filling Polygon Filling Algorithm

42. Panos Trahanias: Computer Graphics Polygon Filling

43. Panos Trahanias: Computer Graphics Filling Ellipse Arcs

44. Panos Trahanias: Computer Graphics Clipping Lines

45. Panos Trahanias: Computer Graphics Clipping Lines Cohen-Sutherland Line-Clipping Algorithm

46. Panos Trahanias: Computer Graphics Clipping Lines

47. Panos Trahanias: Computer Graphics Clipping Lines

48. Panos Trahanias: Computer Graphics Clipping Lines

49. Panos Trahanias: Computer Graphics Clipping Lines

50. Panos Trahanias: Computer Graphics Clipping Lines Parametric Line-Clipping Algorithm

51. Panos Trahanias: Computer Graphics Clipping Lines

52. Panos Trahanias: Computer Graphics Clipping Lines

53. Panos Trahanias: Computer Graphics Clipping Lines

54. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations - Translation

55. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations - Scaling

56. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations - Rotation

57. Panos Trahanias: Computer Graphics Geometrical Transformations Homogeneous Coordinates The XYW homogeneous coordinate space, with the W=1 plane and point P(X,Y,W) projected onto the W=1 plane.

58. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations – Affine Transformations 45 o rotation and then nonuniform scaling of the unit cube. The result is an affine transformation.

59. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations – Shear Transformations

60. Panos Trahanias: Computer Graphics Geometrical Transformations Composition of 2D Transformations

61. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations – the Window-to-Viewport Transformation

62. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations – the Window-to-Viewport Transformation

63. Panos Trahanias: Computer Graphics Geometrical Transformations 2D Transformations – the Window-to-Viewport Transformation

64. Panos Trahanias: Computer Graphics Geometrical Transformations 3D Transformations – Coordinate Systems Right-handed Coordinate System Left-handed Coordinate System

65. Panos Trahanias: Computer Graphics Geometrical Transformations Composition of 3D Transformations

66. Panos Trahanias: Computer Graphics Geometrical Transformations Composition of 3D Transformations – 1 st Approach

67. Panos Trahanias: Computer Graphics Geometrical Transformations Composition of 3D Transformations – 2 nd Approach

68. Panos Trahanias: Computer Graphics Geometrical Transformations Composition of 3D Transformations

69. Panos Trahanias: Computer Graphics Viewing in 3D Conceptual model of 3D viewing

70. Panos Trahanias: Computer Graphics Viewing in 3D Projections - Projectors

71. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projections – 1-point PP

72. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projections – 2-point PP

73. Panos Trahanias: Computer Graphics Viewing in 3D Parallel Projections

74. Panos Trahanias: Computer Graphics Viewing in 3D Parallel Projections – Isometric Projection

75. Panos Trahanias: Computer Graphics Viewing in 3D Parallel Projections – Oblique Projection

76. Panos Trahanias: Computer Graphics Viewing in 3D

77. Panos Trahanias: Computer Graphics Viewing in 3D Specifying an Arbitrary 3D View

78. Panos Trahanias: Computer Graphics Viewing in 3D Specifying an Arbitrary 3D View

79. Panos Trahanias: Computer Graphics Viewing in 3D

80. Panos Trahanias: Computer Graphics Viewing in 3D

81. Panos Trahanias: Computer Graphics Viewing in 3D

82. Panos Trahanias: Computer Graphics Viewing in 3D

83. Panos Trahanias: Computer Graphics Viewing in 3D The Mathematics of Planar Geometric Projections

84. Panos Trahanias: Computer Graphics Viewing in 3D Alternative Perspective Projection

85. Panos Trahanias: Computer Graphics Viewing in 3D Alternative Perspective Projection

86. Panos Trahanias: Computer Graphics Viewing in 3D Implementation of Planar Geometric Projections

87. Panos Trahanias: Computer Graphics Viewing in 3D Implementation of 3D Viewing

88. Panos Trahanias: Computer Graphics Viewing in 3D Parallel Projection

89. Panos Trahanias: Computer Graphics Viewing in 3D Parallel Projection

90. Panos Trahanias: Computer Graphics Viewing in 3D Parallel Projection

91. Panos Trahanias: Computer Graphics Viewing in 3D Parallel Projection

92. Panos Trahanias: Computer Graphics Viewing in 3D Shearing Matrix

93. Panos Trahanias: Computer Graphics Viewing in 3D Final Translation / Scaling Step

94. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

95. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

96. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

97. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

98. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

99. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection Step 4 - Shear

100. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

101. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

102. Panos Trahanias: Computer Graphics Viewing in 3D Perspective Projection

103. Panos Trahanias: Computer Graphics Viewing in 3D Implementation Summary

104. Panos Trahanias: Computer Graphics Visible Surface Determination Image Precision ApproachesObject Precision Approaches for (each pixel in the image) { determine the object closest to the viewer that is pierced by the projector through the pixel; draw the pixel in the appropriate color; } for (each object in the world) { determine those parts of the object whose view is unobstructed by other parts of it or any other object; draw those parts in the appropriate color; }

105. Panos Trahanias: Computer Graphics Techniques for Efficient Visible-surface Algorithms Extents and Bounding Volumes

106. Panos Trahanias: Computer Graphics Techniques for Efficient Visible-surface Algorithms Back-face Culling

107. Panos Trahanias: Computer Graphics Z-Buffer Algorithm

108. Panos Trahanias: Computer Graphics Z-Buffer Algorithm

109. Panos Trahanias: Computer Graphics Z-Buffer Algorithm

110. Panos Trahanias: Computer Graphics Scan-Line Algorithms Much like polygon scan- conversion algorithms Each ET entry contains

111. Panos Trahanias: Computer Graphics Scan-Line Algorithms

112. Panos Trahanias: Computer Graphics Scan-Line Algorithms

113. Panos Trahanias: Computer Graphics Scan-Line Algorithms

114. Panos Trahanias: Computer Graphics Scan-Line Algorithms

115. Panos Trahanias: Computer Graphics Scan-Line Algorithms

116. Panos Trahanias: Computer Graphics Scan-Line Algorithms Pseudocode for a general scan-line algorithm

117. Panos Trahanias: Computer Graphics Visible-Surface Ray Tracing

118. Panos Trahanias: Computer Graphics Visible-Surface Ray Tracing Pseudocode for a simple ray tracer

119. Panos Trahanias: Computer Graphics Visible-Surface Ray Tracing

120. Panos Trahanias: Computer Graphics Visible-Surface Ray Tracing Anti-alised ray tracing

121. Panos Trahanias: Computer Graphics List-Priority Algorithms The Depth-Sort Algorithm

122. Panos Trahanias: Computer Graphics List-Priority Algorithms Depth Comparisons

123. Panos Trahanias: Computer Graphics List-Priority Algorithms The Depth-Sort Algorithm – Tests to resolve ambiguities The Depth-Sort Algorithm – Tests with polygons reversed

124. Panos Trahanias: Computer Graphics List-Priority Algorithms The Depth-Sort Algorithm – Results of Tests

125. Panos Trahanias: Computer Graphics List-Priority Algorithms The Depth-Sort Algorithm – Unnecessary polygon split

126. Panos Trahanias: Computer Graphics Illumination and Shading

127. Panos Trahanias: Computer Graphics Illumination and Shading Diffuse Reflection

128. Panos Trahanias: Computer Graphics Illumination and Shading

129. Panos Trahanias: Computer Graphics Illumination and Shading Atmospheric Attenuation

130. Panos Trahanias: Computer Graphics Illumination and Shading Depth Cueing

131. Panos Trahanias: Computer Graphics Illumination and Shading Specular Reflection

132. Panos Trahanias: Computer Graphics Illumination and Shading

133. Panos Trahanias: Computer Graphics Illumination and Shading

134. Panos Trahanias: Computer Graphics Illumination and Shading

135. Panos Trahanias: Computer Graphics Illumination and Shading

136. Panos Trahanias: Computer Graphics Illumination and Shading Surface Normals

137. Panos Trahanias: Computer Graphics Illumination and Shading

138. Panos Trahanias: Computer Graphics Illumination and Shading Normal Vector Interpolation

139. Panos Trahanias: Computer Graphics Illumination and Shading Gouraud Shading – Phong Shading

140. Panos Trahanias: Computer Graphics Illumination and Shading Texture Mapping

141. Panos Trahanias: Computer Graphics Illumination and Shading Scan-line Shadow Algorithm

142. Panos Trahanias: Computer Graphics Illumination and Shading Two-Pass Object Precision Shadow Algorithm

143. Panos Trahanias: Computer Graphics Illumination and Shading Transparency

144. Panos Trahanias: Computer Graphics Illumination and Shading Calculating the refraction vector