Page 7 - Computer Graphics Handout
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3.15.2 Bezier Curves ................................................................................................................................................ 140
3.15.3 Cubic Splines ................................................................................................................................................. 140
3.15.4 Curve Blending Techniques .......................................................................................................................... 140
SUMMARY AND NOTES.................................................................................................................................................... 140
Exercises .......................................................................................................................................................................... 142
Chapter 4 VIEWING .......................................................................................................................................................... 143
4.1 CLASSICAL AND COMPUTER VIEWING ................................................................................................................... 143
4.1.1 Classical Viewing ............................................................................................................................................. 145
4.1.2 Orthographic Projections ................................................................................................................................ 145
4.1.3 Axonometric Projections ................................................................................................................................ 146
4.1.4 Oblique Projections ........................................................................................................................................ 146
4.1.5 Perspective Viewing ........................................................................................................................................ 147
4.2 VIEWING WITH A COMPUTER ................................................................................................................................ 148
4.3 POSITIONING OF THE CAMERA .............................................................................................................................. 149
4.3.1 Positioning of the Camera Frame ................................................................................................................... 149
4.3.2 Two Viewing APIs ............................................................................................................................................ 153
4.3.3 The Look-At Function ...................................................................................................................................... 156
4.3.4 Other Viewing APIs ......................................................................................................................................... 157
4.4 PARALLEL PROJECTIONS ........................................................................................................................................ 157
4.4.1 Orthogonal Projections ................................................................................................................................... 158
4.4.2 Parallel Viewing with OpenGL......................................................................................................................... 158
4.4.3 Projection Normalization ................................................................................................................................ 159
4.4.4 Orthogonal-Projection Matrices ..................................................................................................................... 160
4.4.5 Oblique Projections ........................................................................................................................................ 162
4.4.6 An Interactive Viewer ..................................................................................................................................... 164
4.5 PERSPECTIVE PROJECTIONS ................................................................................................................................... 166
4.5.1 Simple Perspective Projections ....................................................................................................................... 166
4.6 PERSPECTIVE PROJECTIONS WITH OPENGL ........................................................................................................... 169
4.6.1 Perspective Functions ..................................................................................................................................... 170
4.7 PERSPECTIVE-PROJECTION MATRICES ................................................................................................................... 171
4.7.1 Perspective Normalization .............................................................................................................................. 171
4.7.2 OpenGL Perspective Transformations ............................................................................................................ 175
4.7.3 Perspective Example ....................................................................................................................................... 176
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