Computer Graphics

1. Computer Graphics

2. 3D Transforms • The idea of 3D transforms is the same as that of 2D – A 3D point is represented by (x, y, z) – Homogeneous Coordinates are defined as • A 4th Coordinate is added to every 3D point • (x, y, z, t) represents (x/t, y/t, z/t) • (x, y, z, 0) represents infinity • (0, 0, 0, 0) is not allowed

3. General 3D Homogeneous Transform                                      w z y x p o n m l k j i h g f e d c b a w z y x ' ' ' '

4. Scaling • Scaling matrix                                      w z y x c b a w z y x 1 0 0 0 0 0 0 0 0 0 0 0 0 ' ' '

5. Reflection • Reflection Matrix about yz – plane • What are other reflection matrices                                      w z y x w z y x 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ' ' '

6. Rotation • Rotation about Z – axis                                           w z y x w z y x 1 0 0 0 0 1 0 0 0 0 cos sin 0 0 sin cos ' ' '

7. Rotation • Rotation about Y – axis                                           w z y x w z y x 1 0 0 0 0 cos 0 sin 0 0 1 0 0 sin 0 cos ' ' '

8. Rotation • Rotation about X – axis                                           w z y x w z y x 1 0 0 0 0 cos sin 0 0 sin cos 0 0 0 0 1 ' ' '

Computer Graphics

Computer Graphics

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