Computer Graphics

Chapter 4

Transformations in 3D, projections, quaternions

4.1     3D vectors and matrices: Dot and vector (cross) products

4.2     Linear transformations – scale, reflection, rotation and shear

4.3     Reflection relative to a plane

4.4     Rotation around an arbitrary vector (direction)

4.5     Euler transformation

4.6     Translation, affine transformation and homogeneous coordinates

4.7     Rigid-body transformation

4.8     Normal transformation

4.9     Projections

4.9.1     Parallel (orthographic) projection

4.9.2     Perspective projection

4.10   Coordinate systems in 3D, translations between different coordinate systems

4.11   Quaternions: Representation of orientation in 3D using quaternions, quaternion interpolation

In order to transform ...