1. Derivation of the 2D Rotation Matrix Changing View from Global to Local X Y X’ Y’  P Y Sin  X Cos  X’ = X Cos  + Y Sin  Y Cos  X Sin  Y’ = Y Cos  X Sin 

2. X Y X’ Y’  P X = X’ Cos  - Y’ Sin  Y = X’ Sin  + Y’ Cos  Derivation of the 2D Rotation Matrix Changing View from Local to Global Y’ Sin  X’ Cos  X’ Sin  Y’ Cos 

3. Conversion of Equations to Matrix Form X’ = X Cos  + Y Sin  Y’ = Y Cos  - X Sin  X = X’ Cos  - Y’ Sin  Y = X’ Sin  + Y’ Cos  From Global to Local: From Local to Global: X’ Y’ = Cos Sin -Sin Cos X Y X Y = Cos -Sin Sin Cos X’ Y’

4. Derivation of the 3D Rotation Matrix X Y X’ Y’ zz P X’ = X Cos  + Y Sin  Y’ = Y Cos  X Sin  Z’ = Z Z Z’

5. Z Rotation from Global to Local

6. Z axis rotations From Global to Local: From Local to Global: X’ = X Cos  z + Y Sin  z Y’ = Y Cos  z  - X Sin  z Z’ = Z X = X’ Cos  z - Y’ Sin  z Y = X’ Sin  z + Y’ Cos  z Z = Z’