# Rotation representations

## Pros/Cons

• RM = rotation matrix
• EULER = Euler angles
• AA = Axis-Angle representation
• QUAT = Quaternions
 RM EULER AA QUAT - + + - - + - - - + - - + - + + + - - + + - + + + - + + - - - +

Explanations:

• Human readable?: do the values make some sense for a human?
• Minimal?: for a 3DOF rotation, 3 scalar values are minimal
• Enforcing constraints?: e.g. limit some DOF to some range (angle1,angle2)
• Can concatenate rotations?: can we concatenate directly two rotation representations to get the total one?
• Can directly rotate a vector with?: e.g. for Euler angles you first have to convert them to a rotation matrix, to rotate a vector. E.g. Rodrigues rotation formula for AA representation
• Gimbal lock?: loss of 1 DOF for rotation if two axes align (only the case for Euler)
• Singularities?: can the values suddenly jump from -PI, to PI and vice versa?
• Can easily interpolate between two rots?: E.g. using SLERP for quaternions

public/rotation_representations.txt · Last modified: 2014/01/19 12:19 (external edit) · [] 