Rotation representations

Pros/Cons

  • RM = rotation matrix
  • EULER = Euler angles
  • AA = Axis-Angle representation
  • QUAT = Quaternions
RM EULER AA QUAT
Human readable? - + + -
Minimal? - + - -
Enforcing constraints? (e.g. joint limits) - + - -
Can directly rotate a vector with? + - + +
Can concatentate rotations? + - - +
Gimbal lock? + - + +
Singularities? + - + +
Can easily interpolate between two rots? - - - +

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) · []
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