User Guide

• 1. Introduction to 3D Rigid Transformations
  • 1.1. Basics
  • 1.2. Frames
  • 1.3. Frame Notation
  • 1.4. Duality of Transformations and Poses
  • 1.5. Representations
  • 1.6. References
• 2. SO(3): 3D Rotations
  • 2.1. Rotation Matrix
  • 2.2. Axis-Angle
  • 2.3. Rotation Vector
  • 2.4. Logarithm of Rotation
  • 2.5. Quaternions
  • 2.6. Euler Angles
  • 2.7. Rotors
  • 2.8. Modified Rodrigues Parameters
  • 2.9. References
• 3. SE(3): 3D Transformations
  • 3.1. Transformation Matrix
  • 3.2. Position and Quaternion
  • 3.3. Screw Parameters
  • 3.4. Screw Axis
  • 3.5. Exponential Coordinates
  • 3.6. Logarithm of Transformation
  • 3.7. Twist
  • 3.8. Dual Quaternions
  • 3.9. References
• 4. Transformation Ambiguities and Conventions
  • 4.1. Right-handed vs. Left-handed Coordinate System
  • 4.2. Active (Alibi) vs. Passive (Alias) Transformation
  • 4.3. Pre-multiply vs. Post-multiply Rotations
  • 4.4. Intrinsic vs. Extrinsic Transformations
  • 4.5. Naming and Frame Conventions
  • 4.6. Conventions of Other Software
  • 4.7. References
• 5. Euler Angles
  • 5.1. 24 Conventions
  • 5.2. Range of Angles
  • 5.3. Gimbal Lock
  • 5.4. Other Names
  • 5.5. References
• 6. Modeling Transformations
• 7. Organizing Transformations in a Graph
• 8. Graphs of Time-Dependent Transformations
  • 8.1. Preparing the Transformation Sequences
  • 8.2. Transform Between Coordinate Systems
• 9. Uncertainty in Transformations
  • 9.1. Gaussian Distribution of Transformations
  • 9.2. Visualization of Uncertainty
  • 9.3. Concatenation of Uncertain Transformations
  • 9.4. Fusion of Uncertain Poses
• 10. Camera