Rotation Splines

• Quaternions
  • Quaternion Representations
  • Unit Quaternions
  • Unit Quaternions as Rotations
  • Axes Conventions
  • Quaternion Multiplication
  • Inverse
  • Relative Rotation (Global Frame of Reference)
  • Relative Rotation (Local Frame of Reference)
  • Exponentiation
  • Negation
• Spherical Linear Interpolation (Slerp)
  • Derivation
  • Visualization
  • Piecewise Slerp
  • Slerp vs. Nlerp
• De Casteljau’s Algorithm With Slerp
  • “Cubic”
  • Arbitrary “Degree”
  • Constant Angular Speed
  • Joining Curves
• Uniform Catmull–Rom-Like QuaternionSplines
  • Relative Rotations
  • Tangent Space
  • Example
  • Shoemake’s Approach
• Non-Uniform Catmull–Rom-Like QuaternionSplines
  • Parameterization
• Kochanek–Bartels-like Rotation Splines
  • Examples
• “Natural” End Conditions
  • Examples
• Barry–Goldman Algorithm With Slerp
  • Constant Angular Speed
• Cumulative Form
  • Piecewise Slerp
  • Cumulative Bézier/Bernstein Curve
  • Comparison with De Casteljau’s Algorithm
• Naive 4D Quaternion Interpolation
• Naive Interpolation of EulerAngles