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Slerp(Spherical Linear Interpolation)
Interpolation betwee two orientations, and ?
- and can be represented by
- Euler-angles
- 3x3 matrices
- quaternions
- How can them be interpolated?
- Is the linear interpolation applicable?
When the axis-angle is known,
Rotation between two orientations?
- Rotation between two SO(3) matrices, and
- Rotation between two quaternions, and
Quaternion → Axis-Angle
Rotation Matrix → Axis-Angle
Interpolation
Interpolation
Alternative Method
Quaternion Slerp
2D Complex Number Form
2D Spherical Interpolation
Spherical Linear Interpolation
- SLERP [Shoemake 1985]
- Linear Interpolation of two quaternions
Antipodal Equivalence Problem
- In gerneral, the shorter pass is better
- You should test both and , and choose one
Rotation Matrix vs. Unit Quaternion
- Equivalent in many aspects
- No singularity
- Exp & Log
- Special tangent space
- Why quaternions?
- Fewer parameters
- Simpler algebra
- Easy to fix numerical error
- Why rotation matrices?
- One-to-one correspondence
- Handle rotation and translation in a uniform way
- Eg) 4x4 homogeneous matrices
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