Quaternions

1
Quaternions

• An easy approach to determine the rotation matrix
  around arbitrary axis

2
Complex Numbers

• Imaginary axis I
• ii -1
• General Complex Number abi
• X abi
• X a -bi // conjugate of

3
Complex Numbers

• Addition
• Multiplication
• i,j,k

4
Quaternion is Complex

• Consist of a 3D vector and one scalar
• The 3D vector could be written in i,j,k
• Quaternions are associative but not commutative

5
Quaternions

• The inverse of a quaternion refers to the
  multiplicative inverse
• q (s,v)

6
Rotation

• The rotation about the unit vector A by an angle
• To perform such rotation for point P

7
Rotation Matrix

• Using the quaternion multiplication.