OrienRepr.MathBase

• • Convert a angle between degree and radian

OrienRepr.Orien2D

• Preliminary math
• Skew-symmetric matrix in 2-D
• Orientation in 2D (pure rotation)
  • 2-D Rotation matrix
  • Definition of 2D rotation operations
  • Properties for 2D rotation operations
  • Specifications for 2-D rotation operations

OrienRepr.AxisAngle

• Preliminary math
• Axis-angle representation

OrienRepr.RotationMatrix3D

• Basic Rotation Matrics
  • Definitions of 3D basic rotation matrices
  • Properties of 3D basic rotation matrices

OrienRepr.EulerAngle

• Euler angles under 24 definitions

OrienRepr.Orien3D

• Preliminary math
• 3D rotation operations
  • Basic 3D rotation operations
  • 3D rotation operations

OrienRepr.Quaternion

• Definition of Quaternion
  • Automation for quaternion
• Quaternion operations
  • Zero quaternion 零四元数
  • Square of magnitude (Length) of a quaternion
  • Magnitude (Length) of a quaternion
  • Unit quaternion
  • Quaternion normalization
  • Quaternion addition 四元数加法
  • Quaternion negation 四元数取负
  • Quaternion subtraction 四元数减法
  • Quaternion multiplication
  • Identity quaternion 恒等四元数
  • Quaternion conjugate
  • Quaternion inverse
  • Divide of quaternion
• Unit quaternion <-> Axis-Angle
• Rotate 3D vector by unit quaternion
  • 坐标系旋转的情况
  • Unit quaternions and rotation matrices 单位四元数和旋转矩阵

OrienRepr.QuaternionAdvanced

• • Dot product of quaternion
  • Logrithm of quaternion
  • Exponential of quaternion
  • Exponentiation of quaternion
  • Spherical Linear Interpolation 球面线性插值

OrienRepr.OrienRepr

• Comparison of Extrinsic and Intrinsic Rotation
• Rotate a vector in a given frame to obtain new coordinates
• Conversion between ORs
  • Euler angles <-> Rotation matrix
  • Axis-angle <-> Rotation matrix
  • Unit quaternion <-> Rotation matrix
  • Unit quaternion <-> Euler angles
  • Unit quaternion <-> Axis-angle
• Examples
• 向量就是向量，而不是列矩阵或行矩阵，我们提供 mmulv 和 mvmul 运算，
• 点积、叉积等运算不需要借助矩阵才能实现，而是直接定义
• 四元数是vec 4，做了一些改进。
• Extraction to OCaml code