Background Math and Geometry

Contents:

• Homogeneous Points
• Normalized Lines
• Dual Quaternions Algebra
  • Dual Quaternion Norms, Conjugation, and Inversion
  • Correspondence between Dual Quaternions and Transformation Matrices
  • Dual Quaternion Actions
• Rational Motions and their Factorization
  • Rational Curve and Motion
  • Motion Factorization
• Study’s Kinematics
  • Study Quadric
• Joint Angle to Curve Parameter
• Collision-free Linkages
  • Combinatorial Optimization
• Cubic Interpolation of Four Poses
• Affine Metric and Motion Covering
  • Affine Metric Definition
  • Motion Interpolation and Bezier Splitting
  • Ball Covering of Bezier Curves