OAI/Geometry/SurfaceImmersion/Primitive/VelocityFrame.lean

GitHub source file

21 declarations, 0 contain sorry, 0 declared as axioms

Smooth orthonormal frames obtained by interpolating non-antipodal plane directions.

  1. def OAI.ClosedSurfaceR4.VelocityFrame.normalize line 13
  2. lemma OAI.ClosedSurfaceR4.VelocityFrame.dot_self_pos line 15
  3. lemma OAI.ClosedSurfaceR4.VelocityFrame.normalize_unit line 19
  4. lemma OAI.ClosedSurfaceR4.VelocityFrame.dot_normalize_zero line 27
  5. lemma OAI.ClosedSurfaceR4.VelocityFrame.normalize_nonzero line 30
  6. def OAI.ClosedSurfaceR4.VelocityFrame.blend line 36
  7. lemma OAI.ClosedSurfaceR4.VelocityFrame.blend_nonzero_of_not_opposite line 38
  8. lemma OAI.ClosedSurfaceR4.VelocityFrame.blend_nonzero line 56
  9. def OAI.ClosedSurfaceR4.VelocityFrame.first line 83
  10. lemma OAI.ClosedSurfaceR4.VelocityFrame.first_unit line 85
  11. lemma OAI.ClosedSurfaceR4.VelocityFrame.first_perp line 89
  12. lemma OAI.ClosedSurfaceR4.VelocityFrame.normalize_of_unit line 94
  13. lemma OAI.ClosedSurfaceR4.VelocityFrame.first_zero line 97
  14. lemma OAI.ClosedSurfaceR4.VelocityFrame.first_one line 100
  15. def OAI.ClosedSurfaceR4.VelocityFrame.second line 103
  16. theorem OAI.ClosedSurfaceR4.VelocityFrame.frame_orthonormal_of_nonzero line 105
  17. theorem OAI.ClosedSurfaceR4.VelocityFrame.frame_orthonormal line 122
  18. lemma OAI.ClosedSurfaceR4.VelocityFrame.normalize_smoothAt line 145
  19. lemma OAI.ClosedSurfaceR4.VelocityFrame.first_smoothAt line 152
  20. lemma OAI.ClosedSurfaceR4.VelocityFrame.first_smoothAt_of_nonzero line 160
  21. lemma OAI.ClosedSurfaceR4.VelocityFrame.second_smoothAt line 166