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Translation , 1 2,1 2 3,1 3 0,1 1,1 - PowerPoint PPT Presentation

Oct 29, 2023 β€’183 likes β€’344 views

0 1 2 3 4 5 6 7 3,3 3 3 2,3 2 3 1,3 3 0,3 3 3,2 3 2 2,2 2 2 1,2 2 0,2 2 3,1 3 2,1 2 1,2

  1. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  2. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Coefficient of 𝑦 0 𝑧 0 Translation 1,1 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  3. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Γ— Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Coefficient of 𝑦 2 𝑧 0 Translation 3,1 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  4. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Γ— Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Coefficient of 𝑦 4 𝑧 0 Translation 5,1 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  5. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Γ— Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— Γ— Γ— Coefficient of 𝑦 4 𝑧 1 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 Translation 5,2 𝑐 1,0 𝑦 𝑐 0,0 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  6. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— Γ— Coefficient of 𝑦 1 𝑧 1 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 Translation 2,2 𝑐 1,0 𝑦 𝑐 0,0 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  7. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Γ— Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— Γ— Γ— Coefficient of 𝑦 2 𝑧 2 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 Translation 3,3 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 Γ— Γ— Γ— 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  8. 0 1 2 3 4 5 6 7 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— Coefficient of 𝑦 6 𝑧 2 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 Translation 7,3 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 Γ— 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 4 5 6 7 π‘˜

  9. 0 1 2 3 4 5 6 7 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Γ— Γ— Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— Γ— Γ— Γ— 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 Coefficient of 𝑦 3 𝑧 3 𝑐 0,2 𝑧 2 Translation 4,4 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 Γ— Γ— Γ— Γ— 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 Γ— Γ— Γ— Γ— 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 4 5 6 7 π‘˜

  10. 0 1 2 3 4 5 6 7 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Γ— Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 𝑐 0,3 𝑧 3 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 Coefficient of 𝑦 0 𝑧 3 𝑐 0,2 𝑧 2 Translation 1,4 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 Γ— 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 Γ— 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 4 5 6 7 π‘˜

  11. 0 1 2 3 4 5 6 7 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 Coefficient of 𝑦 0 𝑧 4 𝑐 0,3 𝑧 3 Translation 1,5 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 Γ— 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 Γ— 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 4 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 5 6 7 π‘˜

  12. 0 1 2 3 4 5 6 7 𝑗 0 𝑏 2,0 𝑦 2 𝑏 3,0 𝑦 3 𝑏 0,0 𝑏 1,0 𝑦 Coefficient of 𝑦 π‘—βˆ’1 𝑧 π‘˜βˆ’1 Translation 𝑗, π‘˜ 1 𝑏 2,1 𝑦 2 𝑧 𝑏 3,1 𝑦 3 𝑧 𝑏 0,1 𝑧 𝑏 1,1 𝑦𝑧 Γ— 𝑐 3,3 𝑦 3 𝑧 3 𝑐 2,3 𝑦 2 𝑧 3 𝑐 1,3 𝑦𝑧 3 Coefficient of 𝑦 6 𝑧 4 𝑐 0,3 𝑧 3 Translation 7,5 2 𝑏 1,2 𝑦𝑧 2 𝑏 2,2 𝑦 2 𝑧 2 𝑏 3,2 𝑦 3 𝑧 2 𝑏 0,2 𝑧 2 Γ— 𝑐 3,2 𝑦 3 𝑧 2 𝑐 2,2 𝑦 2 𝑧 2 𝑐 1,2 𝑦𝑧 2 𝑐 0,2 𝑧 2 3 𝑏 1,3 𝑦𝑧 3 𝑏 2,3 𝑦 2 𝑧 3 𝑏 3,3 𝑦 3 𝑧 3 𝑏 1,3 𝑧 3 Γ— 𝑐 3,1 𝑦 3 𝑧 𝑐 2,1 𝑦 2 𝑧 𝑐 1,2 𝑦𝑧 𝑐 0,1 𝑧 4 𝑐 3,0 𝑦 3 𝑐 2,0 𝑦 2 𝑐 1,0 𝑦 𝑐 0,0 5 6 7 π‘˜

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