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3D Affine Transformations

3D Affine Transformations
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2018-05-17 02:41
Solid GeometryTransformationGeometric Construction
In collections Mathematics of Computer Graphics
This example demonstrates affine transformations in three-dimensional space. It involves core mathematical concepts such as rotation, scaling, and translation in 3D. Using GeoGebra commands like Prism, Reverse, and TableText, it dynamically showcases the effects of these transformations. Suitable for high school or university-level solid geometry courses, helping students understand geometric transformations in 3D space.

GeoGebra Commands & Parameters

  1. Prism(A, B, C, D, E) → P, F, edgeAB_1, edgeBC_1, edgeCD_1, edgeAD_1, edgeAE_1, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, G, edgeGH, edgeEH, H, faceABCD_1, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  2. Reverse(W) → W2
  3. Reverse(LH) → K
  4. Prism(A_1, B_1, C_1, D_1, E_1) → P_1, J, edge1, edge4, edge6, edge2, edge3, edge5, edge7, edge8, edge9, edgeJL, L, edgeLM, edge10, M, face1, face2, face4, face5, face3, face6
  5. TableText({W2}, "h") → text1
  6. Textfield(a_2) → InputBox1
  7. Textfield(a_1) → InputBox2
  8. Textfield(b_2) → InputBox3
  9. Textfield(c_2) → InputBox4
  10. Textfield(b_1) → InputBox5
  11. Textfield(c_1) → InputBox6
  12. Textfield(sx) → InputBox7
  13. Textfield(sy) → InputBox8
  14. Textfield(sz) → InputBox9
  15. Textfield(θ_2) → InputBox10
  16. Textfield(α_2) → InputBox11
  17. Textfield(β_2) → InputBox12
  18. Textfield(θ_1) → InputBox13
  19. Textfield(α_1) → InputBox14
  20. Textfield(β_1) → InputBox15
  21. Textfield(A) → InputBox16
  22. Textfield(B) → InputBox17
  23. Textfield(C) → InputBox18
  24. Textfield(D) → InputBox19
  25. Textfield(E) → InputBox20
  26. Pyramid(A, B, C, D, E) → Q, faceABCD, edgeAE, edgeBE, edgeCE, edgeDE, faceABE, faceBCE, faceCDE, faceADE, edgeAB, edgeBC, edgeCD, edgeAD
  27. Pyramid(A_1, B_1, C_1, D_1, E_1) → Q_1, face11, edge13, edge15, edge17, edge18, face7, face9, face10, face8, edge11, edge14, edge16, edge12