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Transform Cubes

Transform Cubes
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2015-08-20 04:27
VectorSolid GeometryTransformation
This example demonstrates the transformation of cubes, involving concepts such as planes, difference, and slope. Using GeoGebra commands like Text, Point, and CurveCartesian, the transformed cube can be constructed. Suitable for high school grade 2 students studying solid geometry transformations.

GeoGebra Commands & Parameters

  1. Text(a) → text1
  2. Text(b) → text3
  3. Text(c) → text4
  4. Text(d) → text5
  5. Text(e) → text6
  6. Text(f) → text7
  7. Text(g) → text8
  8. Text(h) → text9
  9. Text(i) → text10
  10. Point({(-xscale), zed((-xscale))}) → X1
  11. CurveCartesian(t, zed(t), t, -7, 4) → j
  12. Point({Element[PV1, 1, 1], Element[PV1, 2, 1]}) → PPV1
  13. Point({Element[PV2, 1, 1], Element[PV2, 2, 1]}) → PPV2
  14. Point({Element[PV3, 1, 1], Element[PV3, 2, 1]}) → PPV3
  15. Point({Element[PV4, 1, 1], Element[PV4, 2, 1]}) → PPV4
  16. Point({Element[PV5, 1, 1], Element[PV5, 2, 1]}) → PPV5
  17. Point({Element[PV6, 1, 1], Element[PV6, 2, 1]}) → PPV6
  18. Point({Element[PV7, 1, 1], Element[PV7, 2, 1]}) → PPV7
  19. Point({Element[PV8, 1, 1], Element[PV8, 2, 1]}) → PPV8
  20. Polygon(PPV1, PPV2, PPV3, PPV4) → Orig1, k, l, m, n
  21. Polygon(PPV5, PPV6, PPV7, PPV8) → Orig2, ppv5, ppv6, ppv7, ppv8
  22. Polygon(PPV1, PPV5, PPV6, PPV2) → Orig3, ppv1, ppv5_1, ppv6_1, ppv2
  23. Polygon(PPV1, PPV4, PPV8, PPV5) → Orig4, ppv1_1, ppv4, ppv8_1, ppv5_2
  24. Polygon(PPV3, PPV4, PPV8, PPV7) → Orig5, ppv3, ppv4_1, ppv8_2, ppv7_1
  25. Polygon(PPV2, PPV3, PPV7, PPV6) → Orig6, ppv2_1, ppv3_1, ppv7_2, ppv6_2
  26. Point({Element[PTV1, 1, 1], Element[PTV1, 2, 1]}) → PPTV1
  27. Point({Element[PTV2, 1, 1], Element[PTV2, 2, 1]}) → PPTV2
  28. Point({Element[PTV3, 1, 1], Element[PTV3, 2, 1]}) → PPTV3
  29. Point({Element[PTV4, 1, 1], Element[PTV4, 2, 1]}) → PPTV4
  30. Point({Element[PTV5, 1, 1], Element[PTV5, 2, 1]}) → PPTV5
  31. Point({Element[PTV6, 1, 1], Element[PTV6, 2, 1]}) → PPTV6
  32. Point({Element[PTV7, 1, 1], Element[PTV7, 2, 1]}) → PPTV7
  33. Point({Element[PTV8, 1, 1], Element[PTV8, 2, 1]}) → PPTV8
  34. Polygon(PPTV5, PPTV6, PPTV7, PPTV8) → NEW2, pptv5, pptv6, pptv7, pptv8
  35. Polygon(PPTV1, PPTV2, PPTV3, PPTV4) → NEW1, pptv1, pptv2, pptv3, pptv4
  36. Polygon(PPTV1, PPTV5, PPTV6, PPTV2) → NEW3, pptv1_1, pptv5_1, pptv6_1, pptv2_1
  37. Polygon(PPTV1, PPTV4, PPTV8, PPTV5) → NEW4, pptv1_2, pptv4_1, pptv8_1, pptv5_2
  38. Polygon(PPTV3, PPTV4, PPTV8, PPTV7) → NEW5, pptv3_1, pptv4_2, pptv8_2, pptv7_1
  39. Polygon(PPTV2, PPTV3, PPTV7, PPTV6) → NEW6, pptv2_2, pptv3_2, pptv7_2, pptv6_2
  40. Vector(PPV1, PPTV1) → u
  41. Vector(PPV2, PPTV2) → v
  42. Vector(PPV3, PPTV3) → w
  43. Vector(PPV4, PPTV4) → p
  44. Vector(PPV5, PPTV5) → q
  45. Vector(PPV6, PPTV6) → r
  46. Vector(PPV7, PPTV7) → s
  47. Vector(PPV8, PPTV8) → t

AI Drawing Prompt Reference

Draw a 3D demonstration of cube transformation. Start with an original cube whose eight vertices are labeled with letters a through i, with each letter displayed near its vertex. Show a curve representing a function and mark a special point on it. Then, using given vertex coordinates, construct the six faces of the original cube as polygons. Next, using another set of vertex coordinates, construct the six faces of a transformed cube as polygons. Finally, draw vector arrows from each vertex of the original cube to the corresponding vertex of the transformed cube to indicate the transformation direction. The overall figure should clearly show the spatial relationship and vector connections between the two cubes.
The prompt above was compiled from the original drawing commands and is for reference only.