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Oblique Projection Prism

Oblique Projection Prism
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2013-12-15 06:14
Coordinate GeometrySolid GeometryGeometric Construction
In collections Surface Area
This example demonstrates the construction of an oblique projection prism. Key mathematical concepts include the geometry of a prism and its projection. Using GeoGebra commands such as Point, Segment, and Polygon, the faces of the prism are constructed, and the prism is translated using the Translate command. Suitable for high school students learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → O
  2. OrthogonalLine(O, xAxis) → k
  3. Point(k) → T
  4. Point(k) → S
  5. OrthogonalLine(S, k) → g_1
  6. Point(g_1) → P
  7. Sequence(Mat * Element[cube, k], k, 1, 9) → cube'
  8. Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 9) → listepoints
  9. Element(listepoints, 1) → M
  10. Element(listepoints, 7) → L
  11. Element(listepoints, 8) → K
  12. Element(listepoints, 4) → J
  13. Segment(M, J) → m'
  14. Element(listepoints, 5) → N
  15. Element(listepoints, 2) → A
  16. Segment(A, M) → a'_1
  17. Element(listepoints, 6) → Q
  18. Polygon(K, L, Q, N) → poly6, k_3, l_2, q_1, n_2
  19. Point(n_2) → R
  20. Element(listepoints, 3) → C
  21. Polygon(Q, A, C, L) → poly2, q, a_2, c_1, l
  22. Polygon(J, K, L, C) → poly4, j_2, k_1, l_1, c_5
  23. Line(R, k_1) → e
  24. Intersect(e, l_2) → F
  25. Line(F, q) → f
  26. Intersect(f, a_2) → G
  27. Line(G, a'_1) → g
  28. Intersect(g, m') → H
  29. Element(Element[AE, 3], 1) → droite
  30. Element(AB, 3, 1) → avant
  31. Element(AC, 3, 1) → dessus
  32. Polygon(J, M, N, K) → poly5, j_3, m_1, n_1, k_2
  33. Polygon(J, C, A, M) → poly1, j, c, a_1, m
  34. Polygon(A, Q, N, M) → poly3, a_3, q_2, n, m_2
  35. Segment(J, C) → j'_1
  36. Segment(K, L) → k'_3
  37. Segment(L, Q) → l'_2
  38. Segment(N, K) → n'_2
  39. Segment(Q, N) → q'_1
  40. Segment(M, N) → m'_1
  41. Segment(Q, A) → q'
  42. Segment(K, J) → j'
  43. Segment(N, K) → l'
  44. Segment(C, L) → l''
  45. Segment(C, A) → l''''
  46. Segment(M, N) → k''''
  47. If(i ≟ 1, true, false) → h
  48. Segment(C, A) → k'''
  49. PointIn(poly2) → E
  50. Polygon(A, M, J, C) → poly10, p, s, t, b_1
  51. Polygon(C, F', A) → poly7, a_4, c_2, f'
  52. Polygon(J, R', M) → poly8, m_3, j_1, r'
  53. Segment(R, M) → d_1
  54. Line(J, M) → f_1
  55. Line(C, A) → h_1
  56. Segment(R, H) → e_1
  57. Translate(R_2, A - M) → Q_2
  58. Polygon(A, Q_2, R_2, M) → poly9, a_5, q_3, r_2, m_4
  59. Translate(R_3, C - J) → F_3
  60. Polygon(J, R_3, F_3, C) → poly11, j_4, r_3, f_3, c_3
  61. Angle(Line[M, J], Line[M, R']) → ang
  62. Angle(Line[C, A], Line[C, F']) → ang2
  63. Angle(Line[A, M], Line[A, F']) → ang3
  64. Angle(Line[J, C], Line[J, R']) → ang4
  65. Angle(Line[C, J], Line[C, A]) → ang5

AI Drawing Prompt Reference

Draw an oblique projection prism by first taking point O on the x-axis and constructing a perpendicular line through O to get points T and S. Then, construct a perpendicular line through S to get point P. Next, use the Translate command to move the top face to form the prism's side faces. Finally, connect all points to form the prism's faces, including the top, bottom, and side faces, ensuring all segments and polygons are correctly connected.
The prompt above was compiled from the original drawing commands and is for reference only.