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Cylindrical perspective of a prism

Cylindrical perspective of a prism
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2020-05-06 01:18
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the cylindrical perspective of a prism, visually representing the 2D projection of a 3D geometric solid. Core math concepts include solid geometry, similar triangles, and the construction of circles and polygons. It utilizes commands like Line, Circle, Cylinder, Segment, Point, Sequence, CircumcircleArc, Element, Polygon, Prism, Midpoint, Ray, Intersect, Centroid, Sphere in GeoGebra. Suitable for high school geometry education to understand spatial projections and transformations.

GeoGebra Commands & Parameters

  1. Line(A, zAxis) → f
  2. Circle(A, R, f) → c
  3. Cylinder(c, h) → a, d, b
  4. Segment(B, A) → g
  5. Point(g) → C
  6. Sequence(Rotate[T, i, f], i, 0, π, π / oo) → l1
  7. Sequence(Segment[Element[l1, i], Element[l1, i] + (0, 0, h)], i, 1, Length[l1]) → l2
  8. CircumcircleArc(T, B_1, U) → e_2
  9. Sequence(Translate[e_2, Vector[(i * Vector[A, A + (0, 0, 1)])]], i, 1, h) → l3
  10. Segment(C, A) → m_1
  11. Segment(U, U + (0, 0, h)) → n_1
  12. Segment(T, T + (0, 0, h)) → a_1
  13. Element(l3, Length[l3]) → f_2
  14. Polygon(D, E, 4, xOyPlane) → poly1, i, j, k, l, G, H
  15. Line(D, m_1) → m
  16. Point(m) → J
  17. Prism(poly1, Distance[D, J]) → e, M, arêteDM, arêteEN, arêteGO, arêteHP, arêteMN, arêteNO, arêteOP, arêteMP, N, O, P, faceDENM, faceEGON, faceGHPO, faceDHPM, faceMNOP
  18. Midpoint(arêteMN) → Q
  19. Midpoint(i) → S
  20. Midpoint(l) → V
  21. Midpoint(j) → W
  22. Midpoint(arêteMP) → Z
  23. Midpoint(k) → A_1
  24. Midpoint(arêteDM) → C_1
  25. Midpoint(arêteEN) → D_1
  26. Midpoint(arêteGO) → E_1
  27. Midpoint(arêteNO) → F_1
  28. Midpoint(arêteOP) → G_1
  29. Midpoint(arêteHP) → H_1
  30. Ray(E, C) → n
  31. Ray(G, C) → p
  32. Ray(W, C) → q
  33. Intersect(n, b) → I_1, J_1
  34. Intersect(q, b) → K_1, L_1
  35. Intersect(p, b) → M_1, N_1
  36. CircumcircleArc(M_1, K_1, I_1) → r
  37. Ray(P, C) → s
  38. Ray(Z, C) → t
  39. Ray(J, C) → f_1
  40. Intersect(s, d) → O_1,
  41. Intersect(t, d) → P_1,
  42. Intersect(f_1, d) → Q_1,
  43. Intersect(f_1, b) → R_1, S_1
  44. Intersect(t, b) → T_1, U_1
  45. Intersect(s, b) → V_1, W_1
  46. Ray(C_1, C) → g_1
  47. Ray(H_1, C) → h_1
  48. Intersect(g_1, b) → Z_1, A_2
  49. Intersect(h_1, c) → B_2,
  50. Intersect(h_1, b) → C_2, D_2
  51. CircumcircleArc(V_1, T_1, R_1) → c_1
  52. Ray(N, C) → i_1
  53. Ray(O, C) → j_1
  54. Ray(F_1, C) → k_1
  55. Intersect(j_1, b) → E_2, F_2
  56. Intersect(k_1, c) → G_2,
  57. Intersect(k_1, b) → H_2, I_2
  58. Intersect(i_1, b) → J_2, K_2
  59. Ray(E, C) → l_1
  60. Ray(W, C) → p_1
  61. Ray(G, C) → q_1
  62. Intersect(q_1, b) → L_2, M_2
  63. Intersect(p_1, b) → N_2, O_2
  64. Intersect(l_1, c) → P_2,
  65. Intersect(l_1, b) → Q_2, R_2
  66. CircumcircleArc(L_2, N_2, Q_2) → r_1
  67. CircumcircleArc(E_2, H_2, J_2) → s_1
  68. Ray(D_1, C) → t_1
  69. Intersect(t_1, b) → S_2, T_2
  70. CircumcircleArc(J_2, S_2, Q_2) → c_2
  71. Ray(E_1, C) → b_1
  72. Intersect(b_1, b) → U_2, V_2
  73. CircumcircleArc(E_2, U_2, L_2) → d_2
  74. Point(f_2) → W_2
  75. Ray(G_1, C) → i_2
  76. Intersect(i_2, b) → B_3, C_3
  77. CircumcircleArc(V_1, B_3, E_2) → k_2
  78. Ray(Q, C) → j_2
  79. Intersect(j_2, b) → D_3, E_3
  80. CircumcircleArc(R_1, D_3, J_2) → g_2
  81. Ray(H, C) → d_1
  82. Intersect(d_1, b) → Z_2, A_3
  83. Ray(D, C) → e_1
  84. Intersect(e_1, b) → F_3, G_3
  85. Ray(V, C) → h_2
  86. Intersect(h_2, b) → H_3, I_3
  87. CircumcircleArc(Z_2, H_3, F_3) → p_2
  88. Ray(A_1, C) → l_2
  89. Intersect(arêteHP, b) → J_3,
  90. Intersect(l_2, b) → K_3, L_3
  91. CircumcircleArc(L_2, K_3, Z_2) → q_2
  92. CircumcircleArc(V_1, C_2, Z_2) → r_2
  93. Ray(S, C) → m_2
  94. Intersect(m_2, b) → M_3, N_3
  95. CircumcircleArc(F_3, M_3, Q_2) → s_2
  96. Ray(C_1, C) → n_2
  97. Intersect(n_2, b) → O_3, P_3
  98. CircumcircleArc(F_3, O_3, R_1) → t_2
  99. Polygon(I, K, L, F) → q1, i_3, k_3, l_3, f_3
  100. Segment(C, G) → a_2
  101. Segment(C, E) → b_2
  102. Segment(C, N) → g_3
  103. Segment(C, O) → h_3
  104. Segment(C, P) → j_3
  105. Segment(C, J) → m_3
  106. Segment(C, H) → n_3
  107. Segment(C, D) → p_3
  108. Centroid(poly1) → Q_3
  109. Ray(Q_3, C) → q_3
  110. Point(q_3) → R_3
  111. Midpoint(R_3, C) → S_3
  112. Sphere(R_3 - (0, 0.13, -0.05), 0.4) → u
  113. Sphere(Midpoint[T_3, R_3] - (0, 0.1, 0), 0.3) → v

AI Drawing Prompt Reference

Draw the cylindrical perspective projection of a prism, showing its 2D projection. Start by sketching a circle and a cylinder, then draw lines from the center of the circle to the side of the cylinder to form the prism's lateral faces. Next, create a square on the base of the cylinder and extend it to form the top face. Finally, draw rays from the vertices of the top and bottom faces to the side, intersecting with it to create a perspective effect.
The prompt above was compiled from the original drawing commands and is for reference only.