棱柱的圆柱透视

棱柱的圆柱透视
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2020-05-06 01:18
①本范例演示棱柱的圆柱透视效果,直观展示三维几何体的二维投影;②涉及的核心数学概念包括立体几何、相似三角形、圆与多边形构造;③作图要点运用了Line, Circle, Cylinder, Segment, Point, Sequence, CircumcircleArc, Element, Polygon, Prism, Midpoint, Ray, Intersect, Centroid, Sphere等GeoGebra命令与对象;④适合高中立体几何教学,用于理解空间几何体的投影与变换规律。

GeoGebra 命令及参数

  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 绘图提示语参考

画一个棱柱的圆柱透视投影,展示其二维投影。首先绘制一个圆和圆柱,然后从圆心向圆柱侧面引线,形成棱柱的侧面。接着在圆柱底面绘制一个正方形,并延伸出棱柱的顶面。最后,从顶面和底面的顶点引出射线,与侧面相交,形成透视效果。
以上提示语为根据原始绘图命令整理而来,仅供参考。