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斜视图中的立方体及其投影

斜视图中的立方体及其投影
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2020-11-23 21:03
解析几何立体几何变换
这个范例演示了一个立方体及其在斜视图中的投影。核心数学概念包括立体几何和投影变换。通过使用GeoGebra命令如OrthogonalLine, Circle, Intersect等，可以构造出立方体及其投影。适合高中或大学的立体几何课程。

GeoGebra 命令及参数

  1. OrthogonalLine(F, eq1) → i
  2. Circle(F, d) → c
  3. Intersect(c, i, 2) → A
  4. Segment(F, A) → j
  5. Intersect(h, eq1) → B
  6. Segment(B, A) → k
  7. OrthogonalLine(A, k) → l
  8. Intersect(eq1, l) → V_3
  9. Segment(V_3, A) → m
  10. Angle(B, A, V_3) → β
  11. Polygon(B, A, V_3) → t1, i_5, b_6, a_6
  12. Circle(B, A) → e
  13. Rotate(F, 30°, A) → F'
  14. Angle(F, A, F') → α
  15. Line(A, F') → f_5
  16. Intersect(eq1, f_5) → G_1
  17. Segment(G_1, A) → g_5
  18. Circle(F, G_1) → c_5
  19. Intersect(e, eq1, 2) → C
  20. CircleArc(B, C, A) → p
  21. Point(Circle[D, a]) → E
  22. Segment(D, E) → n
  23. Polygon(D, E, 4) → poligon1, q, r, s, t, G, H
  24. Line(C, n) → b
  25. Line(C, r) → g_1
  26. Intersect(h, g_1) → V_2
  27. Segment(C, V_2) → h_1
  28. Intersect(h, b) → V_1
  29. Segment(C, V_1) → i_1
  30. Line(G, E) → j_1
  31. Line(H, D) → k_1
  32. Line(E, D) → l_1
  33. Line(H, G) → m_1
  34. Intersect(f_1, k_1) → K
  35. Segment(K, D) → n_1
  36. Intersect(f_1, j_1) → L
  37. Segment(L, E) → p_1
  38. Intersect(f_1, l_1) → M
  39. Segment(M, E) → q_1
  40. Intersect(f_1, m_1) → N
  41. Segment(G, N) → r_1
  42. Line(L, V_2) → s_1
  43. Line(K, V_2) → t_1
  44. Line(N, V_1) → a_1
  45. Line(M, V_1) → b_1
  46. Intersect(t_1, b_1) → O
  47. Intersect(t_1, a_1) → P
  48. Intersect(s_1, a_1) → Q
  49. Intersect(s_1, b_1) → R
  50. Segment(K, O) → c_1
  51. Segment(O, P) → d_1
  52. Segment(P, V_2) → e_1
  53. Segment(L, R) → f_2
  54. Segment(R, Q) → g_2
  55. Segment(Q, V_2) → h_2
  56. Segment(M, R) → i_2
  57. Segment(R, O) → j_2
  58. Segment(O, V_1) → k_2
  59. Segment(N, Q) → l_2
  60. Segment(P, V_2) → i_6
  61. Segment(Q, P) → m_2
  62. Segment(P, V_1) → n_2
  63. Polygon(O, P, Q, R) → q1, o, p_5, q_5, r_5
  64. Segment(D, C) → p_2
  65. Segment(O, D) → r_2
  66. Segment(E, R) → s_2
  67. Segment(E, C) → t_2
  68. Segment(H, C) → a_2
  69. Segment(H, P) → b_2
  70. Segment(G, C) → c_2
  71. Segment(G, Q) → d_2
  72. Line(K, m) → e_2
  73. Line(L, m) → f_3
  74. Circle(K, a) → c_3
  75. Circle(L, a) → d_3
  76. Intersect(c_3, e_2, 2) → S
  77. Segment(S, K) → g_3
  78. Intersect(d_3, f_3, 2) → T
  79. Segment(T, L) → h_3
  80. Segment(A, V_3) → g
  81. Line(V_3, L) → i_3
  82. Line(V_3, K) → j_3
  83. Line(A, T) → k_3
  84. Line(A, S) → l_3
  85. Intersect(i_3, k_3) → U
  86. Segment(L, U) → m_3
  87. Segment(L, V_3) → f_4
  88. Intersect(j_3, l_3) → V
  89. Segment(K, V) → n_3
  90. Segment(K, V_3) → g_4
  91. Segment(A, U) → p_3
  92. Segment(A, V) → q_3
  93. Intersect(n_3, q_3) → W
  94. Intersect(m_3, p_3) → Z
  95. Line(Z, V_2) → r_3
  96. Line(V_2, W) → s_3
  97. Line(O, V_3) → t_3
  98. Line(R, V_3) → a_3
  99. Line(Q, V_3) → b_3
  100. Line(P, V_3) → e_3
  101. Segment(W, V_2) → h_4
  102. Intersect(s_3, t_3) → A_1
  103. Segment(A_1, V_3) → t_4
  104. Segment(A_1, V_2) → e_5
  105. Intersect(s_3, e_3) → B_1
  106. Segment(A_1, B_1) → i_4
  107. Segment(B_1, V_3) → a_4
  108. Segment(A_1, W) → j_4
  109. Segment(Z, V_2) → n_4
  110. Intersect(s_3, e_3) → C_1
  111. Segment(V_2, C_1) → k_4
  112. Intersect(s_3, t_3) → D_1
  113. Segment(C_1, D_1) → l_4
  114. Segment(D_1, W) → m_4
  115. Segment(E, C) → q_2
  116. Intersect(r_3, a_3) → E_1
  117. Segment(E_1, V_3) → r_4
  118. Segment(Z, E_1) → p_4
  119. Intersect(r_3, b_3) → F_1
  120. Segment(F_1, V_3) → s_4
  121. Segment(F_1, V_2) → g_6
  122. Segment(E_1, F_1) → q_4
  123. Segment(E_1, A_1) → b_4
  124. Segment(A_1, V_1) → c_4
  125. Segment(F_1, B_1) → d_4
  126. Segment(B_1, V_1) → e_4
  127. Polygon(P, B_1, F_1, Q) → q2, p_6, h_5, f_{6}, q_6
  128. Polygon(P, O, A_1, B_1) → q3, p_7, o_1, j_5, k_5
  129. Polygon(A_1, E_1, R, O) → q4, l_5, m_5, r_6, o_2
  130. Polygon(E_1, F_1, Q, R) → q5, n_5, s_5, q_7, r_7
  131. Polygon(A_1, B_1, F_1, E_1) → q6, t_5, a_5, b_5, d_5
  132. Line(V_3, I) → j_6
  133. Intersect(h, j_6) → J
  134. Segment(V_3, J) → k_6
  135. Segment(R, J) → l_6
  136. Segment(E_1, I) → m_6
  137. Intersect(l_6, m_6) → H_1
  138. Segment(Q, J) → n_6
  139. Segment(F_1, I) → s_6
  140. Intersect(n_6, s_6) → I_1
  141. Segment(H_1, V_2) → t_6
  142. Segment(P, J) → c_6
  143. Segment(B_1, I) → d_6
  144. Intersect(c_6, d_6) → J_1
  145. Segment(I_1, V_1) → e_6
  146. Intersect(s_4, e_6) → K_1
  147. Segment(R, H_1) → m_7
  148. Segment(J_1, P) → n_7
  149. Polygon(K_1, I_1, H_1, R, Q) → poligon2, f_7, g_7, h_7, r_8, q_8
  150. Intersect(r_8, q_8) → L_1
  151. Intersect(h_7, r_8) → M_1
  152. Polygon(F_1, L_1, M_1, E_1) → q7, i_7, j_7, k_7, l_7

AI 绘图提示语参考

绘制一个倾斜投影平面上的立方体及其阴影。先确定一个投影平面，并在其上取一点作为投影中心，过该点作平面的垂线，与一个圆相交得到投影点。连接投影中心与投影点，再与平面相交得到另一个点，形成三角形。接着构造一个旋转角，并画出旋转后的线，与平面相交得到新的投影点。然后绘制一个正方形作为立方体的底面，并连接其顶点形成立方体。最后，从立方体的各顶点向投影平面作投影线，并求出这些线与平面的交点，连接这些交点形成立方体在倾斜平面上的投影形状，同时标出投影线与平面交点构成的四边形。
以上提示语为根据原始绘图命令整理而来，仅供参考。