积极 AI Logo 积极 AI

基于 GeoGebra 的 3D 光学错觉几何作图

基于 GeoGebra 的 3D 光学错觉几何作图
几何画板及绘图内容加载中，请稍等……
2020-08-21 00:32
圆立体几何变换几何作图
① 本范例演示通过圆、镜像、正交平面等几何对象构造的 3D 光学错觉图形，营造空间立体视觉效果。② 核心数学概念涵盖圆的性质、轴对称变换（镜像）、点线面正交关系、角平分线、外接圆弧以及几何作图中的位置关系。③ 作图要点：调用了 GeoGebra 命令 Circle、Mirror、Segment、OrthogonalLine、AngularBisector、Intersect、Point、Midpoint、OrthogonalPlane、CircumcircleArc，并使用 A、B、c、B′、O、P 等点与 f、g、h、n、q、r 等线面对象进行逐步构造。④ 适合高中几何课堂教学、课堂演示及立体几何自学，可用于探究透视错觉、对称变换与空间构造的视觉原理。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Mirror(B, A) → B'
  3. Segment(B', B) → f
  4. OrthogonalLine(A, f) → g
  5. AngularBisector(g, f) → h, i
  6. AngularBisector(g, i) → j, k
  7. AngularBisector(i, f) → l, m
  8. Intersect(c, g, 2) → C
  9. Intersect(c, l, 2) → D
  10. Intersect(c, h, 2) → E
  11. Intersect(c, k, 1) → F
  12. Intersect(c, m, 1) → G
  13. Intersect(c, i, 1) → H
  14. Intersect(c, j, 1) → I
  15. Intersect(c, g, 1) → J
  16. Intersect(c, l, 1) → K
  17. Intersect(c, h, 1) → L
  18. Intersect(c, k, 2) → M
  19. Intersect(c, i, 2) → O
  20. Intersect(c, j, 2) → P
  21. Intersect(c, m, 2) → N
  22. Segment(C, J) → n
  23. Segment(P, I) → q
  24. Segment(D, K) → p
  25. Segment(L, E) → r
  26. Segment(F, M) → s
  27. Segment(B', B) → t
  28. Segment(G, N) → a
  29. Segment(O, H) → b
  30. Point(c) → Q
  31. Midpoint(A, Q) → R
  32. Circle(R, Q) → d
  33. Intersect(d, p) → S, T
  34. Intersect(d, r) → U, V
  35. Intersect(d, s) → W, Z
  36. Intersect(d, t) → A_1, B_1
  37. Intersect(d, a) → C_1, D_1
  38. Intersect(d, b) → E_1, F_1
  39. Intersect(d, q) → G_1, H_1
  40. Intersect(d, n) → I_1, J_1
  41. AngularBisector(p, r) → e, f_1
  42. AngularBisector(r, s) → g_1, h_1
  43. AngularBisector(s, t) → i_1, j_1
  44. AngularBisector(t, a) → k_1, l_1
  45. Intersect(c, i_1) → K_1, L_1
  46. Intersect(c, k_1) → M_1, N_1
  47. Intersect(c, f_1) → O_1, P_1
  48. Intersect(c, h_1) → Q_1, R_1
  49. Intersect(c, j_1) → S_1, T_1
  50. Intersect(c, l_1) → U_1, V_1
  51. Intersect(c, e) → W_1, Z_1
  52. Intersect(c, g_1) → A_2, B_2
  53. Segment(N_1, M_1) → m_1
  54. Segment(P_1, O_1) → n_1
  55. Segment(Q_1, R_1) → p_1
  56. Segment(S_1, T_1) → q_1
  57. Segment(U_1, V_1) → r_1
  58. Segment(W_1, Z_1) → s_1
  59. Segment(A_2, B_2) → t_1
  60. Segment(K_1, L_1) → a_1
  61. Intersect(d, s_1) → C_2, D_2
  62. Intersect(d, r_1) → E_2, F_2
  63. Intersect(d, q_1) → G_2, H_2
  64. Intersect(d, p_1) → I_2, J_2
  65. Intersect(d, n_1) → K_2, L_2
  66. Intersect(d, m_1) → M_2, N_2
  67. Intersect(d, a_1) → O_2, P_2
  68. Intersect(d, t_1) → Q_2, R_2
  69. OrthogonalLine(A, xOyPlane) → b_1
  70. Point(b_1) → S_2
  71. OrthogonalPlane(S_2, b_1) → o
  72. OrthogonalLine(B, xOyPlane) → c_1
  73. Midpoint(S_2, A) → U_2
  74. Mirror(B_2, U_2) → V_2
  75. Mirror(P, U_2) → P'
  76. Mirror(K_1, U_2) → W_2
  77. Mirror(C, U_2) → C'
  78. Mirror(N_1, U_2) → Z_2
  79. Mirror(D, U_2) → D'
  80. Mirror(P_1, U_2) → A_3
  81. Mirror(E, U_2) → E'
  82. Mirror(Q_1, U_2) → B_3
  83. Mirror(F, U_2) → F'
  84. Mirror(T_1, U_2) → C_3
  85. Mirror(B, U_2) → B'_1
  86. Mirror(U_1, U_2) → D_3
  87. Mirror(G, U_2) → G'
  88. Mirror(Z_1, U_2) → E_3
  89. Mirror(H, U_2) → H'
  90. Mirror(A_2, U_2) → F_3
  91. Segment(B_2, V_2) → e_1
  92. Segment(P', P) → f_2
  93. Segment(K_1, W_2) → g_2
  94. Segment(C', C) → h_2
  95. Segment(N_1, Z_2) → i_2
  96. Segment(D', D) → j_2
  97. Segment(P_1, A_3) → k_2
  98. Segment(E', E) → l_2
  99. Segment(Q_1, B_3) → m_2
  100. Segment(F', F) → n_2
  101. Segment(T_1, C_3) → p_2
  102. Segment(B'_1, B) → q_2
  103. Segment(U_1, D_3) → r_2
  104. Segment(G', G) → s_2
  105. Segment(Z_1, E_3) → t_2
  106. Segment(H', H) → a_2
  107. Segment(A_2, F_3) → b_2
  108. OrthogonalLine(A_1, xOyPlane) → c_2
  109. OrthogonalLine(G_2, xOyPlane) → d_2
  110. OrthogonalLine(Z, xOyPlane) → e_2
  111. OrthogonalLine(J_2, xOyPlane) → f_3
  112. OrthogonalLine(U, xOyPlane) → g_3
  113. OrthogonalLine(L_2, xOyPlane) → h_3
  114. OrthogonalLine(D_1, xOyPlane) → i_3
  115. OrthogonalLine(H_1, xOyPlane) → j_3
  116. OrthogonalLine(P_2, xOyPlane) → k_3
  117. OrthogonalLine(J_1, xOyPlane) → l_3
  118. OrthogonalLine(N_2, xOyPlane) → m_3
  119. OrthogonalLine(T, xOyPlane) → n_3
  120. OrthogonalLine(F_2, xOyPlane) → p_3
  121. OrthogonalLine(C_2, xOyPlane) → q_3
  122. OrthogonalLine(E_1, xOyPlane) → r_3
  123. OrthogonalLine(R_2, xOyPlane) → s_3
  124. OrthogonalLine(O_2, xOyPlane) → t_3
  125. OrthogonalLine(I_1, xOyPlane) → a_3
  126. OrthogonalLine(G_1, xOyPlane) → b_3
  127. OrthogonalLine(M_2, xOyPlane) → c_3
  128. OrthogonalLine(S, xOyPlane) → d_3
  129. OrthogonalLine(K_2, xOyPlane) → e_3
  130. OrthogonalLine(V, xOyPlane) → f_4
  131. OrthogonalLine(I_2, xOyPlane) → g_4
  132. OrthogonalLine(W, xOyPlane) → h_4
  133. OrthogonalLine(B_1, xOyPlane) → i_4
  134. OrthogonalLine(E_2, xOyPlane) → j_4
  135. OrthogonalLine(C_1, xOyPlane) → k_4
  136. OrthogonalLine(D_2, xOyPlane) → l_4
  137. OrthogonalLine(F_1, xOyPlane) → m_4
  138. OrthogonalLine(Q_2, xOyPlane) → n_4
  139. OrthogonalLine(H_2, xOyPlane) → p_4
  140. Intersect(n_2, h_4) → G_3
  141. Intersect(n_2, e_2) → H_3
  142. Intersect(m_2, g_4) → I_3
  143. Intersect(f_3, m_2) → J_3
  144. Intersect(l_2, g_3) → K_3
  145. Intersect(l_2, f_4) → L_3
  146. Intersect(e_3, k_2) → M_3
  147. Intersect(k_2, h_3) → N_3
  148. Intersect(j_2, d_3) → O_3
  149. Intersect(j_2, n_3) → P_3
  150. Intersect(c_3, i_2) → Q_3
  151. Intersect(i_2, m_3) → R_3
  152. Intersect(l_3, h_2) → S_3
  153. Intersect(a_3, h_2) → T_3
  154. Intersect(g_2, t_3) → U_3
  155. Intersect(k_3, g_2) → V_3
  156. Intersect(f_2, b_3) → W_3
  157. Intersect(f_2, j_3) → Z_3
  158. Intersect(p_2, p_4) → A_4
  159. Intersect(p_2, d_2) → B_4
  160. Intersect(c_2, q_2) → C_4
  161. Intersect(q_2, i_4) → D_4
  162. Intersect(j_4, r_2) → E_4
  163. Intersect(r_2, p_3) → F_4
  164. Intersect(s_2, i_3) → G_4
  165. Intersect(s_2, k_4) → H_4
  166. Intersect(q_3, t_2) → I_4
  167. Intersect(l_4, t_2) → J_4
  168. Intersect(e_1, n_4) → K_4
  169. Intersect(e_1, s_3) → L_4
  170. Intersect(a_2, r_3) → M_4
  171. Intersect(a_2, m_4) → N_4
  172. CircumcircleArc(A_2, Q_1, B_2) → c_4
  173. CircumcircleArc(V_2, B_3, F_3) → d_4

AI 绘图提示语参考

绘制一个三维视觉错觉几何图形。先画一个圆，取圆外一点，作该点关于圆心的对称点，连接两点成线段。过圆心作该线段的垂线，再作垂线与线段、以及垂线与角平分线之间的角平分线，形成多条放射状直线。这些直线与圆相交，得到圆周上的多个交点。连接圆周上相对的点，形成若干条弦。在圆上另取一点，与圆心连线的中点作为新圆心，以该点到圆上点的距离为半径作第二个圆。第二个圆与各弦相交，产生更多交点。最后，在相邻弦之间作角平分线，这些角平分线与第一个圆相交，得到最终的点集，构成复杂的对称图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。