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多面体几何变换演示

多面体几何变换演示
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2020-05-22 20:04
三角函数立体几何变换几何作图
①本范例演示了多面体（dome 3）的几何变换与重心计算；②涉及核心概念包括重心、几何变换（旋转、镜像）、多边形构造；③构造过程中运用了线段、交点、平面、圆弧、旋转、镜像、中点、多边形、序列、距离等GeoGebra命令与对象；④适合高中及以上学生用于学习立体几何、几何变换及重心计算。

GeoGebra 命令及参数

  1. Segment(C, D) → h
  2. Segment(B, C) → g
  3. Intersect(g, yAxis) → G
  4. Plane(B, D, H_1) → diag
  5. CircleArc(G, C, I) → c
  6. Point(c) → K
  7. Line(J_1, h) → s
  8. Rotate(J_1, 90°, zAxis) → P
  9. Point(c) → J
  10. Line(I_1, h) → t
  11. Rotate(I_1, 90°, zAxis) → S_1
  12. Segment(D, A) → i
  13. Line(S_1, i) → g_1
  14. Intersect(g_1, t) → T
  15. Mirror(T, vgl1) → T'
  16. Line(P, i) → f_1
  17. Intersect(f_1, s) → U
  18. Mirror(U, vgl1) → U'
  19. Segment(T', U') → i_2
  20. Segment(A, B) → f
  21. Intersect(f, xAxis) → F
  22. Plane(D, F, F + (0, 0, 1)) → snij
  23. Intersect(i_2, snij) → D_2
  24. Segment(N_3, D_2) → h_6
  25. Mirror(D_2, zAxis) → K_2
  26. Midpoint(D_2, K_2) → L_2
  27. CircleArc(L_2, K_2, M_2) → d_3
  28. Point(d_3) → Q_2
  29. Mirror(V_2, diag) → B_3
  30. Segment(N_3, M_3) → c_5
  31. Point(d_3) → P_2
  32. Mirror(U_2, diag) → A_3
  33. Segment(M_3, L_3) → d_5
  34. Point(d_3) → O_2
  35. Mirror(T_2, diag) → Z_2
  36. Segment(L_3, K_3) → e_5
  37. Point(d_3) → N_2
  38. Mirror(S_2, diag) → W_2
  39. Segment(J_3, E_3) → g_6
  40. Segment(K_3, J_3) → f_6
  41. Intersect(i, yAxis) → E
  42. Point(xAxis) → H
  43. CircleArc(G, I, B) → d
  44. Point(c) → L
  45. Point(c) → M
  46. Point(c) → N
  47. Line(J, g) → j
  48. Line(K, g) → k
  49. Line(L, g) → l
  50. Line(M, g) → m
  51. Line(N, g) → n
  52. Mirror(I_1, vgl1) → N_1
  53. Mirror(J_1, vgl1) → O_1
  54. Mirror(K_1, vgl1) → P_1
  55. Mirror(L_1, vgl1) → Q_1
  56. Mirror(M_1, vgl1) → R_1
  57. Rotate(L_1, 90°, zAxis) → Q
  58. Rotate(M_1, 90°, zAxis) → R
  59. Rotate(I_1, (-(90°)), zAxis) → S
  60. Line(M_1, h) → p
  61. Line(L_1, h) → q
  62. Line(K_1, h) → r
  63. Line(H_1, h) → a
  64. Line(R, i) → b
  65. Line(Q, i) → e
  66. Intersect(r, e) → V
  67. Intersect(p, b) → W
  68. Rotate(K_1, 90°, zAxis) → Z
  69. Line(Z, i) → h_1
  70. Intersect(r, h_1) → A_1
  71. Intersect(q, e) → T_1
  72. Mirror(A_1, vgl1) → U_1
  73. Mirror(T_1, vgl1) → V_1
  74. Mirror(W, vgl1) → W'
  75. Polygon(D, A, W', W) → vierhoek1, d_1, a_1, w', w
  76. Polygon(W, W', V_1, T_1) → vierhoek2, w_1, i_1, v_1, t_1
  77. Polygon(T_1, V_1, U_1, A_1) → vierhoek3, j_1, k_1, u_1, l_1
  78. Polygon(A_1, U_1, U', U) → vierhoek4, m_1, n_1, u', u
  79. Polygon(U, U', T', T) → vierhoek5, u_2, p_1, t', t_2
  80. Polygon(T, T', H_1) → driehoek1, q_1, t_3, r_1
  81. Segment(H_1, T) → s_1
  82. Segment(T, U) → b_1
  83. Segment(U, A_1) → c_1
  84. Segment(A_1, T_1) → e_1
  85. Segment(T_1, W) → f_2
  86. Segment(W, D) → g_2
  87. Segment(H_1, T') → h_2
  88. Segment(U', U_1) → j_2
  89. Segment(U_1, V_1) → k_2
  90. Segment(V_1, W') → l_2
  91. Segment(W', A) → m_2
  92. Sequence(Rotate[vierhoek1, (nn * 90°), zAxis], nn, 1, 4) → l1
  93. Sequence(Rotate[vierhoek2, (nn * 90°), zAxis], nn, 1, 4) → l2
  94. Sequence(Rotate[vierhoek3, (nn * 90°), zAxis], nn, 1, 4) → l3
  95. Sequence(Rotate[vierhoek4, (nn * 90°), zAxis], nn, 1, 4) → l4
  96. Sequence(Rotate[vierhoek5, (nn * 90°), zAxis], nn, 1, 4) → l5
  97. Sequence(Rotate[driehoek1, (nn * 90°), zAxis], nn, 1, 4) → l6
  98. Sequence(Segment[Rotate[H_1, (nn * 90°), zAxis], Rotate[T', (nn * 90°), zAxis]], nn, 1, 2) → l7
  99. Sequence(Segment[Rotate[T', (nn * 90°), zAxis], Rotate[U', (nn * 90°), zAxis]], nn, 1, 2) → l8
  100. Sequence(Segment[Rotate[U', (nn * 90°), zAxis], Rotate[U_1, (nn * 90°), zAxis]], nn, 1, 2) → l9
  101. Sequence(Segment[Rotate[U_1, (nn * 90°), zAxis], Rotate[V_1, (nn * 90°), zAxis]], nn, 1, 2) → l10
  102. Sequence(Segment[Rotate[V_1, (nn * 90°), zAxis], Rotate[W', (nn * 90°), zAxis]], nn, 1, 2) → l11
  103. Sequence(Segment[Rotate[W', (nn * 90°), zAxis], Rotate[A, (nn * 90°), zAxis]], nn, 1, 2) → l12
  104. Midpoint(H, E) → W_1
  105. Line(W_1, zAxis) → n_2
  106. Distance(W_1, E) → horstraal
  107. Rotate(vierhoek1, 90°, zAxis) → vierhoek1'
  108. Rotate(vierhoek2, 90°, zAxis) → vierhoek2'
  109. Rotate(vierhoek3, 90°, zAxis) → vierhoek3'
  110. Rotate(vierhoek4, 90°, zAxis) → vierhoek4'
  111. Rotate(vierhoek5, 90°, zAxis) → vierhoek5'
  112. Intersect(u_2, snij) → Z_1
  113. Intersect(m_1, snij) → A_2
  114. Intersect(j_1, snij) → B_2
  115. Intersect(w_1, snij) → C_2
  116. Intersect(snij, vierhoek4') → E_2, F_2
  117. Intersect(snij, vierhoek2') → G_2, H_2
  118. Segment(D, C_2) → p_2
  119. Segment(C_2, B_2) → q_2
  120. Segment(B_2, A_2) → r_2
  121. Segment(A_2, Z_1) → s_2
  122. Segment(Z_1, D_2) → a_2
  123. Segment(D_2, F_2) → b_2
  124. Segment(F_2, E_2) → c_2
  125. Segment(E_2, H_2) → d_2
  126. Segment(H_2, G_2) → e_2
  127. Segment(G_2, F) → f_3
  128. Mirror(l13, diag) → l13'
  129. Sequence(Rotate[l13, (nn * 90°), zAxis], nn, 1, 3) → l14
  130. Sequence(Rotate[l13', (nn * 90°), zAxis], nn, 1, 3) → l15
  131. Segment(B, E) → g_3
  132. Segment(B, H) → h_3
  133. Segment(C, F) → i_3
  134. Segment(C, E) → j_3
  135. Segment(D, F) → k_3
  136. Segment(D, G) → l_3
  137. Segment(A, G) → m_3
  138. Segment(A, H) → n_3
  139. Rotate(D_2, (-(90°)), zAxis) → I_2
  140. Point(l15) → J_2
  141. Polygon(Z_1, J_2, D_2) → driehoek2, p_3, z_1, q_3
  142. Polygon(J_2, U', D_2) → driehoek3, r_3, s_3, a_3
  143. Plane(D_2, U', D_2 + (0, 0, 1)) → spieg
  144. Mirror(driehoek2, spieg) → driehoek2'
  145. Mirror(driehoek3, spieg) → driehoek3'
  146. Sequence(Rotate[driehoek2, (nn * 90°), zAxis], nn, 1, 3) → l16
  147. Sequence(Rotate[driehoek3, (nn * 90°), zAxis], nn, 1, 3) → l17
  148. Sequence(Rotate[driehoek3', (nn * 90°), zAxis], nn, 1, 3) → l18
  149. Sequence(Rotate[driehoek2', (nn * 90°), zAxis], nn, 1, 3) → l19
  150. Segment(T, H_1) → b_3
  151. Segment(L_2, U) → c_3
  152. Point(s_2) → D_3
  153. Polygon(D_3, D_2, C_3) → driehoek4, e_3, f_4, g_4
  154. Sequence(Rotate[driehoek4, (nn * 90°), zAxis], nn, 1, 3) → l20
  155. Mirror(driehoek4, spieg) → driehoek4'
  156. Sequence(Rotate[driehoek4', (nn * 90°), zAxis], nn, 1, 3) → l21
  157. Polygon(C_3, D_2, N_3, O_3) → vierhoek6, h_4, i_4, j_4, o_3
  158. Rotate(J_3, (-(45°)), zAxis) → P_3
  159. Rotate(K_3, (-(45°)), zAxis) → Q_3
  160. Rotate(L_3, (-(45°)), zAxis) → R_3
  161. Rotate(M_3, (-(45°)), zAxis) → S_3
  162. Rotate(N_3, (-(45°)), zAxis) → T_3
  163. Polygon(P_3, J_3, E_3) → driehoek5, k_4, l_4, m_4
  164. Polygon(P_3, Q_3, K_3, J_3) → vierhoek7, n_4, p_4, q_4, r_4
  165. Polygon(Q_3, R_3, L_3, K_3) → vierhoek8, s_4, t_4, a_4, b_4
  166. Polygon(S_3, M_3, L_3, R_3) → vierhoek9, c_4, d_4, e_4, f_5
  167. Point(o_3) → U_3
  168. Polygon(S_3, U_3, N_3, M_3) → vierhoek10, g_5, u_3, h_5, i_5
  169. Polygon(S_3, T_3, M_3) → driehoek6, j_5, k_5, l_5
  170. Polygon(T_3, N_3, M_3) → driehoek7, m_5, n_5, p_5
  171. Polygon(T_3, C_3, N_3) → driehoek8, q_5, r_5, s_5
  172. Polygon(C_3, N_3, D_2) → driehoek9, t_5, a_5, b_5
  173. Sequence(Rotate[l22, (nn * 90°), zAxis], nn, 1, 3) → l23
  174. Mirror(l22, spieg) → l22'
  175. Sequence(Rotate[l22', (nn * 90°), zAxis], nn, 1, 3) → l24
  176. Sequence(Rotate[l25, (nn * 90°), zAxis], nn, 1, 3) → l26
  177. Segment(D_3, C_3) → i_6
  178. Segment(D_3, T_3) → j_6
  179. Segment(T_3, S_3) → k_6
  180. Segment(S_3, R_3) → l_6
  181. Segment(R_3, Q_3) → m_6
  182. Segment(Q_3, P_3) → n_6
  183. Segment(P_3, E_3) → p_6
  184. Sequence(Rotate[l27, (nn * 90°), zAxis], nn, 1, 3) → l28
  185. Segment(W', A) → q_6
  186. Segment(C_3, D_2) → r_6
  187. Segment(C_3, I_2) → s_6
  188. Sequence(Segment[Rotate[C_3, (nn * 90°), zAxis], Rotate[D_2, (nn * 90°), zAxis]], nn, 1, 3) → l29
  189. Sequence(Segment[Rotate[C_3, (nn * 90°), zAxis], Rotate[I_2, (nn * 90°), zAxis]], nn, 1, 3) → l30

AI 绘图提示语参考

画一个圆顶结构的几何变换和质心计算示例。首先绘制一个多边形，然后通过旋转和镜像操作创建对称结构，并计算质心。展示旋转、反射等几何变换过程，以及多边形的构建和质心位置。
以上提示语为根据原始绘图命令整理而来，仅供参考。