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多步变换演示

多步变换演示
几何画板及绘图内容加载中，请稍等……
2014-06-14 12:12
向量解析几何变换几何作图
所属专题 Transformations Stations
这个范例演示了单个或多个变换步骤的交互式操作。用户可以通过滑块和交互元素控制变换过程，直观展示几何变换的效果。涉及的核心数学概念包括几何变换、相似性、对称性和坐标几何。作图要点使用了GeoGebra命令如Line（线）、Mirror（镜像）、Dilate（缩放）、Polygon（多边形）、Vector（向量）、Rotate（旋转）、Angle（角）、Segment（线段）和Translate（平移）等。适合高中阶段学生学习几何变换和空间几何。

GeoGebra 命令及参数

  1. Line(D, E) → Mirror_1
  2. Mirror(B, Mirror_1) → B'_3
  3. Dilate(T, T_2 / 100, B'_3) → T'
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Dilate(F, T_1 / 100, B) → F'
  6. Vector(B, F') → u
  7. Rotate(A, ((T_1 / 100 * 360))°, G) → A'
  8. Rotate(B, ((T_1 / 100 * 360))°, G) → B'
  9. Rotate(C, ((T_1 / 100 * 360))°, G) → C'
  10. Polygon(A', B', C') → poly1', c', a', b'
  11. Angle(B, G, B') → α
  12. Dilate(B, 0.2, G) → B'_1
  13. Dilate(B', 0.2, G) → B''
  14. Segment(G, B'_1) → d
  15. Segment(G, B'') → e
  16. Translate(A, u) → A'_1
  17. Translate(B, u) → B'_2
  18. Translate(C, u) → C'_1
  19. Polygon(A'_1, B'_2, C'_1) → poly1'_1, c'_1, a'_1, b'_2
  20. Mirror(A, Mirror_1) → A'_2
  21. Mirror(C, Mirror_1) → C'_2
  22. Dilate(A'_2, T_1 / 100, A) → H
  23. Dilate(B'_3, T_1 / 100, B) → I
  24. Dilate(C'_2, T_1 / 100, C) → J
  25. Polygon(J, H, I) → poly2, i, j, h
  26. Rotate(A'_1, ((T_2 / 100 * 360))°, K) → L
  27. Rotate(If[Translate_1, B'_2, I], ((T_2 / 100 * 360))°, K) → M
  28. Rotate(C'_1, ((T_2 / 100 * 360))°, K) → N
  29. Polygon(L, M, N) → poly3, n, l, m
  30. Dilate(M, 0.2, K) → M'
  31. Dilate(If[Translate_1, F, I], 0.2, K) → F'_1
  32. Segment(K, M') → f
  33. Segment(K, F'_1) → g
  34. Angle(F'_1, K, M') → β
  35. Line(O, P) → k
  36. Mirror(F, k) → F'_2
  37. Mirror(C'_1, k) → Q
  38. Mirror(A'_1, k) → R
  39. Dilate(Q, T_2 / 100, C'_1) → Q'
  40. Dilate(F'_2, T_2 / 100, F) → S
  41. Dilate(R, T_2 / 100, A'_1) → R'
  42. Polygon(Q', S, R') → poly4, r', q', s
  43. Vector(B'_3, T') → v
  44. Translate(A'_2, v) → A''
  45. Translate(B'_3, v) → B''_1
  46. Translate(C'_2, v) → C''
  47. Polygon(A'', B''_1, C'') → poly1'', c'', a'', b''_1
  48. Mirror(B', k) → B''_2
  49. Mirror(C', k) → C''_1
  50. Mirror(A', k) → A''_1
  51. Dilate(B''_2, T_2 / 100, B') → U
  52. Dilate(A''_1, T_2 / 100, A') → V
  53. Dilate(C''_1, T_2 / 100, C') → W
  54. Polygon(U, W, V) → poly5, v_1, u_1, w
  55. Dilate(T, T_2 / 100, B') → T'_1
  56. Vector(B', T'_1) → p
  57. Translate(A', p) → A''_2
  58. Translate(B', p) → B''_3
  59. Translate(C', p) → C''_2
  60. Polygon(A''_2, B''_3, C''_2) → poly1''_1, c''_2, a''_2, b''_3
  61. Rotate(J, β, K) → J'
  62. Rotate(H, β, K) → H'
  63. Rotate(I, β, K) → I'
  64. Polygon(J', H', I') → poly2', i', j', h'
  65. Mirror(B'_3, k) → Z
  66. Mirror(A'_2, k) → A_1
  67. Mirror(C'_2, k) → B_1
  68. Dilate(Z, T_2 / 100, B'_3) → Z'
  69. Dilate(A_1, T_2 / 100, A'_2) → C_1
  70. Dilate(B_1, T_2 / 100, C'_2) → D_1
  71. Polygon(Z', C_1, D_1) → poly6, d_1, z', c_1
  72. Dilate(A, Factor, E_1) → A'_3
  73. Dilate(B, Factor, E_1) → B'_4
  74. Dilate(C, Factor, E_1) → C'_3
  75. Polygon(A'_3, B'_4, C'_3) → poly1'_2, c'_3, a'_3, b'_4
  76. Dilate(A'_1, Factor, E_1) → F_1
  77. Dilate(B'_2, Factor, E_1) → G_1
  78. Dilate(C'_1, Factor, E_1) → H_1
  79. Polygon(F_1, G_1, H_1) → poly7, h_1, f_1, g_1
  80. Dilate(A', Factor, E_1) → A''_3
  81. Dilate(B', Factor, E_1) → B''_4
  82. Dilate(C', Factor, E_1) → C''_3
  83. Polygon(A''_3, B''_4, C''_3) → poly1''_2, c''_3, a''_3, b''_4
  84. Dilate(J, Factor, E_1) → J'_1
  85. Dilate(H, Factor, E_1) → H'_1
  86. Dilate(I, Factor, E_1) → I'_1
  87. Polygon(J'_1, H'_1, I'_1) → poly2'_1, i'_1, j'_1, h'_1
  88. Dilate(A'', Factor, E_1) → A'''
  89. Dilate(B''_1, Factor, E_1) → I_1
  90. Dilate(C'', Factor, E_1) → C'''
  91. Polygon(A''', I_1, C''') → poly1''', c''', a''', i_1
  92. Segment(E_1, C''') → q
  93. Segment(E_1, A''') → r
  94. Segment(E_1, I_1) → t
  95. Segment(J'_1, E_1) → a_1
  96. Segment(I'_1, E_1) → b_1
  97. Segment(H'_1, E_1) → e_1
  98. Dilate(J', Factor, E_1) → J''
  99. Dilate(H', Factor, E_1) → H''
  100. Dilate(I', Factor, E_1) → I''
  101. Polygon(J'', H'', I'') → poly2'', i'', j'', h''
  102. Segment(E_1, H'') → j_1
  103. Segment(E_1, J'') → k_1
  104. Segment(E_1, I'') → l_1
  105. Dilate(Z', Factor, E_1) → Z''
  106. Dilate(C_1, Factor, E_1) → J_1
  107. Dilate(D_1, Factor, E_1) → K_1
  108. Polygon(Z'', J_1, K_1) → poly6', k_2, z'', j_2
  109. Segment(E_1, K_1) → m_1
  110. Segment(E_1, J_1) → n_1
  111. Segment(E_1, Z'') → p_1
  112. Segment(E_1, C''_3) → q_1
  113. Segment(E_1, A''_3) → r_1
  114. Segment(E_1, B''_4) → s_1
  115. Dilate(A''_2, Factor, E_1) → L_1
  116. Dilate(B''_3, Factor, E_1) → M_1
  117. Dilate(C''_2, Factor, E_1) → N_1
  118. Polygon(L_1, M_1, N_1) → poly8, n_2, l_2, m_2
  119. Segment(E_1, L_1) → t_1
  120. Segment(E_1, N_1) → a_2
  121. Segment(E_1, M_1) → b_2
  122. Dilate(U, Factor, E_1) → U'
  123. Dilate(W, Factor, E_1) → W'
  124. Dilate(V, Factor, E_1) → V'
  125. Polygon(U', W', V') → poly5', v', u', w'
  126. Segment(E_1, W') → c_2
  127. Segment(E_1, U') → d_2
  128. Segment(E_1, V') → e_2
  129. Segment(E_1, G_1) → f_2
  130. Segment(E_1, F_1) → g_2
  131. Segment(E_1, H_1) → h_2
  132. Dilate(L, Factor, E_1) → L'
  133. Dilate(M, Factor, E_1) → M'_1
  134. Dilate(N, Factor, E_1) → N'
  135. Polygon(L', M'_1, N') → poly3', n', l', m'_1
  136. Segment(E_1, L') → i_2
  137. Segment(E_1, N') → p_2
  138. Segment(E_1, M'_1) → q_2
  139. Dilate(Q', Factor, E_1) → Q''
  140. Dilate(S, Factor, E_1) → S'
  141. Dilate(R', Factor, E_1) → R''
  142. Polygon(Q'', S', R'') → poly4', r'', q'', s'
  143. Segment(E_1, R'') → r_2
  144. Segment(E_1, S') → s_2
  145. Segment(E_1, Q'') → t_2
  146. Segment(E_1, A'_3) → a_3
  147. Segment(E_1, B'_4) → b_3
  148. Segment(E_1, C'_3) → c_3
  149. Vector(B, B'_4) → w_1
  150. Vector(C, C'_3) → u_2
  151. Vector(A, A'_3) → v_2
  152. Vector(F, G_1) → w_2
  153. Vector(A'_1, F_1) → u_3
  154. Vector(C'_1, H_1) → v_3
  155. Vector(C', C''_3) → w_3
  156. Vector(A', A''_3) → d_3
  157. Vector(B', B''_4) → e_3
  158. Vector(A'_2, H'_1) → f_3
  159. Vector(B'_3, I'_1) → g_3
  160. Vector(C'_2, J'_1) → h_3
  161. Vector(M, M'_1) → i_3
  162. Vector(N, N') → j_3
  163. Vector(L, L') → k_3
  164. Vector(Q, Q'') → l_3
  165. Vector(F'_2, S') → m_3
  166. Vector(R, R'') → n_3
  167. Vector(C''_2, N_1) → p_3
  168. Vector(A''_2, L_1) → q_3
  169. Vector(T, M_1) → r_3
  170. Vector(B''_2, U') → s_3
  171. Vector(C''_1, W') → t_3
  172. Vector(A''_1, V') → u_4
  173. Vector(T, I_1) → v_4
  174. Vector(C'', C''') → w_4
  175. Vector(A'', A''') → a_4
  176. Vector(H', H'') → b_4
  177. Vector(J', J'') → c_4
  178. Vector(I', I'') → d_4
  179. Vector(B_1, K_1) → e_4
  180. Vector(Z, Z'') → f_4
  181. Vector(A_1, J_1) → g_4

AI 绘图提示语参考

画一个几何变换演示图，包含初始多边形和一系列变换：首先通过镜像和缩放创建新图形，然后利用旋转和向量移动生成多个变形版本，最后通过镜像和进一步缩放展示对称性和相似性。整个过程通过滑块控制变换参数，展示几何变换、相似性、对称性和坐标几何的核心概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。