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多阶段动画几何作图示例

多阶段动画几何作图示例
几何画板及绘图内容加载中，请稍等……
2015-06-26 03:11
立体几何几何作图滑块动画
本范例演示了通过多阶段动画展示几何图形变换的过程。涉及的核心数学概念包括棱柱、体积计算、二次函数、勾股定理和对数函数。作图要点包括使用GeoGebra命令如If、Vector、Translate、Line、Point、OrthogonalLine、Segment、Polygon和Circle来构造图形。适合初中生及以上学习者，用于理解几何变换与函数图像的关联。

GeoGebra 命令及参数

  1. If(o < 1, o, 1) → o1
  2. Vector(A, E) → q
  3. If(o1 < 0.2, Vector[(0 * q)], Vector[If[o1 < 0.8, Vector[(((5 / 3 * o1) - 1 / 3) * q)], q]]) → q1
  4. Translate(A, q1) → A'
  5. Vector(A', A) → m
  6. If(k1 < 1, Vector[(k1 * m)], Vector[If[k1 < 4, m, Vector[((5 - k1) * m)]]]) → m1
  7. Translate(A', m1) → A''
  8. Line(A, B_1) → a
  9. Point(a) → B
  10. Vector(A, C) → u
  11. OrthogonalLine(A, a) → b
  12. Point(b) → D
  13. Vector(A, B) → v
  14. Vector(A, D) → w
  15. Translate(C, w) → C'
  16. Vector(C, C') → c
  17. Translate(B, w) → B'
  18. Vector(B, B') → d
  19. Segment(C, B) → e
  20. Segment(C', B') → f
  21. Segment(D, B') → g
  22. Segment(D, C') → h
  23. Segment(A, C) → i
  24. Segment(D, A) → j
  25. Segment(C', C) → k_2
  26. Segment(B', B) → l_2
  27. Segment(C', A) → m_2
  28. Segment(A, B') → n_2
  29. Segment(B', C) → p_2
  30. Vector(A, G) → s
  31. If(o < 1, 0, o - 1) → o2
  32. If(o2 < 0.2, Vector[(0 * s)], Vector[If[o2 < 0.8, Vector[(((5 / 3 * o2) - 1 / 3) * s)], s]]) → s1
  33. Translate(D, q1) → D'
  34. Translate(C', q1) → C''
  35. Translate(B', q1) → B''
  36. Segment(C'', B'') → t
  37. Segment(B'', D') → a_1
  38. Segment(A', B'') → b_1
  39. Segment(C'', A') → c_1
  40. Segment(A', D') → d_1
  41. Segment(D', C'') → e_1
  42. Translate(A, s1) → A'_1
  43. Translate(C, s1) → C'_1
  44. Translate(B, s1) → B'_1
  45. Translate(B', s1) → B''_1
  46. Segment(A'_1, B'_1) → r
  47. Segment(B'_1, C'_1) → f_1
  48. Segment(C'_1, A'_1) → g_1
  49. Segment(B''_1, B'_1) → h_1
  50. Segment(B''_1, C'_1) → i_1
  51. Segment(B''_1, A'_1) → j_1
  52. Segment(C', D) → k_1
  53. Segment(D, A) → l_1
  54. Segment(D, B') → m_1
  55. Segment(B, A) → n_1
  56. Segment(B, B') → p_1
  57. Segment(B, C) → q_1
  58. Vector(A'_1, A) → n
  59. Point(n) → F
  60. Vector(F, A') → p
  61. If(k2 < 1, Vector[(k2 * n)], Vector[If[k2 < 4, n, Vector[((5 - k2) * n)]]]) → n1
  62. If(k3 < 1, Vector[(k3 * p)], Vector[If[k3 < 4, p, Vector[((5 - k3) * p)]]]) → p1
  63. Polygon(C'', D', H) → poly1, h_2, c'', d'
  64. Polygon(C', A, C) → poly2, c_2, c', a_2
  65. Translate(C'', m1) → C'''
  66. Translate(D', m1) → D''
  67. Translate(H, m1) → H'
  68. Polygon(C''', D'', H') → poly1', h', c''', d''
  69. Translate(C'', m1) → C'''_1
  70. Translate(B'', m1) → B'''
  71. Segment(C'''_1, B''') → t'
  72. Translate(B'', m1) → B'''_1
  73. Translate(D', m1) → D''_1
  74. Segment(B'''_1, D''_1) → k
  75. Translate(B'', m1) → B'''_2
  76. Segment(A'', B'''_2) → l
  77. Translate(C'', m1) → C'''_2
  78. Translate(A', m1) → A''_1
  79. Segment(C'''_2, A''_1) → r_1
  80. Translate(A', m1) → A''_2
  81. Translate(D', m1) → D''_2
  82. Segment(A''_2, D''_2) → s_1
  83. Translate(D', m1) → D''_3
  84. Translate(C'', m1) → C'''_3
  85. Segment(D''_3, C'''_3) → t_1
  86. Polygon(C', C, B') → poly3, b', c'_1, c_3
  87. Polygon(C'_1, B'_1, B''_1) → poly4, b''_1, c'_2, b'_1
  88. Translate(C'_1, n1) → I
  89. Translate(B'_1, n1) → J
  90. Translate(B''_1, n1) → K
  91. Polygon(I, J, K) → poly4', k_3, i_2, j_2
  92. Translate(A'_1, n1) → L
  93. Translate(B'_1, n1) → M
  94. Segment(L, M) → r'
  95. Translate(B'_1, n1) → N
  96. Translate(C'_1, n1) → O
  97. Segment(N, O) → b_2
  98. Translate(C'_1, n1) → P
  99. Translate(A'_1, n1) → Q
  100. Segment(P, Q) → d_2
  101. Translate(B''_1, n1) → R
  102. Translate(B'_1, n1) → S
  103. Segment(R, S) → e_2
  104. Translate(B''_1, n1) → T
  105. Translate(C'_1, n1) → U
  106. Segment(T, U) → f_2
  107. Translate(B''_1, n1) → V
  108. Translate(A'_1, n1) → W
  109. Segment(V, W) → g_2
  110. Translate(F, n1) → F'
  111. Polygon(C''', D'', B''') → poly5, b''', c'''_1, d''_1
  112. Polygon(I, F, J) → poly6, j_3, i_3, f_3
  113. Translate(I, p1) → I'
  114. Translate(F, p1) → F'_1
  115. Translate(J, p1) → J'
  116. Polygon(I', F'_1, J') → poly6', j', i', f'_1
  117. Translate(A'_1, p1) → Z
  118. Translate(B'_1, p1) → A_1
  119. Segment(Z, A_1) → r'_1
  120. Translate(B'_1, p1) → C_1
  121. Translate(C'_1, p1) → D_1
  122. Segment(C_1, D_1) → q_2
  123. Translate(C'_1, p1) → E_1
  124. Translate(A'_1, p1) → F_1
  125. Segment(E_1, F_1) → r_2
  126. Translate(B''_1, p1) → G_1
  127. Translate(B'_1, p1) → H_1
  128. Segment(G_1, H_1) → s_2
  129. Translate(B''_1, p1) → I_1
  130. Translate(C'_1, p1) → J_1
  131. Segment(I_1, J_1) → t_2
  132. Translate(B''_1, p1) → K_1
  133. Translate(A'_1, p1) → L_1
  134. Segment(K_1, L_1) → a_3
  135. Translate(K, p1) → K'
  136. Translate(I, p1) → I'_1
  137. Segment(K', I'_1) → b_3
  138. Translate(J, p1) → J'_1
  139. Translate(K, p1) → K'_1
  140. Segment(J'_1, K'_1) → d_3
  141. Translate(L, p1) → L'
  142. Translate(M, p1) → M'
  143. Segment(L', M') → r''
  144. Translate(N, p1) → N'
  145. Translate(O, p1) → O'
  146. Segment(N', O') → e_3
  147. Translate(P, p1) → P'
  148. Translate(Q, p1) → Q'
  149. Segment(P', Q') → g_3
  150. Translate(R, p1) → R'
  151. Translate(S, p1) → S'
  152. Segment(R', S') → h_3
  153. Translate(T, p1) → T'
  154. Translate(U, p1) → U'
  155. Segment(T', U') → l_3
  156. Translate(V, p1) → V'
  157. Translate(W, p1) → W'
  158. Segment(V', W') → m_3
  159. Translate(F', p1) → F''
  160. Segment(G_1, J') → n_3
  161. Segment(D'', H) → p_3
  162. Polygon(H, B''', C''') → poly7, c'''_2, h_4, b'''_1
  163. Polygon(F, K, C') → poly8, c'_3, f_4, k_4
  164. Polygon(F, K, I) → poly9, i_4, f_5, k_5
  165. Polygon(A, B', C) → poly10, c_4, a_4, b'_2
  166. Segment(I', F'_1) → q_3
  167. Segment(I', J') → r_3
  168. Segment(G_1, J') → s_3
  169. Segment(G_1, I') → t_3
  170. Circle(B''', 0.3) → d_4
  171. Circle(A, 0.3) → e_4

AI 绘图提示语参考

绘制一个多阶段动画的三棱柱几何构造：先画底面三角形，再通过向量平移生成顶面三角形，连接对应顶点形成侧棱；引入两个滑块分别控制第一阶段沿一向量的渐进平移、第二阶段沿另一向量的分段平移，使棱柱在两个方向上依次展开再收回，展示体积变化、勾股关系及二次函数轨迹。
以上提示语为根据原始绘图命令整理而来，仅供参考。