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点的变换

点的变换
几何画板及绘图内容加载中，请稍等……
2026-05-15 23:34
向量函数变换
所属专题 complex-numbers
该范例演示了点的变换过程。核心数学概念包括函数变换、向量和相似变换。通过使用GeoGebra命令如Vector、Sequence、Length等，可以构造出点的变换效果。适合中学阶段学生学习几何变换。

GeoGebra 命令及参数

  1. Vector(A, A + (B - A) / n) → u
  2. Vector(A, A + (C - A) / n) → v
  3. Sequence(Sequence[A + (k * u) + (j * v), k, 0, n, 1 / n], j, 0, n, 1 / n) → m1
  4. Length(m1) → c
  5. Textfield(a) → CampEntradaSortida1
  6. Textfield(b) → CampEntradaSortida2
  7. Sequence(Sequence[(a(x(m1(i, j)), y(m1(i, j))), b(x(m1(i, j)), y(m1(i, j)))), i, 1, tt], j, 1, tt) → m2
  8. Sequence(m1(k, tt), k, 1, c) → l1
  9. Sequence(Segmentparamètric[Element[m1, k, 1], Element[m1, k, c]], k, 1, tt) → l2
  10. Sequence(Segmentparamètric[Element[m1, 1, k], Element[m1, c, k]], k, 1, tt) → l3
  11. Element(l2, A1) → B1
  12. Element(l2, A2) → B2
  13. Element(l2, A3) → B3
  14. Element(l2, A4) → B4
  15. Element(l2, A5) → B5
  16. Element(l2, A6) → B6
  17. Element(l2, A7) → B7
  18. Element(l2, A8) → B8
  19. Element(l2, A9) → B9
  20. Element(l2, A10) → B10
  21. Element(l2, A11) → B11
  22. Element(l2, A12) → B12
  23. Element(l2, A13) → B13
  24. Element(l2, A14) → B14
  25. Element(l2, A15) → B15
  26. Element(l2, A16) → B16
  27. Element(l2, A17) → B17
  28. Element(l2, A18) → B18
  29. Element(l2, A19) → B19
  30. Element(l2, A20) → B20
  31. Element(l2, A21) → B21
  32. Element(l2, A22) → B22
  33. Element(l2, A23) → B23
  34. Element(l2, A24) → B24
  35. Element(l2, A25) → B25
  36. Element(l2, A26) → B26
  37. Element(l2, A27) → B27
  38. Element(l2, A28) → B28
  39. Element(l2, A29) → B29
  40. Element(l2, A30) → B30
  41. Element(l2, A31) → B31
  42. Element(l2, A32) → B32
  43. Element(l2, A33) → B33
  44. Element(l2, A34) → B34
  45. Element(l2, A35) → B35
  46. Element(l2, A36) → B36
  47. Element(l2, A37) → B37
  48. Element(l3, A1) → C1
  49. Element(l3, A2) → C2
  50. Element(l3, A3) → C3
  51. Element(l3, A4) → C4
  52. Element(l3, A5) → C5
  53. Element(l3, A6) → C6
  54. Element(l3, A7) → C7
  55. Element(l3, A8) → C8
  56. Element(l3, A9) → C9
  57. Element(l3, A10) → C10
  58. Element(l3, A11) → C11
  59. Element(l3, A12) → C12
  60. Element(l3, A13) → C13
  61. Element(l3, A14) → C14
  62. Element(l3, A15) → C15
  63. Element(l3, A16) → C16
  64. Element(l3, A17) → C17
  65. Element(l3, A18) → C18
  66. Element(l3, A19) → C19
  67. Element(l3, A20) → C20
  68. Element(l3, A21) → C21
  69. Element(l3, A22) → C22
  70. Element(l3, A23) → C23
  71. Element(l3, A24) → C24
  72. Element(l3, A25) → C25
  73. Element(l3, A26) → C26
  74. Element(l3, A27) → C27
  75. Element(l3, A28) → C28
  76. Element(l3, A29) → C29
  77. Element(l3, A30) → C30
  78. Element(l3, A31) → C31
  79. Element(l3, A32) → C32
  80. Element(l3, A33) → C33
  81. Element(l3, A34) → C34
  82. Element(l3, A35) → C35
  83. Element(l3, A36) → C36
  84. Element(l3, A37) → C37
  85. CurveCartesian(a(x(B1(t)), y(B1(t))), b(x(B1(t)), y(B1(t))), t, 0, 1) → D1
  86. CurveCartesian(a(x(B2(t)), y(B2(t))), b(x(B2(t)), y(B2(t))), t, 0, 1) → D2
  87. CurveCartesian(a(x(B3(t)), y(B3(t))), b(x(B3(t)), y(B3(t))), t, 0, 1) → D3
  88. CurveCartesian(a(x(B4(t)), y(B4(t))), b(x(B4(t)), y(B4(t))), t, 0, 1) → D4
  89. CurveCartesian(a(x(B5(t)), y(B5(t))), b(x(B5(t)), y(B5(t))), t, 0, 1) → D5
  90. CurveCartesian(a(x(B6(t)), y(B6(t))), b(x(B6(t)), y(B6(t))), t, 0, 1) → D6
  91. CurveCartesian(a(x(B7(t)), y(B7(t))), b(x(B7(t)), y(B7(t))), t, 0, 1) → D7
  92. CurveCartesian(a(x(B8(t)), y(B8(t))), b(x(B8(t)), y(B8(t))), t, 0, 1) → D8
  93. CurveCartesian(a(x(B9(t)), y(B9(t))), b(x(B9(t)), y(B9(t))), t, 0, 1) → D9
  94. CurveCartesian(a(x(B10(t)), y(B10(t))), b(x(B10(t)), y(B10(t))), t, 0, 1) → D10
  95. CurveCartesian(a(x(B11(t)), y(B11(t))), b(x(B11(t)), y(B11(t))), t, 0, 1) → D11
  96. CurveCartesian(a(x(B12(t)), y(B12(t))), b(x(B12(t)), y(B12(t))), t, 0, 1) → D12
  97. CurveCartesian(a(x(B13(t)), y(B13(t))), b(x(B13(t)), y(B13(t))), t, 0, 1) → D13
  98. CurveCartesian(a(x(B14(t)), y(B14(t))), b(x(B14(t)), y(B14(t))), t, 0, 1) → D14
  99. CurveCartesian(a(x(B15(t)), y(B15(t))), b(x(B15(t)), y(B15(t))), t, 0, 1) → D15
  100. CurveCartesian(a(x(B16(t)), y(B16(t))), b(x(B16(t)), y(B16(t))), t, 0, 1) → D16
  101. CurveCartesian(a(x(B17(t)), y(B17(t))), b(x(B17(t)), y(B17(t))), t, 0, 1) → D17
  102. CurveCartesian(a(x(B18(t)), y(B18(t))), b(x(B18(t)), y(B18(t))), t, 0, 1) → D18
  103. CurveCartesian(a(x(B19(t)), y(B19(t))), b(x(B19(t)), y(B19(t))), t, 0, 1) → D19
  104. CurveCartesian(a(x(B20(t)), y(B20(t))), b(x(B20(t)), y(B20(t))), t, 0, 1) → D20
  105. CurveCartesian(a(x(B21(t)), y(B21(t))), b(x(B21(t)), y(B21(t))), t, 0, 1) → D21
  106. CurveCartesian(a(x(B22(t)), y(B22(t))), b(x(B22(t)), y(B22(t))), t, 0, 1) → D22
  107. CurveCartesian(a(x(B23(t)), y(B23(t))), b(x(B23(t)), y(B23(t))), t, 0, 1) → D23
  108. CurveCartesian(a(x(B24(t)), y(B24(t))), b(x(B24(t)), y(B24(t))), t, 0, 1) → D24
  109. CurveCartesian(a(x(B25(t)), y(B25(t))), b(x(B25(t)), y(B25(t))), t, 0, 1) → D25
  110. CurveCartesian(a(x(B26(t)), y(B26(t))), b(x(B26(t)), y(B26(t))), t, 0, 1) → D26
  111. CurveCartesian(a(x(B27(t)), y(B27(t))), b(x(B27(t)), y(B27(t))), t, 0, 1) → D27
  112. CurveCartesian(a(x(B28(t)), y(B28(t))), b(x(B28(t)), y(B28(t))), t, 0, 1) → D28
  113. CurveCartesian(a(x(B29(t)), y(B29(t))), b(x(B29(t)), y(B29(t))), t, 0, 1) → D29
  114. CurveCartesian(a(x(B30(t)), y(B30(t))), b(x(B30(t)), y(B30(t))), t, 0, 1) → D30
  115. CurveCartesian(a(x(B31(t)), y(B31(t))), b(x(B31(t)), y(B31(t))), t, 0, 1) → D31
  116. CurveCartesian(a(x(B32(t)), y(B32(t))), b(x(B32(t)), y(B32(t))), t, 0, 1) → D32
  117. CurveCartesian(a(x(B33(t)), y(B33(t))), b(x(B33(t)), y(B33(t))), t, 0, 1) → D33
  118. CurveCartesian(a(x(B34(t)), y(B34(t))), b(x(B34(t)), y(B34(t))), t, 0, 1) → D34
  119. CurveCartesian(a(x(B35(t)), y(B35(t))), b(x(B35(t)), y(B35(t))), t, 0, 1) → D35
  120. CurveCartesian(a(x(B36(t)), y(B36(t))), b(x(B36(t)), y(B36(t))), t, 0, 1) → D36
  121. CurveCartesian(a(x(B37(t)), y(B37(t))), b(x(B37(t)), y(B37(t))), t, 0, 1) → D37
  122. CurveCartesian(a(x(C1(t)), y(C1(t))), b(x(C1(t)), y(C1(t))), t, 0, 1) → E1
  123. CurveCartesian(a(x(C2(t)), y(C2(t))), b(x(C2(t)), y(C2(t))), t, 0, 1) → E2
  124. CurveCartesian(a(x(C3(t)), y(C3(t))), b(x(C3(t)), y(C3(t))), t, 0, 1) → E3
  125. CurveCartesian(a(x(C4(t)), y(C4(t))), b(x(C4(t)), y(C4(t))), t, 0, 1) → E4
  126. CurveCartesian(a(x(C5(t)), y(C5(t))), b(x(C5(t)), y(C5(t))), t, 0, 1) → E5
  127. CurveCartesian(a(x(C6(t)), y(C6(t))), b(x(C6(t)), y(C6(t))), t, 0, 1) → E6
  128. CurveCartesian(a(x(C7(t)), y(C7(t))), b(x(C7(t)), y(C7(t))), t, 0, 1) → E7
  129. CurveCartesian(a(x(C8(t)), y(C8(t))), b(x(C8(t)), y(C8(t))), t, 0, 1) → E8
  130. CurveCartesian(a(x(C9(t)), y(C9(t))), b(x(C9(t)), y(C9(t))), t, 0, 1) → E9
  131. CurveCartesian(a(x(C10(t)), y(C10(t))), b(x(C10(t)), y(C10(t))), t, 0, 1) → E10
  132. CurveCartesian(a(x(C11(t)), y(C11(t))), b(x(C11(t)), y(C11(t))), t, 0, 1) → E11
  133. CurveCartesian(a(x(C12(t)), y(C12(t))), b(x(C12(t)), y(C12(t))), t, 0, 1) → E12
  134. CurveCartesian(a(x(C13(t)), y(C13(t))), b(x(C13(t)), y(C13(t))), t, 0, 1) → E13
  135. CurveCartesian(a(x(C14(t)), y(C14(t))), b(x(C14(t)), y(C14(t))), t, 0, 1) → E14
  136. CurveCartesian(a(x(C15(t)), y(C15(t))), b(x(C15(t)), y(C15(t))), t, 0, 1) → E15
  137. CurveCartesian(a(x(C16(t)), y(C16(t))), b(x(C16(t)), y(C16(t))), t, 0, 1) → E16
  138. CurveCartesian(a(x(C17(t)), y(C17(t))), b(x(C17(t)), y(C17(t))), t, 0, 1) → E17
  139. CurveCartesian(a(x(C18(t)), y(C18(t))), b(x(C18(t)), y(C18(t))), t, 0, 1) → E18
  140. CurveCartesian(a(x(C19(t)), y(C19(t))), b(x(C19(t)), y(C19(t))), t, 0, 1) → E19
  141. CurveCartesian(a(x(C20(t)), y(C20(t))), b(x(C20(t)), y(C20(t))), t, 0, 1) → E20
  142. CurveCartesian(a(x(C21(t)), y(C21(t))), b(x(C21(t)), y(C21(t))), t, 0, 1) → E21
  143. CurveCartesian(a(x(C22(t)), y(C22(t))), b(x(C22(t)), y(C22(t))), t, 0, 1) → E22
  144. CurveCartesian(a(x(C23(t)), y(C23(t))), b(x(C23(t)), y(C23(t))), t, 0, 1) → E23
  145. CurveCartesian(a(x(C24(t)), y(C24(t))), b(x(C24(t)), y(C24(t))), t, 0, 1) → E24
  146. CurveCartesian(a(x(C25(t)), y(C25(t))), b(x(C25(t)), y(C25(t))), t, 0, 1) → E25
  147. CurveCartesian(a(x(C26(t)), y(C26(t))), b(x(C26(t)), y(C26(t))), t, 0, 1) → E26
  148. CurveCartesian(a(x(C27(t)), y(C27(t))), b(x(C27(t)), y(C27(t))), t, 0, 1) → E27
  149. CurveCartesian(a(x(C28(t)), y(C28(t))), b(x(C28(t)), y(C28(t))), t, 0, 1) → E28
  150. CurveCartesian(a(x(C29(t)), y(C29(t))), b(x(C29(t)), y(C29(t))), t, 0, 1) → E29
  151. CurveCartesian(a(x(C30(t)), y(C30(t))), b(x(C30(t)), y(C30(t))), t, 0, 1) → E30
  152. CurveCartesian(a(x(C31(t)), y(C31(t))), b(x(C31(t)), y(C31(t))), t, 0, 1) → E31
  153. CurveCartesian(a(x(C32(t)), y(C32(t))), b(x(C32(t)), y(C32(t))), t, 0, 1) → E32
  154. CurveCartesian(a(x(C33(t)), y(C33(t))), b(x(C33(t)), y(C33(t))), t, 0, 1) → E33
  155. CurveCartesian(a(x(C34(t)), y(C34(t))), b(x(C34(t)), y(C34(t))), t, 0, 1) → E34
  156. CurveCartesian(a(x(C35(t)), y(C35(t))), b(x(C35(t)), y(C35(t))), t, 0, 1) → E35
  157. CurveCartesian(a(x(C36(t)), y(C36(t))), b(x(C36(t)), y(C36(t))), t, 0, 1) → E36
  158. CurveCartesian(a(x(C37(t)), y(C37(t))), b(x(C37(t)), y(C37(t))), t, 0, 1) → E37

AI 绘图提示语参考

画一个点变换的示例，展示函数变换、向量和相似变换。首先绘制两个点，然后基于这两个点创建两个向量，接着用这两个向量生成一系列点，这些点通过线性组合形成网格。测量网格的长度，并根据输入参数a和b调整网格中每个点的位置，最终绘制出变换后的网格，并用线段连接相邻点，展示变换效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。