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Plotter 6 双曲抛物面

Plotter 6 双曲抛物面
几何画板及绘图内容加载中，请稍等……
2014-12-26 00:17
向量函数解析几何立体几何参数方程
①本范例演示了双曲抛物面的三维几何图形及其参数化构造；②涉及的核心数学概念包括解析几何、立体几何、参数方程以及向量运算；③作图要点提炼自构造摘要，使用了 Corner, If, Mod, Element, Sequence, Polygon, Vector, Segment, Ray, Textfield, ImplicitCurve 等GeoGebra命令和对象；④适合高中及以上学生及数学爱好者用于理解复杂空间曲面的可视化与交互式探索。

GeoGebra 命令及参数

  1. Corner(1) → Eckpunkt1
  2. Corner(2) → Eckpunkt2
  3. If(c, α, (x(C - Eckpunkt1) / dEx * c_{Move})) → α1
  4. Mod(α1, 6.283) → α2
  5. Corner(3) → Eckpunkt3
  6. If(c, β, (y(C - Eckpunkt2) / dEy * c_{Move})) → β1
  7. Mod(β1, 6.283) → β2
  8. Element(lF, Funktion) → g0
  9. Sequence((a11' * Element[zWX1, i]) + (a12 * Element[zWY1, i]) + (a13 * Element[zWZ1, i]), i, 1, 4) → zWX1'
  10. Element(zWW_0, 3) → zW_2
  11. Element(zWW_0, 4) → zW_1
  12. Element(zWW_0, 2) → zW_3
  13. Polygon(Eckpunkt1, Eck11, Eck12, (x(Eckpunkt1), y(Eck12))) → Vieleck2, eckpunkt1, eck11, eck12, a_1
  14. Sequence(Segment[Element[zl10, i], Element[zl10, i + 1]], i, 1, 7) → BoxStr
  15. Vector(Element[zl10, 4], Element[zl10, 1]) → zVectx
  16. Vector(Element[zl10, 4], Element[zl10, 3]) → zVectzy
  17. Vector(Element[zl10, 4], Element[zl10, 5]) → zVectz
  18. Polygon(Eck11, Eckpunkt2, Eckpunkt3, Eck12) → Vieleck1, eck11_1, eckpunkt2, eckpunkt3, eck12_1
  19. Element(zTT, zW_1) → zY1
  20. Element(zTT, zW_2) → zY2
  21. Element(zTT, zW_3) → zY3
  22. Polygon(zTT) → zTTPoly, , , ,
  23. Element(zl10, zW_1) → zlN11
  24. Element(zl10, 9 - zW_1) → zlN111
  25. Element(zl10, zW_2) → zlN22
  26. Element(zl10, 9 - zW_2) → zlN222
  27. Element(zl10, zW_3) → zlN33
  28. Element(zWW_0, 1) → zW_4
  29. Element(zl10, zW_4) → zlN44
  30. Polygon({zlN11, zlN22, zlN222, zlN111}) → Vgrund01, , , ,
  31. Polygon(Sequence[Element[zl10, i], i, 1, 4]) → Vgrund000, , , ,
  32. Element(zl10, 7) → P_R
  33. Element(zl10, 8) → P_L
  34. Polygon({Element[zl10, 1], Element[zl10, 2], Element[zl10, 7], Element[zl10, 8]}) → Vvrd0, , , ,
  35. Segment(P_R, P_L) → StrRL
  36. Polygon(Sequence[Element[zl10, i], i, 9, 12]) → zlPoly, , , ,
  37. Ray(B, Element[zl10, 13]) → Stry
  38. Ray(B, Element[zl10, 14]) → Strzy
  39. Ray(B, Element[zl10, 15]) → Strx
  40. Textfield(x_{min}) → inputBox1
  41. Textfield(x_{max}) → inputBox4
  42. Textfield(v_{Animation}) → inputBox8
  43. Textfield(Step) → inputBox7
  44. Textfield(N) → inputBox9
  45. If(b_2, t, cos(((2 * π) * t0))) → Rot
  46. If(b_2, ℯ^(t), sin(((8 * π) * t0))) → Grün
  47. If(b_2, ℯ^((-t)), 1 - t0^(2)) → Blau
  48. Textfield(t) → inputBox10
  49. Textfield(g00) → textfield1
  50. Textfield(Funktion) → Textfeld1
  51. ImplicitCurve(wx3(x - x(B), y - y(B), t)) → ex1
  52. Vector(B, B2) → u
  53. Segment(B1, B) → e_2
  54. Polygon(Q1, Q3, Q4, Q2) → poly1, q1, q3, q4, q2
  55. Textfield(f) → inputBox2
  56. Textfield(Th) → inputBox3
  57. Textfield(g) → inputBox5
  58. Textfield(Stepg) → inputBox6
  59. Sequence(If[i > g, ¬j, j], i, 1, N + 1) → ltrue
  60. If(j, N + 1, 0) → trueb
  61. ImplicitCurve(wx3(x - x(B), y - y(B), (-4))) → M2_{1}
  62. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.92))) → M2_{2}
  63. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.84))) → M2_{3}
  64. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.76))) → M2_{4}
  65. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.68))) → M2_{5}
  66. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.6))) → M2_{6}
  67. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.52))) → M2_{7}
  68. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.44))) → M2_{8}
  69. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.36))) → M2_{9}
  70. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.2800000000000002))) → M2_{10}
  71. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.2))) → M2_{11}
  72. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.12))) → M2_{12}
  73. ImplicitCurve(wx3(x - x(B), y - y(B), (-3.04))) → M2_{13}
  74. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.96))) → M2_{14}
  75. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.88))) → M2_{15}
  76. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.8))) → M2_{16}
  77. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.7199999999999998))) → M2_{17}
  78. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.6399999999999997))) → M2_{18}
  79. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.56))) → M2_{19}
  80. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.48))) → M2_{20}
  81. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.4))) → M2_{21}
  82. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.3200000000000003))) → M2_{22}
  83. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.24))) → M2_{23}
  84. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.16))) → M2_{24}
  85. ImplicitCurve(wx3(x - x(B), y - y(B), (-2.08))) → M2_{25}
  86. ImplicitCurve(wx3(x - x(B), y - y(B), (-2))) → M2_{26}
  87. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.92))) → M2_{27}
  88. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.8399999999999999))) → M2_{28}
  89. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.7599999999999998))) → M2_{29}
  90. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.6800000000000002))) → M2_{30}
  91. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.6))) → M2_{31}
  92. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.52))) → M2_{32}
  93. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.44))) → M2_{33}
  94. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.3599999999999999))) → M2_{34}
  95. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.2799999999999998))) → M2_{35}
  96. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.1999999999999997))) → M2_{36}
  97. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.12))) → M2_{37}
  98. ImplicitCurve(wx3(x - x(B), y - y(B), (-1.04))) → M2_{38}
  99. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.96))) → M2_{39}
  100. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.8799999999999999))) → M2_{40}
  101. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.7999999999999998))) → M2_{41}
  102. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.7199999999999998))) → M2_{42}
  103. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.6400000000000001))) → M2_{43}
  104. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.56))) → M2_{44}
  105. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.48))) → M2_{45}
  106. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.3999999999999999))) → M2_{46}
  107. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.31999999999999984))) → M2_{47}
  108. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.23999999999999977))) → M2_{48}
  109. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.16000000000000014))) → M2_{49}
  110. ImplicitCurve(wx3(x - x(B), y - y(B), (-0.08000000000000007))) → M2_{50}
  111. ImplicitCurve(wx3(x - x(B), y - y(B), 0)) → M2_{51}
  112. ImplicitCurve(wx3(x - x(B), y - y(B), 0.08000000000000007)) → M2_{52}
  113. ImplicitCurve(wx3(x - x(B), y - y(B), 0.16000000000000014)) → M2_{53}
  114. ImplicitCurve(wx3(x - x(B), y - y(B), 0.2400000000000002)) → M2_{54}
  115. ImplicitCurve(wx3(x - x(B), y - y(B), 0.3200000000000003)) → M2_{55}
  116. ImplicitCurve(wx3(x - x(B), y - y(B), 0.40000000000000036)) → M2_{56}
  117. ImplicitCurve(wx3(x - x(B), y - y(B), 0.4800000000000004)) → M2_{57}
  118. ImplicitCurve(wx3(x - x(B), y - y(B), 0.5600000000000005)) → M2_{58}
  119. ImplicitCurve(wx3(x - x(B), y - y(B), 0.6399999999999997)) → M2_{59}
  120. ImplicitCurve(wx3(x - x(B), y - y(B), 0.7199999999999998)) → M2_{60}
  121. ImplicitCurve(wx3(x - x(B), y - y(B), 0.7999999999999998)) → M2_{61}
  122. ImplicitCurve(wx3(x - x(B), y - y(B), 0.8799999999999999)) → M2_{62}
  123. ImplicitCurve(wx3(x - x(B), y - y(B), 0.96)) → M2_{63}
  124. ImplicitCurve(wx3(x - x(B), y - y(B), 1.04)) → M2_{64}
  125. ImplicitCurve(wx3(x - x(B), y - y(B), 1.12)) → M2_{65}
  126. ImplicitCurve(wx3(x - x(B), y - y(B), 1.2000000000000002)) → M2_{66}
  127. ImplicitCurve(wx3(x - x(B), y - y(B), 1.2800000000000002)) → M2_{67}
  128. ImplicitCurve(wx3(x - x(B), y - y(B), 1.3600000000000003)) → M2_{68}
  129. ImplicitCurve(wx3(x - x(B), y - y(B), 1.4400000000000004)) → M2_{69}
  130. ImplicitCurve(wx3(x - x(B), y - y(B), 1.5200000000000005)) → M2_{70}
  131. ImplicitCurve(wx3(x - x(B), y - y(B), 1.6000000000000005)) → M2_{71}
  132. ImplicitCurve(wx3(x - x(B), y - y(B), 1.6799999999999997)) → M2_{72}
  133. ImplicitCurve(wx3(x - x(B), y - y(B), 1.7599999999999998)) → M2_{73}
  134. ImplicitCurve(wx3(x - x(B), y - y(B), 1.8399999999999999)) → M2_{74}
  135. ImplicitCurve(wx3(x - x(B), y - y(B), 1.92)) → M2_{75}
  136. ImplicitCurve(wx3(x - x(B), y - y(B), 2)) → M2_{76}
  137. ImplicitCurve(wx3(x - x(B), y - y(B), 2.08)) → M2_{77}
  138. ImplicitCurve(wx3(x - x(B), y - y(B), 2.16)) → M2_{78}
  139. ImplicitCurve(wx3(x - x(B), y - y(B), 2.24)) → M2_{79}
  140. ImplicitCurve(wx3(x - x(B), y - y(B), 2.3200000000000003)) → M2_{80}
  141. ImplicitCurve(wx3(x - x(B), y - y(B), 2.4000000000000004)) → M2_{81}
  142. ImplicitCurve(wx3(x - x(B), y - y(B), 2.4800000000000004)) → M2_{82}
  143. ImplicitCurve(wx3(x - x(B), y - y(B), 2.5600000000000005)) → M2_{83}
  144. ImplicitCurve(wx3(x - x(B), y - y(B), 2.6400000000000006)) → M2_{84}
  145. ImplicitCurve(wx3(x - x(B), y - y(B), 2.7199999999999998)) → M2_{85}
  146. ImplicitCurve(wx3(x - x(B), y - y(B), 2.8)) → M2_{86}
  147. ImplicitCurve(wx3(x - x(B), y - y(B), 2.88)) → M2_{87}
  148. ImplicitCurve(wx3(x - x(B), y - y(B), 2.96)) → M2_{88}
  149. ImplicitCurve(wx3(x - x(B), y - y(B), 3.04)) → M2_{89}
  150. ImplicitCurve(wx3(x - x(B), y - y(B), 3.12)) → M2_{90}
  151. ImplicitCurve(wx3(x - x(B), y - y(B), 3.2)) → M2_{91}
  152. ImplicitCurve(wx3(x - x(B), y - y(B), 3.2800000000000002)) → M2_{92}
  153. ImplicitCurve(wx3(x - x(B), y - y(B), 3.3600000000000003)) → M2_{93}
  154. ImplicitCurve(wx3(x - x(B), y - y(B), 3.4400000000000004)) → M2_{94}
  155. ImplicitCurve(wx3(x - x(B), y - y(B), 3.5200000000000005)) → M2_{95}
  156. ImplicitCurve(wx3(x - x(B), y - y(B), 3.6000000000000005)) → M2_{96}
  157. ImplicitCurve(wx3(x - x(B), y - y(B), 3.6799999999999997)) → M2_{97}
  158. ImplicitCurve(wx3(x - x(B), y - y(B), 3.76)) → M2_{98}
  159. ImplicitCurve(wx3(x - x(B), y - y(B), 3.84)) → M2_{99}
  160. ImplicitCurve(wx3(x - x(B), y - y(B), 3.92)) → M2_{100}
  161. ImplicitCurve(wx3(x - x(B), y - y(B), 4)) → M2_{101}

AI 绘图提示语参考

绘制一个双曲抛物面，展示其三维几何形态和参数化构造。首先构建基础网格，通过点、向量、多边形和射线形成立方体框架，并利用参数化方程生成曲面。关键对象包括顶点、向量、多边形和射线，它们共同定义了曲面的结构和空间关系。整体构造顺序从基础网格开始，逐步添加曲面元素，最终呈现一个清晰的双曲抛物面。
以上提示语为根据原始绘图命令整理而来，仅供参考。