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三维曲面绘制 - 同时绘制三个函数

三维曲面绘制 - 同时绘制三个函数
几何画板及绘图内容加载中，请稍等……
2013-11-07 03:44
向量函数立体几何
所属专题 surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
该范例展示了如何同时绘制三个三维函数的曲面。核心数学概念包括三维函数、曲面绘制和曲面层叠。使用了If, Corner, Mod, Sequence, Element, Polygon, Vector, Segment, Ray, Textfield, Point, Locus等GeoGebra命令。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. If(jg, t, x_{min} + x_{max} - t) → tj
  2. Corner(3) → Eckpunkt3
  3. Corner(2) → Eckpunkt2
  4. If(c, β, y(C - Eckpunkt2) / dEy * c_{Move}) → β1
  5. Corner(1) → Eckpunkt1
  6. If(c, α, x(C - Eckpunkt1) / dEx * c_{Move}) → α1
  7. If(Funktion ≟ 1, f1(x, y), If[Funktion ≟ 2, f2(x, y), f3(x, y)]) → f
  8. If(a ∧ bP, tj) → tt2
  9. Mod(β1, 6.283) → β2
  10. Mod(α1, 6.283) → α2
  11. If(x ≟ 0, 1, sin(x) / x) → sinc
  12. Sequence(a11 * Element[zWX1, i] + a12 * Element[zWY1, i] + a13 * Element[zWZ1, i], i, 1, 4) → zWX1'
  13. Element(zWW_0, 3) → zW_2
  14. Element(zWW_0, 4) → zW_1
  15. Element(zWW_0, 2) → zW_3
  16. Polygon(Eckpunkt1, Eck11, Eck12, (x(Eckpunkt1), y(Eck12))) → Vieleck2, eckpunkt1, eck11, eck12, a_1
  17. Sequence(Segment[Element[zl10, i], Element[zl10, i + 1]], i, 1, 7) → BoxStr
  18. Vector(Element[zl10, 4], Element[zl10, 1]) → zVectx
  19. Vector(Element[zl10, 4], Element[zl10, 3]) → zVecty
  20. Vector(Element[zl10, 4], Element[zl10, 5]) → zVectz
  21. Polygon(Eck11, Eckpunkt2, Eckpunkt3, Eck12) → Vieleck1, eck11_1, eckpunkt2, eckpunkt3, eck12_1
  22. Element(zTT, zW_1) → zY1
  23. Element(zTT, zW_2) → zY2
  24. Element(zTT, zW_3) → zY3
  25. Polygon(zTT) → zTTPoly, , , ,
  26. Element(zl10, zW_1) → zlN11
  27. Element(zl10, 9 - zW_1) → zlN111
  28. Element(zl10, zW_2) → zlN22
  29. Element(zl10, 9 - zW_2) → zlN222
  30. Element(zl10, zW_3) → zlN33
  31. Element(zWW_0, 1) → zW_4
  32. Element(zl10, zW_4) → zlN44
  33. Polygon({zlN11, zlN22, zlN222, zlN111}) → Vgrund01, , , ,
  34. Polygon(Sequence[Element[zl10, i], i, 1, 4]) → Vgrund000, , , ,
  35. Element(zl10, 7) → P_R
  36. Element(zl10, 8) → P_L
  37. Polygon({Element[zl10, 1], Element[zl10, 2], Element[zl10, 7], Element[zl10, 8]}) → Vvrd0, , , ,
  38. Segment(P_R, P_L) → StrRL
  39. Polygon(Sequence[Element[zl10, i], i, 9, 12]) → zlPoly, n, r, s, c_1
  40. Ray(B, Element[zl10, 13]) → Strx
  41. Ray(B, Element[zl10, 14]) → Stry
  42. Ray(B, Element[zl10, 15]) → Strz
  43. Textfield(x_{min}) → inputBox1
  44. Textfield(x_{max}) → inputBox4
  45. Textfield(v_{Animation}) → inputBox8
  46. Textfield(Step) → inputBox7
  47. Textfield(N) → inputBox9
  48. Textfield(t) → inputBox10
  49. Textfield(Th) → inputBox3
  50. Textfield(y_{min}) → inputBox5
  51. Textfield(z_{min}) → inputBox6
  52. Textfield(z_{max}) → inputBox11
  53. Textfield(y_{max}) → inputBox12
  54. Textfield(f1) → inputBox2
  55. Segment((x_{min}, 0), (x_{max}, 0)) → Sx
  56. Segment((0, y_{min}), (0, y_{max})) → Sy
  57. Point(Sx) → Ax
  58. Point(Sy) → Ay
  59. Locus(A', y0) → locu
  60. If(a ∧ (¬bP), tj) → tt1
  61. Locus(A', x0) → locv
  62. Textfield(f2) → Textfeld1
  63. Textfield(f3) → Textfeld2
  64. Locus(M51_{1}, Ay) → M61_{1}
  65. Locus(M52_{1}, Ay) → M62_{1}
  66. Locus(M53_{1}, Ay) → M63_{1}
  67. Locus(M51_{2}, Ay) → M61_{2}
  68. Locus(M52_{2}, Ay) → M62_{2}
  69. Locus(M53_{2}, Ay) → M63_{2}
  70. Locus(M51_{3}, Ay) → M61_{3}
  71. Locus(M52_{3}, Ay) → M62_{3}
  72. Locus(M53_{3}, Ay) → M63_{3}
  73. Locus(M51_{4}, Ay) → M61_{4}
  74. Locus(M52_{4}, Ay) → M62_{4}
  75. Locus(M53_{4}, Ay) → M63_{4}
  76. Locus(M51_{5}, Ay) → M61_{5}
  77. Locus(M52_{5}, Ay) → M62_{5}
  78. Locus(M53_{5}, Ay) → M63_{5}
  79. Locus(M51_{6}, Ay) → M61_{6}
  80. Locus(M52_{6}, Ay) → M62_{6}
  81. Locus(M53_{6}, Ay) → M63_{6}
  82. Locus(M51_{7}, Ay) → M61_{7}
  83. Locus(M52_{7}, Ay) → M62_{7}
  84. Locus(M53_{7}, Ay) → M63_{7}
  85. Locus(M51_{8}, Ay) → M61_{8}
  86. Locus(M52_{8}, Ay) → M62_{8}
  87. Locus(M53_{8}, Ay) → M63_{8}
  88. Locus(M51_{9}, Ay) → M61_{9}
  89. Locus(M52_{9}, Ay) → M62_{9}
  90. Locus(M53_{9}, Ay) → M63_{9}
  91. Locus(M51_{10}, Ay) → M61_{10}
  92. Locus(M52_{10}, Ay) → M62_{10}
  93. Locus(M53_{10}, Ay) → M63_{10}
  94. Locus(M51_{11}, Ay) → M61_{11}
  95. Locus(M52_{11}, Ay) → M62_{11}
  96. Locus(M53_{11}, Ay) → M63_{11}
  97. Locus(M51_{12}, Ay) → M61_{12}
  98. Locus(M52_{12}, Ay) → M62_{12}
  99. Locus(M53_{12}, Ay) → M63_{12}
  100. Locus(M51_{13}, Ay) → M61_{13}
  101. Locus(M52_{13}, Ay) → M62_{13}
  102. Locus(M53_{13}, Ay) → M63_{13}
  103. Locus(M51_{14}, Ay) → M61_{14}
  104. Locus(M52_{14}, Ay) → M62_{14}
  105. Locus(M53_{14}, Ay) → M63_{14}
  106. Locus(M51_{15}, Ay) → M61_{15}
  107. Locus(M52_{15}, Ay) → M62_{15}
  108. Locus(M53_{15}, Ay) → M63_{15}
  109. Locus(M51_{16}, Ay) → M61_{16}
  110. Locus(M52_{16}, Ay) → M62_{16}
  111. Locus(M53_{16}, Ay) → M63_{16}
  112. Locus(M51_{17}, Ay) → M61_{17}
  113. Locus(M52_{17}, Ay) → M62_{17}
  114. Locus(M53_{17}, Ay) → M63_{17}
  115. Locus(M51_{18}, Ay) → M61_{18}
  116. Locus(M52_{18}, Ay) → M62_{18}
  117. Locus(M53_{18}, Ay) → M63_{18}
  118. Locus(M51_{19}, Ay) → M61_{19}
  119. Locus(M52_{19}, Ay) → M62_{19}
  120. Locus(M53_{19}, Ay) → M63_{19}
  121. Locus(M51_{20}, Ay) → M61_{20}
  122. Locus(M52_{20}, Ay) → M62_{20}
  123. Locus(M53_{20}, Ay) → M63_{20}
  124. Locus(M51_{21}, Ay) → M61_{21}
  125. Locus(M52_{21}, Ay) → M62_{21}
  126. Locus(M53_{21}, Ay) → M63_{21}
  127. Locus(M51_{22}, Ay) → M61_{22}
  128. Locus(M52_{22}, Ay) → M62_{22}
  129. Locus(M53_{22}, Ay) → M63_{22}
  130. Locus(M51_{23}, Ay) → M61_{23}
  131. Locus(M52_{23}, Ay) → M62_{23}
  132. Locus(M53_{23}, Ay) → M63_{23}
  133. Locus(M51_{24}, Ay) → M61_{24}
  134. Locus(M52_{24}, Ay) → M62_{24}
  135. Locus(M53_{24}, Ay) → M63_{24}
  136. Locus(M51_{25}, Ay) → M61_{25}
  137. Locus(M52_{25}, Ay) → M62_{25}
  138. Locus(M53_{25}, Ay) → M63_{25}
  139. Locus(M51_{26}, Ay) → M61_{26}
  140. Locus(M52_{26}, Ay) → M62_{26}
  141. Locus(M53_{26}, Ay) → M63_{26}
  142. Locus(M51_{27}, Ay) → M61_{27}
  143. Locus(M52_{27}, Ay) → M62_{27}
  144. Locus(M53_{27}, Ay) → M63_{27}
  145. Locus(M51_{28}, Ay) → M61_{28}
  146. Locus(M52_{28}, Ay) → M62_{28}
  147. Locus(M53_{28}, Ay) → M63_{28}
  148. Locus(M51_{29}, Ay) → M61_{29}
  149. Locus(M52_{29}, Ay) → M62_{29}
  150. Locus(M53_{29}, Ay) → M63_{29}
  151. Locus(M51_{30}, Ay) → M61_{30}
  152. Locus(M52_{30}, Ay) → M62_{30}
  153. Locus(M53_{30}, Ay) → M63_{30}
  154. Locus(M51_{31}, Ay) → M61_{31}
  155. Locus(M52_{31}, Ay) → M62_{31}
  156. Locus(M53_{31}, Ay) → M63_{31}
  157. Locus(M51_{32}, Ay) → M61_{32}
  158. Locus(M52_{32}, Ay) → M62_{32}
  159. Locus(M53_{32}, Ay) → M63_{32}
  160. Locus(M51_{33}, Ay) → M61_{33}
  161. Locus(M52_{33}, Ay) → M62_{33}
  162. Locus(M53_{33}, Ay) → M63_{33}
  163. Locus(M51_{34}, Ay) → M61_{34}
  164. Locus(M52_{34}, Ay) → M62_{34}
  165. Locus(M53_{34}, Ay) → M63_{34}
  166. Locus(M51_{35}, Ay) → M61_{35}
  167. Locus(M52_{35}, Ay) → M62_{35}
  168. Locus(M53_{35}, Ay) → M63_{35}
  169. Locus(M51_{36}, Ay) → M61_{36}
  170. Locus(M52_{36}, Ay) → M62_{36}
  171. Locus(M53_{36}, Ay) → M63_{36}
  172. Locus(M51_{37}, Ay) → M61_{37}
  173. Locus(M52_{37}, Ay) → M62_{37}
  174. Locus(M53_{37}, Ay) → M63_{37}
  175. Locus(M51_{38}, Ay) → M61_{38}
  176. Locus(M52_{38}, Ay) → M62_{38}
  177. Locus(M53_{38}, Ay) → M63_{38}
  178. Locus(M51_{39}, Ay) → M61_{39}
  179. Locus(M52_{39}, Ay) → M62_{39}
  180. Locus(M53_{39}, Ay) → M63_{39}
  181. Locus(M51_{40}, Ay) → M61_{40}
  182. Locus(M52_{40}, Ay) → M62_{40}
  183. Locus(M53_{40}, Ay) → M63_{40}
  184. Locus(M51_{41}, Ay) → M61_{41}
  185. Locus(M52_{41}, Ay) → M62_{41}
  186. Locus(M53_{41}, Ay) → M63_{41}
  187. Locus(M51_{42}, Ay) → M61_{42}
  188. Locus(M52_{42}, Ay) → M62_{42}
  189. Locus(M53_{42}, Ay) → M63_{42}
  190. Locus(M51_{43}, Ay) → M61_{43}
  191. Locus(M52_{43}, Ay) → M62_{43}
  192. Locus(M53_{43}, Ay) → M63_{43}
  193. Locus(M51_{44}, Ay) → M61_{44}
  194. Locus(M52_{44}, Ay) → M62_{44}
  195. Locus(M53_{44}, Ay) → M63_{44}
  196. Locus(M51_{45}, Ay) → M61_{45}
  197. Locus(M52_{45}, Ay) → M62_{45}
  198. Locus(M53_{45}, Ay) → M63_{45}
  199. Locus(M51_{46}, Ay) → M61_{46}
  200. Locus(M52_{46}, Ay) → M62_{46}
  201. Locus(M53_{46}, Ay) → M63_{46}
  202. Locus(M51_{47}, Ay) → M61_{47}
  203. Locus(M52_{47}, Ay) → M62_{47}
  204. Locus(M53_{47}, Ay) → M63_{47}
  205. Locus(M51_{48}, Ay) → M61_{48}
  206. Locus(M52_{48}, Ay) → M62_{48}
  207. Locus(M53_{48}, Ay) → M63_{48}
  208. Locus(M51_{49}, Ay) → M61_{49}
  209. Locus(M52_{49}, Ay) → M62_{49}
  210. Locus(M53_{49}, Ay) → M63_{49}
  211. Locus(M51_{50}, Ay) → M61_{50}
  212. Locus(M52_{50}, Ay) → M62_{50}
  213. Locus(M53_{50}, Ay) → M63_{50}
  214. Locus(M51_{51}, Ay) → M61_{51}
  215. Locus(M52_{51}, Ay) → M62_{51}
  216. Locus(M53_{51}, Ay) → M63_{51}
  217. Locus(M51_{52}, Ay) → M61_{52}
  218. Locus(M52_{52}, Ay) → M62_{52}
  219. Locus(M53_{52}, Ay) → M63_{52}
  220. Locus(M51_{53}, Ay) → M61_{53}
  221. Locus(M52_{53}, Ay) → M62_{53}
  222. Locus(M53_{53}, Ay) → M63_{53}
  223. Locus(M51_{54}, Ay) → M61_{54}
  224. Locus(M52_{54}, Ay) → M62_{54}
  225. Locus(M53_{54}, Ay) → M63_{54}
  226. Locus(M51_{55}, Ay) → M61_{55}
  227. Locus(M52_{55}, Ay) → M62_{55}
  228. Locus(M53_{55}, Ay) → M63_{55}
  229. Locus(M51_{56}, Ay) → M61_{56}
  230. Locus(M52_{56}, Ay) → M62_{56}
  231. Locus(M53_{56}, Ay) → M63_{56}
  232. Locus(M51_{57}, Ay) → M61_{57}
  233. Locus(M52_{57}, Ay) → M62_{57}
  234. Locus(M53_{57}, Ay) → M63_{57}
  235. Locus(M51_{58}, Ay) → M61_{58}
  236. Locus(M52_{58}, Ay) → M62_{58}
  237. Locus(M53_{58}, Ay) → M63_{58}
  238. Locus(M51_{59}, Ay) → M61_{59}
  239. Locus(M52_{59}, Ay) → M62_{59}
  240. Locus(M53_{59}, Ay) → M63_{59}
  241. Locus(M51_{60}, Ay) → M61_{60}
  242. Locus(M52_{60}, Ay) → M62_{60}
  243. Locus(M53_{60}, Ay) → M63_{60}
  244. Locus(M51_{61}, Ay) → M61_{61}
  245. Locus(M52_{61}, Ay) → M62_{61}
  246. Locus(M53_{61}, Ay) → M63_{61}
  247. Locus(M51_{62}, Ay) → M61_{62}
  248. Locus(M52_{62}, Ay) → M62_{62}
  249. Locus(M53_{62}, Ay) → M63_{62}
  250. Locus(M51_{63}, Ay) → M61_{63}
  251. Locus(M52_{63}, Ay) → M62_{63}
  252. Locus(M53_{63}, Ay) → M63_{63}
  253. Locus(M51_{64}, Ay) → M61_{64}
  254. Locus(M52_{64}, Ay) → M62_{64}
  255. Locus(M53_{64}, Ay) → M63_{64}
  256. Locus(M51_{65}, Ay) → M61_{65}
  257. Locus(M52_{65}, Ay) → M62_{65}
  258. Locus(M53_{65}, Ay) → M63_{65}
  259. Locus(M51_{66}, Ay) → M61_{66}
  260. Locus(M52_{66}, Ay) → M62_{66}
  261. Locus(M53_{66}, Ay) → M63_{66}
  262. Locus(M51_{67}, Ay) → M61_{67}
  263. Locus(M52_{67}, Ay) → M62_{67}
  264. Locus(M53_{67}, Ay) → M63_{67}
  265. Locus(M51_{68}, Ay) → M61_{68}
  266. Locus(M52_{68}, Ay) → M62_{68}
  267. Locus(M53_{68}, Ay) → M63_{68}
  268. Locus(M51_{69}, Ay) → M61_{69}
  269. Locus(M52_{69}, Ay) → M62_{69}
  270. Locus(M53_{69}, Ay) → M63_{69}
  271. Locus(M51_{70}, Ay) → M61_{70}
  272. Locus(M52_{70}, Ay) → M62_{70}
  273. Locus(M53_{70}, Ay) → M63_{70}
  274. Locus(M51_{71}, Ay) → M61_{71}
  275. Locus(M52_{71}, Ay) → M62_{71}
  276. Locus(M53_{71}, Ay) → M63_{71}
  277. Locus(M51_{72}, Ay) → M61_{72}
  278. Locus(M52_{72}, Ay) → M62_{72}
  279. Locus(M53_{72}, Ay) → M63_{72}
  280. Locus(M51_{73}, Ay) → M61_{73}
  281. Locus(M52_{73}, Ay) → M62_{73}
  282. Locus(M53_{73}, Ay) → M63_{73}
  283. Locus(M51_{74}, Ay) → M61_{74}
  284. Locus(M52_{74}, Ay) → M62_{74}
  285. Locus(M53_{74}, Ay) → M63_{74}
  286. Locus(M51_{75}, Ay) → M61_{75}
  287. Locus(M52_{75}, Ay) → M62_{75}
  288. Locus(M53_{75}, Ay) → M63_{75}
  289. Locus(M51_{76}, Ay) → M61_{76}
  290. Locus(M52_{76}, Ay) → M62_{76}
  291. Locus(M53_{76}, Ay) → M63_{76}
  292. Locus(M51_{77}, Ay) → M61_{77}
  293. Locus(M52_{77}, Ay) → M62_{77}
  294. Locus(M53_{77}, Ay) → M63_{77}
  295. Locus(M51_{78}, Ay) → M61_{78}
  296. Locus(M52_{78}, Ay) → M62_{78}
  297. Locus(M53_{78}, Ay) → M63_{78}
  298. Locus(M51_{79}, Ay) → M61_{79}
  299. Locus(M52_{79}, Ay) → M62_{79}
  300. Locus(M53_{79}, Ay) → M63_{79}
  301. Locus(M51_{80}, Ay) → M61_{80}
  302. Locus(M52_{80}, Ay) → M62_{80}
  303. Locus(M53_{80}, Ay) → M63_{80}
  304. Locus(M51_{81}, Ay) → M61_{81}
  305. Locus(M52_{81}, Ay) → M62_{81}
  306. Locus(M53_{81}, Ay) → M63_{81}

AI 绘图提示语参考

绘制三个3D函数的图形，包括三个函数f1、f2和f3，通过If语句同时绘制。使用角点函数Corner定义角点，通过Mod函数对角点进行模运算。绘制一系列线段和向量，形成一个立体图形。设置输入框输入参数，控制图形的动画效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。