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3D Surface Plot - Plotting Three Functions Simultaneously

3D Surface Plot - Plotting Three Functions Simultaneously
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2013-11-07 03:44
VectorFunctionSolid Geometry
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates how to plot three 3D functions simultaneously. Key mathematical concepts include 3D functions, surface plotting, and surface layering. It uses commands such as If, Corner, Mod, Sequence, Element, Polygon, Vector, Segment, Ray, Textfield, Point, and Locus in GeoGebra. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Plot three 3D functions f1, f2, and f3 simultaneously using If statements. Define corner points with the Corner function and apply Mod to them. Draw a series of segments and vectors to form a 3D shape. Set input fields to control the animation of the plot.
The prompt above was compiled from the original drawing commands and is for reference only.