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3D Surface Plotter with Contour Lines

3D Surface Plotter with Contour Lines
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2013-11-05 19:47
FunctionSolid GeometryCalculusGraphing
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the plotting of 3D surfaces z = f(x,y) and the animation of contour lines in three-dimensional space. Key mathematical concepts include function mapping, 3D coordinate systems, parametric surfaces, and contour mapping. The construction utilizes GeoGebra commands and objects such as If, Corner, Mod, Sequence, Element, Polygon, Vector, Segment, Ray, Textfield, Point, Locus, and LaTeX. It is suitable for high school and above students to understand the representation and dynamic changes of function graphs in 3D space.

GeoGebra Commands & Parameters

  1. If(x ≟ 0, 1, sin(x) / x) → sinc
  2. Corner(1) → Eckpunkt1
  3. Corner(2) → Eckpunkt2
  4. Corner(3) → Eckpunkt3
  5. If(c, α, x(C - Eckpunkt1) / dEx * c_{Move}) → α1
  6. If(c, β, y(C - Eckpunkt2) / dEy * c_{Move}) → β1
  7. If(jg, t, x_{min} + x_{max} - t) → tj
  8. If(a ∧ bP, tj) → tt2
  9. If(a ∧ (¬bP), tj) → tt1
  10. Mod(β1, 6.283) → β2
  11. Mod(α1, 6.283) → α2
  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. If(b, t, t0) → Rot
  49. If(b, exp(t), sin(π * t0)) → Grün
  50. If(b, ℯ^(-t), 1 - (t0 - 0.5)^(2)) → Blau
  51. Textfield(t) → inputBox10
  52. Textfield(Th) → inputBox3
  53. Textfield(y_{min}) → inputBox5
  54. Textfield(z_{min}) → inputBox6
  55. Textfield(z_{max}) → inputBox11
  56. Textfield(y_{max}) → inputBox12
  57. Segment((x_{min}, 0), (x_{max}, 0)) → Sx
  58. Segment((0, y_{min}), (0, y_{max})) → Sy
  59. Point(Sx) → Ax
  60. Point(Sy) → Ay
  61. Locus(A', y0) → locu
  62. Locus(A, y0) → locy
  63. Locus(A', x0) → locv
  64. Textfield(f) → inputBox2
  65. LaTeX(f, true, true) → Text3_1
  66. LaTeX(f, true, true) → Text12_1
  67. Locus(M5_{1}, Ay) → M6_{1}
  68. Locus(M5_{2}, Ay) → M6_{2}
  69. Locus(M5_{3}, Ay) → M6_{3}
  70. Locus(M5_{4}, Ay) → M6_{4}
  71. Locus(M5_{5}, Ay) → M6_{5}
  72. Locus(M5_{6}, Ay) → M6_{6}
  73. Locus(M5_{7}, Ay) → M6_{7}
  74. Locus(M5_{8}, Ay) → M6_{8}
  75. Locus(M5_{9}, Ay) → M6_{9}
  76. Locus(M5_{10}, Ay) → M6_{10}
  77. Locus(M5_{11}, Ay) → M6_{11}
  78. Locus(M5_{12}, Ay) → M6_{12}
  79. Locus(M5_{13}, Ay) → M6_{13}
  80. Locus(M5_{14}, Ay) → M6_{14}
  81. Locus(M5_{15}, Ay) → M6_{15}
  82. Locus(M5_{16}, Ay) → M6_{16}
  83. Locus(M5_{17}, Ay) → M6_{17}
  84. Locus(M5_{18}, Ay) → M6_{18}
  85. Locus(M5_{19}, Ay) → M6_{19}
  86. Locus(M5_{20}, Ay) → M6_{20}
  87. Locus(M5_{21}, Ay) → M6_{21}
  88. Locus(M5_{22}, Ay) → M6_{22}
  89. Locus(M5_{23}, Ay) → M6_{23}
  90. Locus(M5_{24}, Ay) → M6_{24}
  91. Locus(M5_{25}, Ay) → M6_{25}
  92. Locus(M5_{26}, Ay) → M6_{26}
  93. Locus(M5_{27}, Ay) → M6_{27}
  94. Locus(M5_{28}, Ay) → M6_{28}
  95. Locus(M5_{29}, Ay) → M6_{29}
  96. Locus(M5_{30}, Ay) → M6_{30}
  97. Locus(M5_{31}, Ay) → M6_{31}
  98. Locus(M5_{32}, Ay) → M6_{32}
  99. Locus(M5_{33}, Ay) → M6_{33}
  100. Locus(M5_{34}, Ay) → M6_{34}
  101. Locus(M5_{35}, Ay) → M6_{35}
  102. Locus(M5_{36}, Ay) → M6_{36}
  103. Locus(M5_{37}, Ay) → M6_{37}
  104. Locus(M5_{38}, Ay) → M6_{38}
  105. Locus(M5_{39}, Ay) → M6_{39}
  106. Locus(M5_{40}, Ay) → M6_{40}
  107. Locus(M5_{41}, Ay) → M6_{41}
  108. Locus(M5_{42}, Ay) → M6_{42}
  109. Locus(M5_{43}, Ay) → M6_{43}
  110. Locus(M5_{44}, Ay) → M6_{44}
  111. Locus(M5_{45}, Ay) → M6_{45}
  112. Locus(M5_{46}, Ay) → M6_{46}
  113. Locus(M5_{47}, Ay) → M6_{47}
  114. Locus(M5_{48}, Ay) → M6_{48}
  115. Locus(M5_{49}, Ay) → M6_{49}
  116. Locus(M5_{50}, Ay) → M6_{50}
  117. Locus(M5_{51}, Ay) → M6_{51}
  118. Locus(M5_{52}, Ay) → M6_{52}
  119. Locus(M5_{53}, Ay) → M6_{53}
  120. Locus(M5_{54}, Ay) → M6_{54}
  121. Locus(M5_{55}, Ay) → M6_{55}
  122. Locus(M5_{56}, Ay) → M6_{56}
  123. Locus(M5_{57}, Ay) → M6_{57}
  124. Locus(M5_{58}, Ay) → M6_{58}
  125. Locus(M5_{59}, Ay) → M6_{59}
  126. Locus(M5_{60}, Ay) → M6_{60}
  127. Locus(M5_{61}, Ay) → M6_{61}
  128. Locus(M5_{62}, Ay) → M6_{62}
  129. Locus(M5_{63}, Ay) → M6_{63}
  130. Locus(M5_{64}, Ay) → M6_{64}
  131. Locus(M5_{65}, Ay) → M6_{65}
  132. Locus(M5_{66}, Ay) → M6_{66}
  133. Locus(M5_{67}, Ay) → M6_{67}
  134. Locus(M5_{68}, Ay) → M6_{68}
  135. Locus(M5_{69}, Ay) → M6_{69}
  136. Locus(M5_{70}, Ay) → M6_{70}
  137. Locus(M5_{71}, Ay) → M6_{71}
  138. Locus(M5_{72}, Ay) → M6_{72}
  139. Locus(M5_{73}, Ay) → M6_{73}
  140. Locus(M5_{74}, Ay) → M6_{74}
  141. Locus(M5_{75}, Ay) → M6_{75}
  142. Locus(M5_{76}, Ay) → M6_{76}
  143. Locus(M5_{77}, Ay) → M6_{77}
  144. Locus(M5_{78}, Ay) → M6_{78}
  145. Locus(M5_{79}, Ay) → M6_{79}
  146. Locus(M5_{80}, Ay) → M6_{80}
  147. Locus(M5_{81}, Ay) → M6_{81}
  148. Locus(M5_{82}, Ay) → M6_{82}
  149. Locus(M5_{83}, Ay) → M6_{83}
  150. Locus(M5_{84}, Ay) → M6_{84}
  151. Locus(M5_{85}, Ay) → M6_{85}
  152. Locus(M5_{86}, Ay) → M6_{86}
  153. Locus(M5_{87}, Ay) → M6_{87}
  154. Locus(M5_{88}, Ay) → M6_{88}
  155. Locus(M5_{89}, Ay) → M6_{89}
  156. Locus(M5_{90}, Ay) → M6_{90}
  157. Locus(M5_{91}, Ay) → M6_{91}
  158. Locus(M5_{92}, Ay) → M6_{92}
  159. Locus(M5_{93}, Ay) → M6_{93}
  160. Locus(M5_{94}, Ay) → M6_{94}
  161. Locus(M5_{95}, Ay) → M6_{95}
  162. Locus(M5_{96}, Ay) → M6_{96}
  163. Locus(M5_{97}, Ay) → M6_{97}
  164. Locus(M5_{98}, Ay) → M6_{98}
  165. Locus(M5_{99}, Ay) → M6_{99}
  166. Locus(M5_{100}, Ay) → M6_{100}
  167. Locus(M5_{101}, Ay) → M6_{101}
  168. Locus(M5_{102}, Ay) → M6_{102}
  169. Locus(M5_{103}, Ay) → M6_{103}
  170. Locus(M5_{104}, Ay) → M6_{104}
  171. Locus(M5_{105}, Ay) → M6_{105}
  172. Locus(M5_{106}, Ay) → M6_{106}
  173. Locus(M5_{107}, Ay) → M6_{107}
  174. Locus(M5_{108}, Ay) → M6_{108}
  175. Locus(M5_{109}, Ay) → M6_{109}
  176. Locus(M5_{110}, Ay) → M6_{110}
  177. Locus(M5_{111}, Ay) → M6_{111}
  178. Locus(M5_{112}, Ay) → M6_{112}
  179. Locus(M5_{113}, Ay) → M6_{113}
  180. Locus(M5_{114}, Ay) → M6_{114}
  181. Locus(M5_{115}, Ay) → M6_{115}
  182. Locus(M5_{116}, Ay) → M6_{116}
  183. Locus(M5_{117}, Ay) → M6_{117}
  184. Locus(M5_{118}, Ay) → M6_{118}
  185. Locus(M5_{119}, Ay) → M6_{119}
  186. Locus(M5_{120}, Ay) → M6_{120}
  187. Locus(M5_{121}, Ay) → M6_{121}
  188. Locus(M5_{122}, Ay) → M6_{122}
  189. Locus(M5_{123}, Ay) → M6_{123}
  190. Locus(M5_{124}, Ay) → M6_{124}
  191. Locus(M5_{125}, Ay) → M6_{125}
  192. Locus(M5_{126}, Ay) → M6_{126}
  193. Locus(M5_{127}, Ay) → M6_{127}
  194. Locus(M5_{128}, Ay) → M6_{128}
  195. Locus(M5_{129}, Ay) → M6_{129}
  196. Locus(M5_{130}, Ay) → M6_{130}
  197. Locus(M5_{131}, Ay) → M6_{131}
  198. Locus(M5_{132}, Ay) → M6_{132}
  199. Locus(M5_{133}, Ay) → M6_{133}
  200. Locus(M5_{134}, Ay) → M6_{134}
  201. Locus(M5_{135}, Ay) → M6_{135}
  202. Locus(M5_{136}, Ay) → M6_{136}
  203. Locus(M5_{137}, Ay) → M6_{137}
  204. Locus(M5_{138}, Ay) → M6_{138}
  205. Locus(M5_{139}, Ay) → M6_{139}
  206. Locus(M5_{140}, Ay) → M6_{140}
  207. Locus(M5_{141}, Ay) → M6_{141}
  208. Locus(M5_{142}, Ay) → M6_{142}
  209. Locus(M5_{143}, Ay) → M6_{143}
  210. Locus(M5_{144}, Ay) → M6_{144}
  211. Locus(M5_{145}, Ay) → M6_{145}
  212. Locus(M5_{146}, Ay) → M6_{146}
  213. Locus(M5_{147}, Ay) → M6_{147}
  214. Locus(M5_{148}, Ay) → M6_{148}
  215. Locus(M5_{149}, Ay) → M6_{149}
  216. Locus(M5_{150}, Ay) → M6_{150}
  217. Locus(M5_{151}, Ay) → M6_{151}
  218. Locus(M5_{152}, Ay) → M6_{152}
  219. Locus(M5_{153}, Ay) → M6_{153}
  220. Locus(M5_{154}, Ay) → M6_{154}
  221. Locus(M5_{155}, Ay) → M6_{155}
  222. Locus(M5_{156}, Ay) → M6_{156}
  223. Locus(M5_{157}, Ay) → M6_{157}
  224. Locus(M5_{158}, Ay) → M6_{158}
  225. Locus(M5_{159}, Ay) → M6_{159}
  226. Locus(M5_{160}, Ay) → M6_{160}
  227. Locus(M5_{161}, Ay) → M6_{161}
  228. Locus(M5_{162}, Ay) → M6_{162}
  229. Locus(M5_{163}, Ay) → M6_{163}
  230. Locus(M5_{164}, Ay) → M6_{164}
  231. Locus(M5_{165}, Ay) → M6_{165}
  232. Locus(M5_{166}, Ay) → M6_{166}
  233. Locus(M5_{167}, Ay) → M6_{167}
  234. Locus(M5_{168}, Ay) → M6_{168}
  235. Locus(M5_{169}, Ay) → M6_{169}
  236. Locus(M5_{170}, Ay) → M6_{170}
  237. Locus(M5_{171}, Ay) → M6_{171}
  238. Locus(M5_{172}, Ay) → M6_{172}
  239. Locus(M5_{173}, Ay) → M6_{173}
  240. Locus(M5_{174}, Ay) → M6_{174}
  241. Locus(M5_{175}, Ay) → M6_{175}
  242. Locus(M5_{176}, Ay) → M6_{176}
  243. Locus(M5_{177}, Ay) → M6_{177}
  244. Locus(M5_{178}, Ay) → M6_{178}
  245. Locus(M5_{179}, Ay) → M6_{179}
  246. Locus(M5_{180}, Ay) → M6_{180}
  247. Locus(M5_{181}, Ay) → M6_{181}
  248. Locus(M5_{182}, Ay) → M6_{182}
  249. Locus(M5_{183}, Ay) → M6_{183}
  250. Locus(M5_{184}, Ay) → M6_{184}
  251. Locus(M5_{185}, Ay) → M6_{185}
  252. Locus(M5_{186}, Ay) → M6_{186}
  253. Locus(M5_{187}, Ay) → M6_{187}
  254. Locus(M5_{188}, Ay) → M6_{188}
  255. Locus(M5_{189}, Ay) → M6_{189}
  256. Locus(M5_{190}, Ay) → M6_{190}
  257. Locus(M5_{191}, Ay) → M6_{191}
  258. Locus(M5_{192}, Ay) → M6_{192}
  259. Locus(M5_{193}, Ay) → M6_{193}
  260. Locus(M5_{194}, Ay) → M6_{194}
  261. Locus(M5_{195}, Ay) → M6_{195}
  262. Locus(M5_{196}, Ay) → M6_{196}
  263. Locus(M5_{197}, Ay) → M6_{197}
  264. Locus(M5_{198}, Ay) → M6_{198}
  265. Locus(M5_{199}, Ay) → M6_{199}
  266. Locus(M5_{200}, Ay) → M6_{200}
  267. Locus(M5_{201}, Ay) → M6_{201}

AI Drawing Prompt Reference

Create a 3D surface plot of a function z = f(x,y) with animated contour lines. The plot features a square base and four sides forming a cube frame. A central point on the base connects three rays representing the x, y, and z axes. The contour lines dynamically change around the surface, indicating the function's gradient. Below the surface, label the range x_min to x_max and include parameters for animation speed and step size.
The prompt above was compiled from the original drawing commands and is for reference only.