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Plotting Colored Parametric Surfaces with Trace Method

Plotting Colored Parametric Surfaces with Trace Method
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2015-07-20 19:11
FunctionCoordinate GeometrySolid GeometryParametric EquationGraphing
This example demonstrates how to plot colored parametric surfaces using the trace method. Key mathematical concepts include parametric equations and color mapping. The construction involves commands such as Sequence, Join, Zip, RemoveUndefined, Max, Min, Surface, CurveCartesian, Textfield, and Point. Suitable for high school and above students or teachers for teaching or research on the visualization of parametric surfaces.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(u_{min} + (i * dx), v_{min} + (j * dy)), i, 0, Na], j, 0, Na) → l1a
  2. Join(l1a) → uv
  3. Zip(fz(a, b), a, u0, b, v0) → Z1
  4. Zip(fy(a, b), a, u0, b, v0) → Y1
  5. Zip(fx(a, b), a, u0, b, v0) → X1
  6. RemoveUndefined(X1) → X1E
  7. Max(X1E) → x1maxa
  8. Min(X1E) → x1mina
  9. RemoveUndefined(Y1) → Y1E
  10. Max(Y1E) → x2maxa
  11. Min(Y1E) → x2mina
  12. RemoveUndefined(Z1) → Z1E
  13. Max(Z1E) → x3maxa
  14. Min(Z1E) → x3mina
  15. Surface((((r_X * 5) * cos(u)) * sin(v)), (((r_Y * 5) * sin(u)) * sin(v)), ((r_Z * 5) * (cos(v) + log(tan(v / 2)))) + (1.3 * u), u, u_{min}, u_{max}, v, v_{min}, v_{max}) → h
  16. CurveCartesian((fx(t, a_v) * r_X), (fy(t, a_v) * r_Y), (fz(t, a_v) * r_Z), t, u_{min}, u_{max}) → f_u
  17. CurveCartesian((fx(a_u, t) * r_X), (fy(a_u, t) * r_Y), (fz(a_u, t) * r_Z), t, v_{min}, v_{max}) → f_v
  18. Textfield(u_{min}) → inputBox4
  19. Textfield(u_{max}) → inputBox5
  20. Textfield(v_{min}) → inputBox6
  21. Textfield(v_{max}) → inputBox7
  22. Textfield(Pstyle) → Textfeld1
  23. Textfield(Nx) → Textfeld2
  24. Textfield(v_u) → Textfeld3
  25. Textfield(v_v) → Textfeld4
  26. Textfield(r_X) → inputBox8
  27. Textfield(r_Y) → inputBox9
  28. Textfield(r_Z) → inputBox10
  29. Point(f_u, 0) → Pr_{0}
  30. Point(f_u, 0.02) → Pr_{1}
  31. Point(f_u, 0.04) → Pr_{2}
  32. Point(f_u, 0.06) → Pr_{3}
  33. Point(f_u, 0.08) → Pr_{4}
  34. Point(f_u, 0.1) → Pr_{5}
  35. Point(f_u, 0.12) → Pr_{6}
  36. Point(f_u, 0.14) → Pr_{7}
  37. Point(f_u, 0.16) → Pr_{8}
  38. Point(f_u, 0.18) → Pr_{9}
  39. Point(f_u, 0.2) → Pr_{10}
  40. Point(f_u, 0.22) → Pr_{11}
  41. Point(f_u, 0.24) → Pr_{12}
  42. Point(f_u, 0.26) → Pr_{13}
  43. Point(f_u, 0.28) → Pr_{14}
  44. Point(f_u, 0.3) → Pr_{15}
  45. Point(f_u, 0.32) → Pr_{16}
  46. Point(f_u, 0.34) → Pr_{17}
  47. Point(f_u, 0.36) → Pr_{18}
  48. Point(f_u, 0.38) → Pr_{19}
  49. Point(f_u, 0.4) → Pr_{20}
  50. Point(f_u, 0.42) → Pr_{21}
  51. Point(f_u, 0.44) → Pr_{22}
  52. Point(f_u, 0.46) → Pr_{23}
  53. Point(f_u, 0.48) → Pr_{24}
  54. Point(f_u, 0.5) → Pr_{25}
  55. Point(f_u, 0.52) → Pr_{26}
  56. Point(f_u, 0.54) → Pr_{27}
  57. Point(f_u, 0.56) → Pr_{28}
  58. Point(f_u, 0.58) → Pr_{29}
  59. Point(f_u, 0.6) → Pr_{30}
  60. Point(f_u, 0.62) → Pr_{31}
  61. Point(f_u, 0.64) → Pr_{32}
  62. Point(f_u, 0.66) → Pr_{33}
  63. Point(f_u, 0.68) → Pr_{34}
  64. Point(f_u, 0.7) → Pr_{35}
  65. Point(f_u, 0.72) → Pr_{36}
  66. Point(f_u, 0.74) → Pr_{37}
  67. Point(f_u, 0.76) → Pr_{38}
  68. Point(f_u, 0.78) → Pr_{39}
  69. Point(f_u, 0.8) → Pr_{40}
  70. Point(f_u, 0.82) → Pr_{41}
  71. Point(f_u, 0.84) → Pr_{42}
  72. Point(f_u, 0.86) → Pr_{43}
  73. Point(f_u, 0.88) → Pr_{44}
  74. Point(f_u, 0.9) → Pr_{45}
  75. Point(f_u, 0.92) → Pr_{46}
  76. Point(f_u, 0.94) → Pr_{47}
  77. Point(f_u, 0.96) → Pr_{48}
  78. Point(f_u, 0.98) → Pr_{49}
  79. Point(f_u, 1) → Pr_{50}
  80. Point(f_v, 0) → Pr_{51}
  81. Point(f_v, 0.02) → Pr_{52}
  82. Point(f_v, 0.04) → Pr_{53}
  83. Point(f_v, 0.06) → Pr_{54}
  84. Point(f_v, 0.08) → Pr_{55}
  85. Point(f_v, 0.1) → Pr_{56}
  86. Point(f_v, 0.12) → Pr_{57}
  87. Point(f_v, 0.14) → Pr_{58}
  88. Point(f_v, 0.16) → Pr_{59}
  89. Point(f_v, 0.18) → Pr_{60}
  90. Point(f_v, 0.2) → Pr_{61}
  91. Point(f_v, 0.22) → Pr_{62}
  92. Point(f_v, 0.24) → Pr_{63}
  93. Point(f_v, 0.26) → Pr_{64}
  94. Point(f_v, 0.28) → Pr_{65}
  95. Point(f_v, 0.3) → Pr_{66}
  96. Point(f_v, 0.32) → Pr_{67}
  97. Point(f_v, 0.34) → Pr_{68}
  98. Point(f_v, 0.36) → Pr_{69}
  99. Point(f_v, 0.38) → Pr_{70}
  100. Point(f_v, 0.4) → Pr_{71}
  101. Point(f_v, 0.42) → Pr_{72}
  102. Point(f_v, 0.44) → Pr_{73}
  103. Point(f_v, 0.46) → Pr_{74}
  104. Point(f_v, 0.48) → Pr_{75}
  105. Point(f_v, 0.5) → Pr_{76}
  106. Point(f_v, 0.52) → Pr_{77}
  107. Point(f_v, 0.54) → Pr_{78}
  108. Point(f_v, 0.56) → Pr_{79}
  109. Point(f_v, 0.58) → Pr_{80}
  110. Point(f_v, 0.6) → Pr_{81}
  111. Point(f_v, 0.62) → Pr_{82}
  112. Point(f_v, 0.64) → Pr_{83}
  113. Point(f_v, 0.66) → Pr_{84}
  114. Point(f_v, 0.68) → Pr_{85}
  115. Point(f_v, 0.7) → Pr_{86}
  116. Point(f_v, 0.72) → Pr_{87}
  117. Point(f_v, 0.74) → Pr_{88}
  118. Point(f_v, 0.76) → Pr_{89}
  119. Point(f_v, 0.78) → Pr_{90}
  120. Point(f_v, 0.8) → Pr_{91}
  121. Point(f_v, 0.82) → Pr_{92}
  122. Point(f_v, 0.84) → Pr_{93}
  123. Point(f_v, 0.86) → Pr_{94}
  124. Point(f_v, 0.88) → Pr_{95}
  125. Point(f_v, 0.9) → Pr_{96}
  126. Point(f_v, 0.92) → Pr_{97}
  127. Point(f_v, 0.94) → Pr_{98}
  128. Point(f_v, 0.96) → Pr_{99}
  129. Point(f_v, 0.98) → Pr_{100}
  130. Point(f_v, 1) → Pr_{101}
  131. Textfield(fx) → inputBox1
  132. Textfield(fy) → inputBox2
  133. Textfield(fz) → inputBox3

AI Drawing Prompt Reference

Draw a colored parametric surface defined by x = r_X·5·cos(u)·sin(v), y = r_Y·5·sin(u)·sin(v), z = r_Z·5·(cos(v)+ln(tan(v/2)))+1.3·u. Show two families of parameter curves on the surface (constant‑v curves in u and constant‑u curves in v) and place a series of equally spaced trace points along one u‑curve. Provide interactive input fields for u_min, u_max, v_min, v_max, r_X, r_Y, and r_Z to adjust the domain and scaling.
The prompt above was compiled from the original drawing commands and is for reference only.