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CAD with GeoGebra for STEM - Design a Glass (Solid of Revolution)

CAD with GeoGebra for STEM - Design a Glass (Solid of Revolution)
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2013-11-29 18:11
Coordinate GeometrySolid GeometryTransformationGeometric ConstructionLocus
This GeoGebra applet demonstrates a CAD-style workflow for designing a glass by defining six free points that determine the profile of a solid of revolution about the y-axis. It integrates the Graphic, Algebra, and Spreadsheet views to support parametric modeling. Core mathematical concepts include solids of revolution, symmetry, coordinate geometry, and geometric transformations. The construction uses commands such as Point, Intersect, Line, Mirror, Sort, Element, Locus, Rotate, Segment, Dilate, Ellipse, OrthogonalLine, and Midpoint to build the profile, mirror it, generate the locus, and rotate it into a 3D surface. This example is ideal for high school to early college STEM courses, helping students connect algebra, geometry, and engineering design while developing spatial reasoning and parametric thinking skills.

GeoGebra Commands & Parameters

  1. Point(xAxis) → F
  2. Intersect(xAxis, yAxis) → G
  3. Line(H, G) → a
  4. Mirror(A, a) → A'
  5. Mirror(B, a) → B'
  6. Mirror(C, a) → C'
  7. Mirror(D, a) → D'
  8. Mirror(E, a) → E'
  9. Mirror(F, a) → F'
  10. Sort(prof) → prof2
  11. Element(s, 1, 1) → I3
  12. Element(s, 2, 1) → I4
  13. Element(s, 3, 1) → I5
  14. Element(s, 4, 1) → I6
  15. Mirror(O, a) → O'
  16. Locus(O', t) → loc1
  17. Mirror(O', yAxis) → O''
  18. Locus(O'', t) → loc2
  19. Mirror(L, a) → L'
  20. Mirror(L', yAxis) → L''
  21. Locus(L', t) → loc3
  22. Locus(L'', t) → loc4
  23. Mirror(K, a) → K'
  24. Mirror(K', yAxis) → K''
  25. Locus(K', t) → loc5
  26. Locus(K'', t) → loc6
  27. Mirror(J, a) → J'
  28. Mirror(J', yAxis) → J''
  29. Mirror(I, a) → I'
  30. Mirror(I', yAxis) → I''
  31. Locus(J', t) → loc7
  32. Locus(I', t) → loc8
  33. Locus(J'', t) → loc9
  34. Locus(I'', t) → loc10
  35. Rotate(F, 270*°, G) → F'_1
  36. Segment(G, F'_1) → aa
  37. Point(aa) → P
  38. Segment(G, F) → c
  39. Segment(G, P) → bb
  40. Dilate(F, ee, G) → F'_2
  41. Mirror(F'_2, G) → Q
  42. Ellipse(Q, F'_2, F) → d
  43. Point(xAxis) → R
  44. OrthogonalLine(R, xAxis) → b
  45. Intersect(d, b, 1) → S
  46. Locus(S, R) → loc11
  47. Mirror(E, yAxis) → E'_1
  48. Mirror(D, yAxis) → D'_1
  49. Mirror(C, yAxis) → C'_1
  50. Mirror(B, yAxis) → B'_1
  51. Mirror(A, yAxis) → A'_1
  52. Midpoint(E'_1, E) → T
  53. Midpoint(D'_1, D) → U
  54. Midpoint(C'_1, C) → V
  55. Midpoint(B'_1, B) → W
  56. Midpoint(A'_1, A) → Z
  57. Dilate(E, ee, T) → E'_2
  58. Dilate(D, ee, U) → D'_2
  59. Dilate(C, ee, V) → C'_2
  60. Dilate(B, ee, W) → B'_2
  61. Dilate(A, ee, Z) → A'_2
  62. Mirror(A'_2, Z) → A_1
  63. Mirror(B'_2, W) → B_1
  64. Mirror(C'_2, V) → C_1
  65. Mirror(E'_2, T) → D_1
  66. Ellipse(D_1, E'_2, E) → e
  67. Ellipse(C_1, C'_2, C) → f
  68. Ellipse(B_1, B'_2, B) → g
  69. Ellipse(A_1, A'_2, A) → h
  70. Mirror(D'_2, U) → E_1
  71. Ellipse(E_1, D'_2, D) → k
  72. Segment(A'_1, A) → i
  73. Segment(B'_1, B) → j
  74. Segment(C'_1, C) → l
  75. Segment(D'_1, D) → m
  76. Segment(E'_1, E) → n
  77. Point(i) → F_1
  78. Point(j) → G_1
  79. Point(l) → H_1
  80. Point(m) → I_1
  81. Point(n) → J_1
  82. OrthogonalLine(F_1, i) → p
  83. Intersect(h, p, 1) → K_1
  84. Locus(K_1, F_1) → loc12
  85. OrthogonalLine(G_1, j) → q
  86. Intersect(g, q, 1) → L_1
  87. Locus(L_1, G_1) → loc13
  88. OrthogonalLine(J_1, n) → r
  89. Intersect(e, r, 1) → M_1
  90. Locus(M_1, J_1) → loc14
  91. OrthogonalLine(H_1, l) → a_1
  92. OrthogonalLine(I_1, m) → b_1
  93. Intersect(f, a_1, 1) → N_1
  94. Intersect(k, b_1, 1) → O_1
  95. Locus(N_1, H_1) → loc15
  96. Locus(O_1, I_1) → loc16

AI Drawing Prompt Reference

Draw a 3D glass formed by revolving a profile around the y-axis. Start with six free points on the coordinate plane defining one side of the glass profile. Mirror these points across a slanted line through the origin to create the symmetric other side. Connect all points in order to form a smooth outline. Revolve this outline around the y-axis to generate the solid surface. Add an elliptical base at the bottom, and use a vertical line perpendicular to the x-axis to intersect the ellipse, marking the base edge. Finally, mirror key profile points across the y-axis to ensure full symmetry, completing the glass shape.
The prompt above was compiled from the original drawing commands and is for reference only.