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Water Warfare Demo: GeoGebra Surface Processing

Water Warfare Demo: GeoGebra Surface Processing
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2016-12-05 00:09
VectorTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the use of GeoGebra in handling complex 3D surface graphics. It involves core math concepts like vectors, coordinate geometry, solid geometry, and trigonometry. Key GeoGebra commands and objects used include CurveCartesian, Surface, Point, CircumcircleArc, Center, Radius, Angle, Mirror, Circle, and Segment. Suitable for high school students and educators/researchers working with 3D graphics.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, (-t^(2)) + 1, 0, t, -1, 1) → a
  2. CurveCartesian(t, 0, (-2 * t^(2)) + 2, t, -1, 1) → b
  3. Surface(t, ((1 - u) * ((-t^(2)) + 1)), (u * ((-2 * t^(2)) + 2)), t, -1, 1, u, 0, 1) → d
  4. Point(yAxis) → C
  5. CircumcircleArc(A, C, B) → c
  6. Center(c) → D
  7. Radius(c) → e
  8. Angle(B, D, (0, 0)) → α
  9. CurveCartesian(x(D) + (e * cos(t)), y(D) + (e * sin(t)), 0, t, π / 2 + α, (2 * π) + π / 2 - α) → f
  10. Point(zAxis) → E
  11. Surface(t, ((1 - f_1(u)) * ((-t^(2)) + 1)), (f_2(u) * ((-2 * t^(2)) + 2)), t, -1, 1, u, π / 2 - α, π / 2 + α) → i
  12. Mirror(F, z = 0) → F'
  13. Circle(F', e, zAxis) → p
  14. Surface(x(D) + (e * cos(t)), y(D) + (e * sin(t)), ((-u) * z(F)), t, π / 2 + α, (2 * π) + π / 2 - α, u, 0, 1) → h
  15. Surface(f_1(t), (((1 - u) * (1 - f_3(t))) * ((-f_1(t)^(2)) + 1)) + (u * f_2(t)), (((-(1 - u)) * f_3(t)) * ((-2 * f_1(t)^(2)) + 2)) + (u * z(F')), u, 0, 1, t, π / 2 - α, π / 2 + α) → m
  16. Surface(((1 - u) * cos(t)) + (u * f_1(t)), ((u * (1 - f_3(t))) * ((-f_1(t)^(2)) + 1)) + ((1 - u) * ((-cos(t)^(2)) + 1)), (((-u) * f_3(t)) * ((-2 * f_1(t)^(2)) + 2)), u, 0, 1, t, π / 2 - α, π / 2 + α) → o
  17. CurveCartesian(f_1(t), ((1 - f_3(t)) * ((-f_1(t)^(2)) + 1)), ((-f_3(t)) * ((-2 * f_1(t)^(2)) + 2)), t, π / 2 - α, π / 2 + α) → j
  18. CurveCartesian(x(F) + (e * cos(t)), y(F) + (e * sin(t)), z(F'), t, π / 2 + α, (2 * π) + π / 2 - α) → g
  19. CurveCartesian(x(F') + (e * cos(t)), y(F') + (e * sin(t)), z(F'), t, π / 2 - α, π / 2 + α) → l
  20. Mirror(b, z = 0) → b'
  21. Surface(t, ((1 - u) * ((-t^(2)) + 1)), ((-u) * ((-2 * t^(2)) + 2)), t, -1, 1, u, 0, 1) → n
  22. Segment(D, B) → q
  23. CurveCartesian(x(F) + (e * cos(t)), y(F) + (e * sin(t)), 0, t, π / 2 - α, π / 2 + α) → r

AI Drawing Prompt Reference

Create a 3D water warfare demo model: two parabolas lie in the horizontal and vertical planes, enclosing a surface region. Use this region as a base to construct a tilted cylinder with a circular arc bottom, a mirrored arc top, and a side surface connecting them. Above the cylinder, add a cone-like surface formed by rotating a parabola, smoothly joining the cylinder's side. The whole figure includes mirrored surfaces, arc boundaries, and connecting segments, showing symmetric solid geometry.
The prompt above was compiled from the original drawing commands and is for reference only.