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3D Parametric Curves Explorer

3D Parametric Curves Explorer
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2018-02-14 20:22
Coordinate GeometrySolid GeometryParametric Equation
This example demonstrates parametric curves in 3D space. It involves parametric equations, coordinate geometry, and vectors. Using GeoGebra commands such as Intersect, Point, and OrthogonalLine, complex 3D curves can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → K
  3. OrthogonalLine(K, xAxis) → f
  4. Point(f) → B
  5. Point(f) → C
  6. Point(f) → D
  7. Spline(Sort[{A, E, F, B}], 3) → a
  8. Spline(Sort[{A, G, H, C}], 3) → b
  9. Spline(Sort[{A, I, J, D}], 3) → c
  10. CurveCartesian(y(a(t)), y(b(t)), y(c(t)), t, 0, 1) → d
  11. Point(d) → L
  12. Point(xAxis) → M
  13. Line(L, M) → g
  14. Point(yAxis) → N
  15. Line(L, N) → h
  16. Point(zAxis) → O
  17. Line(L, O) → i
  18. Sequence((a, 0, 0), a, -5, 5) → L_1
  19. Sequence((0, a, 0), a, -5, 5) → L_2
  20. Sequence((0, 0, a), a, -5, 5) → L_3