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Parametric Surface and Geometric Construction

Parametric Surface and Geometric Construction
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2017-04-03 16:30
Coordinate GeometrySolid GeometryParametric Equation
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates how to construct a parametric surface using two functions. One function serves as the base, while the other as the height. Through the construction of curves and surfaces, it provides a clear understanding of parametric equations and solid geometry. Commands used include CurveCartesian, Intersect, Surface, Segment, and Vector. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, f(t), g(t), t, -5, 5) → a
  2. CurveCartesian(t, g(t), f(t), t, -5, 5) → b
  3. Intersect(f, g, (-0.8241323136805904, 0.679194070452523)) → A
  4. Intersect(g, f, (0.8241323126131453, 0.679194067953118)) → B
  5. Surface(t, (u * g(t)) + ((1 - u) * f(t)), f(t), t, x(A), x(B), u, 0, 1) → c
  6. Surface(t, (u * g(t)) + ((1 - u) * f(t)), 0, t, x(A), x(B), u, 0, 1) → d
  7. Surface(t, (u * g(t)) + ((1 - u) * f(t)), g(t), t, x(A), x(B), u, 0, 1) → e
  8. Surface(t, g(t), (u * f(t)), t, x(A), x(B), u, 0, 1) → i
  9. Surface(t, f(t), (u * g(t)), t, x(A), x(B), u, 0, 1) → h
  10. Surface(t, f(t), (u * f(t)), t, x(A), x(B), u, 0, 1) → j
  11. Surface(t, g(t), (u * g(t)), t, x(A), x(B), u, 0, 1) → k
  12. Segment(A', B') → l
  13. Vector(A', B') → u
  14. CurveCartesian(x(A) + (t * x(u)), y(A), f(x(A)), t, -5, 5) → m
  15. Textfield(f) → CampEntradaSortida1
  16. Textfield(g) → CampEntradaSortida2
  17. Surface(t, (u * y(A)) + ((1 - u) * g(t)), (u * f(x(A))) + ((1 - u) * f(t)), t, x(A), x(B), u, 0, 1) → n
  18. Surface(t, (u * y(A)) + ((1 - u) * f(t)), (u * f(x(A))) + ((1 - u) * g(t)), t, x(A), x(B), u, 0, 1) → o
  19. Segment(A', A) → p
  20. Segment(B', B) → q