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3D Surface Figure Construction: Points, Polygons, and Curves

3D Surface Figure Construction: Points, Polygons, and Curves
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2015-07-30 10:57
PolygonCoordinate GeometrySolid GeometryGraphing
This example demonstrates the generation and visualization of surface figures in 3D space. It involves core mathematical concepts such as solid geometry, parametric equations, and surface equations. The construction utilizes GeoGebra commands including Point, Polygon, Intersect, CurveCartesian, and Surface, combined with objects like p, A, and poly1. Suitable for high school or university math courses to intuitively understand spatial surface properties and transformations.

GeoGebra Commands & Parameters

  1. Point(Segment[(1, 0), (5, 0)]) → A
  2. Polygon(A, (x(A), p(x(A))), (x(A), p(x(A)), p(x(A))), (x(A), 0, p(x(A)))) → poly1, a, b, c, d
  3. Intersect(d, c) → B
  4. Intersect(c, b) → C
  5. CurveCartesian(t, 0, p(t), t, 1, 5) → e
  6. Intersect(p, a, (1.157425943792635, 0.6049208473915384)) → D
  7. CurveCartesian(t, p(t), p(t), t, 1, 5) → f
  8. Surface((u * t) + ((1 - u) * t), (u * 0) + ((1 - u) * p(t)), (u * p(t)) + ((1 - u) * p(t)), t, 1, 5, u, 0, 1) → g
  9. Surface((u * t) + ((1 - u) * t), (u * p(t)) + ((1 - u) * p(t)), (0 * t) + ((1 - u) * p(t)), t, 1, 5, u, 0, 1) → h
  10. Surface((t * u) + ((1 - u) * t), ((1 - u) * p(t)), 0, t, 1, 5, u, 0, 1) → i
  11. Surface(t, 0, (u * p(t)), t, 1, 5, u, 0, 1) → j