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Elliptical Regular Surface

Elliptical Regular Surface
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2017-08-07 17:57
FunctionCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of a regular surface composed of ellipses. It involves core mathematical concepts such as analytical geometry, three-dimensional geometry, ellipse equations, and surface generation. The construction utilizes GeoGebra commands/objects like Point, Plane, OrthogonalPlane, IntersectPath, CurveCartesian, and Surface. Suitable for high school students and math enthusiasts studying three-dimensional geometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Point(yAxis) → B
  2. Plane(zAxis, xAxis) → d
  3. Plane(zAxis, yAxis) → c
  4. Point(zAxis) → C
  5. OrthogonalPlane(C, zAxis) → b
  6. IntersectPath(b, d) → g
  7. Point(g) → D
  8. IntersectPath(b, c) → f
  9. Point(f) → E
  10. Point(xAxis) → A
  11. CurveCartesian((x(D) * cos(t - s)), (y(E) * sin(t - s)), z(C), t, 0, (2 * π)) → e
  12. CurveCartesian((x(A) * cos(t)), (y(B) * sin(t)), 0, t, 0, (2 * π)) → a
  13. Surface((u * x(a(t))) + ((1 - u) * x(e(t))), (u * y(a(t))) + ((1 - u) * y(e(t))), (u * z(a(t))) + ((1 - u) * z(e(t))), t, 0, (2 * π), u, 0, 1) → h

AI Drawing Prompt Reference

Draw a regular surface composed of ellipses to demonstrate core mathematical concepts. First, create two perpendicular planes in 3D space and find their intersection line. Then, determine key points on these planes and use them to generate two elliptical curves. Finally, construct the complete regular surface by linearly interpolating between these two curves.
The prompt above was compiled from the original drawing commands and is for reference only.