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3D Ellipse

3D Ellipse
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2022-07-20 14:59
Coordinate GeometrySolid GeometryGeometric Construction
In collections circles, ovals, ellipses and architecture
This example demonstrates an ellipse in 3D space. Key mathematical concepts include the geometric properties of ellipses and their representation in 3D coordinate systems. Using GeoGebra commands such as Polygon, PointIn, Translate, and Rotate, a 3D ellipse can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  2. PointIn(poly3) → C
  3. Translate((0, 0, 0), Vector[B, C]) → A
  4. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  5. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  6. Rotate(D, 120°, (0, 0, 0)) → E
  7. Cone((0, 0, 0), (0, 0, 4), 2) → m, e_1, o
  8. Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
  9. PointIn(poly2) → G
  10. PointIn(poly2) → H
  11. PointIn(poly2) → I
  12. Plane(G, I, H) → n
  13. IntersectPath(n, m) → poly6
  14. OrthogonalLine(A, n) → d_1
  15. Ends(m) → g_1, g_1_1
  16. Mirror(m, T) → m'
  17. QuadricSide(m') → o'
  18. IntersectPath(n, m') → f_1
  19. Ends(m') → h_1, h_1_1

AI Drawing Prompt Reference

Draw a 3D ellipse by creating a rectangle, translating it to get a point, rotating the rectangle around this point to form the side of the ellipse, then drawing a cone and intersecting it with the rotated rectangle to get the projection of the ellipse. Finally, mirror the ellipse side and cone to achieve a more complete elliptical shape.
The prompt above was compiled from the original drawing commands and is for reference only.