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Circular Paraboloid of Revolution 3D Augmented Reality Template

Circular Paraboloid of Revolution 3D Augmented Reality Template
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2019-05-03 21:08
Coordinate GeometrySolid GeometryGeometric Construction
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources
This example demonstrates the visualization of a rotated paraboloid in 3D space, involving concepts like conic sections, rotational geometry, and spatial transformations. Construction uses GeoGebra commands such as OrthogonalLine, Plane, IntersectPath, Dilate, and Rotate to build the paraboloid model dynamically. Suitable for high school students or college freshmen learning coordinate geometry and solid geometry, also useful for mathematical modeling education.

GeoGebra Commands & Parameters

  1. OrthogonalLine(P, c) → f
  2. Segment(F, P) → g
  3. Intersect(f, c) → C
  4. Segment(P, C) → h
  5. Dilate(F, If[0 < Animate ≤ 1, 1 - Animate, 0], P) → B'
  6. Segment(F, B') → j
  7. Dilate(P, If[1 < Animate ≤ 2, 2 - Animate, 0], C) → A'
  8. Segment(P, A') → k
  9. Plane(P, C, F) → l
  10. IntersectPath(l, c) → m
  11. Point(m) → D
  12. Angle(P, C, D) → α
  13. Angle(F, P, C) → β
  14. Rotate(F, If[2 < Animate ≤ 3, ((-(Animate - 2)) * β), (-β)], P, l) → B'_1
  15. Rotate(B', If[2 < Animate ≤ 3, ((-(Animate - 2)) * β), (-β)], P, l) → B''
  16. Segment(B'_1, B'') → j'
  17. IntersectPath(l, b) → p

AI Drawing Prompt Reference

Draw a 3D model of a rotated paraboloid. The model should include a paraboloid, a rotation axis, and related spatial transformations. The construction order starts with the paraboloid, then rotates it around the axis, and finally shows the rotated shape.
The prompt above was compiled from the original drawing commands and is for reference only.