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3D Curves

3D Curves
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2020-03-17 07:29
VectorCoordinate GeometryParametric Equation
This example demonstrates curves in three-dimensional space. It involves parametric equations and vector concepts. Using GeoGebra commands such as OrthogonalLine, Plane, Circle, etc., complex 3D curves can be constructed. Suitable for high school mathematics education and learning 3D geometry.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xOyPlane) → f
  2. OrthogonalLine(B, xOyPlane) → g
  3. Plane(g, f) → a
  4. Circle(C, D, E) → c
  5. IntersectPath(xOyPlane, a) → h
  6. Rotate(c, 90°, h) → c'
  7. Point(c) → F
  8. Center(c) → G
  9. Center(c') → H
  10. Point(c') → I
  11. OrthogonalLine(G, xOyPlane) → i
  12. OrthogonalLine(H, a) → j
  13. OrthogonalLine(I, a) → k
  14. OrthogonalLine(F, xOyPlane) → l
  15. OrthogonalPlane(I, l) → e
  16. Intersect(l, e) → J
  17. OrthogonalLine(J, k, space) → m
  18. Intersect(k, m) → K
  19. Midpoint(J, K) → L

AI Drawing Prompt Reference

In 3D space, draw two vertical lines from two given points down to the horizontal plane. These two lines define a vertical plane, which intersects the horizontal plane in a line. On the horizontal plane, construct a circle through three given points, then rotate this circle by 90 degrees about the intersection line to get a second circle. Pick a point on each circle and find their centers. From the first center, drop a perpendicular to the horizontal plane; from the second center, drop a perpendicular to the vertical plane; also from the point on the second circle, drop a perpendicular to the vertical plane; and from the point on the first circle, drop a perpendicular to the horizontal plane. Through this last perpendicular, construct a plane perpendicular to it, intersecting the perpendicular at a point. Through this point, draw a line in space perpendicular to another perpendicular line, meeting that line at another point. Finally, take the midpoint of these two points.
The prompt above was compiled from the original drawing commands and is for reference only.