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Opaque Cone

Opaque Cone
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2014-05-07 21:04
FunctionCoordinate GeometrySolid GeometryParametric EquationGeometric Construction
This example demonstrates a 3D model of an opaque cone, involving core math concepts like solid geometry, coordinate geometry, parametric equations, and function graphing. It utilizes GeoGebra commands such as CurveCartesian, Point, Conic, Tangent, Intersect, Segment, Sequence, Defined, ClosestPoint, and PathParameter for construction, suitable for high school and above learning 3D shapes and geometric modeling.

GeoGebra Commands & Parameters

  1. CurveCartesian((r * cos(t)), ((r * sin(t)) * sin(v)), t, 0, 6.283185307179586) → e
  2. Point(e) → E
  3. Point(e) → D
  4. Point(e) → C
  5. Conic(B, C, D, E, A) → f
  6. Tangent(S, f) → g, i
  7. Intersect(f, i) → F
  8. Segment(A, S) → b_1
  9. Segment(B, S) → a_1
  10. Sequence(CurveCartesian[((r * (1 - i / h)) * cos(t)), (((r * (1 - i / h)) * sin(t)) * sin(v)) + (i * cos(v)), t, 0, 6.283185307179586], i, 0, h, h / m) → liste3
  11. Defined(F) → j
  12. Sequence(Segment[S, ((r * cos(i)), ((r * sin(i)) * sin(v)))], i, 0, 6.283185307179586, (2 * π / n)) → liste1
  13. ClosestPoint(e, F) → FF
  14. PathParameter(FF) → pf
  15. Intersect(f, g) → G
  16. ClosestPoint(e, G) → GG
  17. PathParameter(GG) → pg
  18. Sequence(Segment[S, Point[e, i - floor(i)]], i, pg, 1 + pf, 1 / n) → liste2
  19. CurveCartesian((r * cos(t)), ((r * sin(t)) * sin(v)), t, ang, anf) → ee
  20. CurveCartesian((r * cos(t)), ((r * sin(t)) * sin(v)), t, anf - (2 * π), ang) → eee
  21. Sequence(CurveCartesian[((r * (1 - i / h)) * cos(t)), (((r * (1 - i / h)) * sin(t)) * sin(v)) + (i * cos(v)), t, ang, anf], i, 0, h, h / m) → liste6
  22. Sequence(CurveCartesian[(((kxx * r) * (1 - i / h)) * cos(t)) + (((kyx * r) * (1 - i / h)) * sin(t)), (((kxy * r) * (1 - i / h)) * cos(t)) + (((kyy * r) * (1 - i / h)) * sin(t)) + (kzy * i), t, ang, anf], i, 0, h, h / m) → liste7

AI Drawing Prompt Reference

Draw a 3D model of an opaque cone, highlighting its geometric structure. Begin by sketching the cone's lateral surface using parametric equations, showing the tapering edges from base to apex. Then, add the base and apex of the cone, along with several generatrix lines connecting them. Finally, use curves to link the lateral surface to the base, creating a complete cone with a clear three-dimensional appearance and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.