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Triaxial Tear Drop Curve

Triaxial Tear Drop Curve
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2023-03-15 20:42
AngleFunctionCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the construction of a triaxial tear drop curve. It involves concepts of ellipses and angles. Using GeoGebra commands such as Segment, Point, Ellipse, and Intersect, the triaxial tear drop curve can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(Q3, Q4) → p2
  2. Point(p2) → P3
  3. Segment(P3, Q4) → p4
  4. Point(p4) → P4
  5. Segment(Q1, Q2) → p1
  6. Point(p1) → P1
  7. Segment(P1, Q2) → p3
  8. Point(p3) → P2
  9. OrthogonalLine(C, yAxis) → zz1
  10. Circle(C, 0.62) → zz0
  11. Intersect(zz0, zz1, 1) → ZZ1
  12. Intersect(zz0, zz1, 2) → ZZ2
  13. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  14. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  15. Point(zElipse1) → XY
  16. Angle(ZZ6, C, XY) → zAngRot
  17. OrthogonalLine(C, xAxis) → zz2
  18. Intersect(zz0, zz2, 2) → ZZ3
  19. Intersect(zz0, zz2, 1) → ZZ4
  20. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  21. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  22. Point(zElipse2) → Z
  23. Angle(ZZ8, C, Z) → zAngInc
  24. Segment(Q5, Q6) → p5
  25. Point(p5) → P5
  26. Segment(ZZ5, ZZ6) → zz4
  27. Segment(ZZ7, ZZ8) → zz3
  28. Intersect(zElipse2, zElipse1, 1) → zPunto1
  29. Intersect(zElipse2, zElipse1, 4) → zPunto2
  30. Segment(zPunto1, zPunto2) → zSeg2
  31. CurveCartesian(((2 * r) * (((((1 - cos(α)) * cos(α + (2 * 3.14159 / 3))) * cos(v + (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) + ((((1 - cos(α)) * cos(α + (2 * 3.14159 / 3))) * cos(v - (2 * 3.14159 / 3)) / 2) * cos(zAngRot)))), ((2 * r) * ((((((-(1 - cos(α))) * cos(α + (2 * 3.14159 / 3))) * cos(v + (2 * 3.14159 / 3)) / 2) * cos(zAngRot)) * sin(zAngInc)) + (((((1 - cos(α)) * cos(α + (2 * 3.14159 / 3))) * cos(v - (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) * sin(zAngInc)) + (cos(α - (2 * 3.14159 / 3)) * cos(zAngInc)))) - 3, v, v1, v2) → curva2
  32. CurveCartesian(((2 * r) * (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(3.14159 + (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) + ((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(3.14159 - (2 * 3.14159 / 3)) / 2) * cos(zAngRot)))), ((2 * r) * ((((((-(1 - cos(u))) * cos(u + (2 * 3.14159 / 3))) * cos(3.14159 + (2 * 3.14159 / 3)) / 2) * cos(zAngRot)) * sin(zAngInc)) + (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(3.14159 - (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * 3.14159 / 3)) * cos(zAngInc)))) - 3, u, u1, u2) → curva1
  33. CurveCartesian(((2 * r) * (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(β + (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) + ((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(β - (2 * 3.14159 / 3)) / 2) * cos(zAngRot)))), ((2 * r) * ((((((-(1 - cos(u))) * cos(u + (2 * 3.14159 / 3))) * cos(β + (2 * 3.14159 / 3)) / 2) * cos(zAngRot)) * sin(zAngInc)) + (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(β - (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * 3.14159 / 3)) * cos(zAngInc)))) - 3, u, u1, u2) → a1
  34. Sequence(CurveCartesian[((2 * r) * (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(v + (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) + ((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(v - (2 * 3.14159 / 3)) / 2) * cos(zAngRot)))), ((2 * r) * ((((((-(1 - cos(u))) * cos(u + (2 * 3.14159 / 3))) * cos(v + (2 * 3.14159 / 3)) / 2) * cos(zAngRot)) * sin(zAngInc)) + (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(v - (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * 3.14159 / 3)) * cos(zAngInc)))) - 3, v, v1, v2], u, u1, u2, paso) → list2
  35. Sequence(CurveCartesian[((2 * r) * (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(v + (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) + ((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(v - (2 * 3.14159 / 3)) / 2) * cos(zAngRot)))), ((2 * r) * ((((((-(1 - cos(u))) * cos(u + (2 * 3.14159 / 3))) * cos(v + (2 * 3.14159 / 3)) / 2) * cos(zAngRot)) * sin(zAngInc)) + (((((1 - cos(u)) * cos(u + (2 * 3.14159 / 3))) * cos(v - (2 * 3.14159 / 3)) / 2) * sin(zAngRot)) * sin(zAngInc)) + (cos(u - (2 * 3.14159 / 3)) * cos(zAngInc)))) - 3, u, u1, u2], v, v1, v2, paso) → list1

AI Drawing Prompt Reference

Draw a triaxial tear drop curve. The figure includes two ellipses, multiple intersection points, angles, and curves. Construction order: first draw line segments and points, then construct ellipses using circles and intersecting lines, then calculate angles between ellipses and lines, then construct another ellipse, and finally generate curves through intersection points of ellipses.
The prompt above was compiled from the original drawing commands and is for reference only.