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Bezier Racetrack

Bezier Racetrack
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2019-11-24 01:42
CircleVectorParametric EquationGeometric Construction
This example illustrates the turning mechanism in the racing game prototype formulky, named after a Czech term meaning 'little formula cars'. It uses vectors, circles, and curves to demonstrate the motion of cars on the track. The example involves constructing geometric objects like vectors, circles, and parametric curves, suitable for high school and above students learning geometry and parametric equations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 1) → c
  3. PointIn(c) → B
  4. Circle(B, (inertia * Distance[A, B])) → d
  5. Ray(A, B) → g
  6. Intersect(d, g, 2) → C
  7. Rotate(B, α, C) → B'
  8. Ray(C, B') → l
  9. Circle(C, o) → r
  10. Intersect(r, l) → C',
  11. Circle(C', 1) → e
  12. PointIn(e) → D
  13. Circle(D, (inertia * Distance[B, D])) → k
  14. Ray(B, D) → h
  15. Intersect(k, h) → E, F
  16. Rotate(D, α, F) → D'
  17. Ray(D', F) → n
  18. Circle(F, o) → s
  19. Intersect(s, n) → F', J
  20. Circle(F', 1) → p
  21. PointIn(p) → G
  22. Ray(D, G) → i
  23. Vector(A, B) → u
  24. Vector(B, D) → v
  25. Vector(D, G) → w
  26. Center(e) → I
  27. Midpoint(C, F) → K
  28. Circle(G, (inertia * Distance[D, G])) → q
  29. Intersect(q, i) → H, L
  30. Midpoint(L, F) → M
  31. Vector(A, B) → a
  32. CurveCartesian((((1 - t) * (1 - t)) * B) + (((2 * (1 - t)) * t) * C) + ((t * t) * K), t, 0, 1) → f
  33. Vector(C, K) → b
  34. CurveCartesian((((1 - t) * (1 - t)) * K) + (((2 * t) * (1 - t)) * F) + ((t * t) * M), t, 0, 1) → f2
  35. Vector(F, M) → j
  36. Vector(C, C') → m
  37. Vector(F, F') → t
  38. Angle(D, F, F') → α_2
  39. Angle(B, C, C') → α_3

AI Drawing Prompt Reference

Draw a racetrack with a circle c and a point B inside it. Use rotation and intersection to generate a series of circles and points, forming two Bézier curves f and f2 to represent the car's movement on the track.
The prompt above was compiled from the original drawing commands and is for reference only.