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Boat Grid Animation

Boat Grid Animation
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2016-05-28 03:25
VectorCoordinate GeometryParametric EquationGeometric Construction
This example illustrates the application of parametric equations in geometry by dynamically showing the movement path of a boat within a grid. Key math concepts include parametric equations, vector operations, geometric transformations, and derivative applications. GeoGebra commands and objects used in construction are OrthogonalLine, Point, Rotate, CircleArc, Circle, Intersect, Angle, Ray, Vector, If, CircleSector, Sequence, Segment, Polygon. Suitable for high school and above learners to understand the practical application of parametric equations and dynamic geometric relationships.

GeoGebra Commands & Parameters

  1. OrthogonalLine(C0, xAxis) → c
  2. Point(c) → Zcenit
  3. Rotate(Zcenit, 75.00000000000001°, C0) → Zangmin
  4. CircleArc(C0, Zcenit, Zangmin) → f
  5. Point(f) → Z
  6. Circle(C0, Zcenit) → e
  7. OrthogonalLine(C0, c) → d
  8. Intersect(e, d, 2) → Zang0
  9. Angle(Z, C0, Zang0) → α
  10. Point(yAxis) → B_1
  11. Ray(B_1, B_2) → a
  12. Vector(B_1, B_2) → v
  13. Point(xAxis) → A_1
  14. Ray(A_1, A_2) → b
  15. Intersect(a, b) → C
  16. Vector(B14, C) → v4
  17. Vector(B13, C) → v3
  18. Vector(B_1, C) → v1
  19. Vector(A_1, A_2) → u
  20. Vector(A14, C) → u4
  21. Vector(A13, C) → u3
  22. If((tB3 ≤ tA3) ∧ (tA3 ≤ tB4), tA3, If[(tA3 ≤ tB3) ∧ (tB3 ≤ tA4), tB3, 1000]) → tImpacto
  23. If(t < tImpacto, B0, B_1 + (tImpacto * v)) → B
  24. Vector(B'_1, B') → uB
  25. Vector(B', B' - (0, 200)) → wB
  26. Angle(wB, uB) → βB3
  27. Rotate(B4', ((-βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B4Proa
  28. Rotate(B4', ((180° - βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B4Popa
  29. If(tB < tImpacto, B4Popa, B4Proa) → B4''
  30. If(t < tImpacto, B4', If[t - tImpacto < tGiro, B4'', If[y(B4') - y(B4''') < 200 - Ship_B / 2, B4''', B' - (0, 200 - Ship_B / 2)]]) → BB4Proa
  31. Rotate(B3', ((-βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B3Proa
  32. Rotate(B3', ((180° - βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B3Popa
  33. If(tB < tImpacto, B3Popa, B3Proa) → B3''
  34. If(t < tImpacto, B4', If[t - tImpacto < tGiro, B4'', If[y(B') - y(B4''') < 200, B4''', B' - (0, 200)]]) → BB4Popa
  35. If(t < tImpacto, B3', If[t - tImpacto < tGiro, B3'', If[y(B3') - y(B3''') < 200, B3''', B' - (0, 200)]]) → BB3Proa
  36. If(t < tImpacto, B3', If[t - tImpacto < tGiro, B3'', If[y(B') - y(B3''') < 200 - Ship_B / 2, B3''', B' - (0, 200 - Ship_B / 2)]]) → BB3Popa
  37. Rotate(B5', ((180° - βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B5Popa
  38. Rotate(B5', ((-βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B5Proa
  39. If(tB < tImpacto, B5Popa, B5Proa) → B5''
  40. If(t < tImpacto, B5', If[t - tImpacto < tGiro, B5'', If[y(B5') - y(B5''') < 200, B5''', B' - (40, 200)]]) → BB5Popa
  41. If(t < tImpacto, B5', If[t - tImpacto < tGiro, B5'', If[y(B5') - y(B5''') < 200 - Ship_B / 2, B5''', B' - (-40, 200 - Ship_B / 2)]]) → BB5Proa
  42. If(t < tImpacto, A0, A_1 + (tImpacto * u)) → A
  43. CircleSector(C0, Zcenit, Zang0) → g
  44. Sequence(Segment[((s * cos(α)), (s * sin(α)) + k), ((s * cos(α)) + 1200, (s * sin(α)) + k)], s, 0, 1200, 100) → LowerGridHorizontal
  45. Sequence(Segment[(s, k), (s + (1200 * cos(α)), (1200 * sin(α)) + k)], s, 0, 1200, 100) → LowerGridVertical
  46. Sequence(Segment[(0, s), (1200, s)], s, 100, 1200, 100) → UpperGridHorizontal
  47. Sequence(Segment[(s, 0), (s, 1200)], s, 100, 1200, 100) → UpperGridVeritical
  48. Ray(B'_1, B') → h
  49. Ray(A'_1, A') → i
  50. Segment(B'_1, C') → j
  51. Segment(A'_1, C') → l
  52. Segment(B3, B4) → m
  53. Segment(A3, A4) → n
  54. Intersect(m, n) → D
  55. Vector(A', A' - (0, 200)) → wA
  56. Vector(A_1, C) → u1
  57. Vector(A'_1, A') → uA
  58. Angle(wA, uA) → βA3
  59. If(t < tImpacto, A3', If[y(A3') - y(A3'') < 200, A3'', A3' - (0, 200)]) → AA3
  60. If(t < tImpacto, A4', If[y(A4') - y(A4'') < 200, A4'', A4' - (0, 200)]) → AA4
  61. If(t < tImpacto, A5', If[y(A5') - y(A5'') < 200, A5'', A5' - (0, 200)]) → AA5
  62. If(tB < tImpacto, BB5Popa, BB5Proa) → BB5
  63. If(tB < tImpacto, BB3Popa, BB3Proa) → BB3
  64. If(tB < tImpacto, BB4Popa, BB4Proa) → BB4
  65. Polygon(E, F, H, G) → p1, p11, p12, p13, p14
  66. Polygon(E, G, G - (0, 200), E - (0, 200)) → p2, p21, p22, p23, p24
  67. Polygon(G, H, H - (0, 200), G - (0, 200)) → p3, p33, p34, p31, p32

AI Drawing Prompt Reference

Draw an animated boat moving within a grid. Start by drawing the center point and grid lines, then create a circular arc to represent the boat's path. Define the boat's initial position and direction, and use rotations and movements to create the boat's parts. Finally, use parametric equations to dynamically show the boat's movement path within the grid, including the rotation of the bow and stern, and the boat's turning after a collision. The process includes arcs, circles, rotations, vectors, angles, and parametric equations.
The prompt above was compiled from the original drawing commands and is for reference only.