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Kevin Durant Logo Geometric Construction

Kevin Durant Logo Geometric Construction
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2020-06-17 22:51
CircleVectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates how to construct the Kevin Durant Logo using 2D vectors and geometric transformations. Key math concepts include 2D vectors, circles, functions, ratios, and geometric transformations such as rotation and reflection. The construction involves GeoGebra commands like LineBisector, Line, OrthogonalLine, Vector, OrthogonalVector, Intersect, Mirror, Polygon, Rotate, Circle, and CurveCartesian. It is suitable for high school students learning the application of vectors and geometric transformations in graphic design.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Line(A, B) → s
  3. OrthogonalLine(A, s) → b
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. OrthogonalLine(F, b) → f
  7. LineBisector(A_1, A) → l
  8. Intersect(m, l) → I
  9. Mirror(f, l) → f'
  10. OrthogonalLine(D, s) → i
  11. Intersect(i, f') → E
  12. OrthogonalLine(Z, i) → h
  13. OrthogonalLine(H, i) → k
  14. OrthogonalLine(N, h) → p
  15. Intersect(p, k) → O
  16. Mirror(O, m) → O'
  17. OrthogonalLine(G, b) → t
  18. OrthogonalLine(A_1, b) → r
  19. OrthogonalLine(K, l) → j
  20. Intersect(t, j) → I_1
  21. OrthogonalLine(B, u, xOyPlane) → g
  22. Intersect(g, r) → C
  23. Mirror(f, l) → f'_1
  24. Mirror(F, l) → F'
  25. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  26. Intersect(m, f') → J
  27. Intersect(l, i) → L
  28. Intersect(m, k) → M
  29. Intersect(l, p) → P
  30. Mirror(G, l) → G'
  31. Mirror(K, l) → K'_1
  32. Mirror(G, m) → G'_1
  33. Mirror(K'_1, m) → T
  34. Mirror(G', m) → G''
  35. Mirror(O, l) → O'_1
  36. Mirror(O', l) → O''
  37. Polygon(O', O'', O'_1, O) → c1, o', o'', o'_1, o
  38. Rotate(O', (-(30°)), I) → O''_1
  39. Rotate(O'', (-(30°)), I) → O'''
  40. Rotate(O'_1, (-(30°)), I) → Q
  41. Rotate(O, (-(30°)), I) → O'_2
  42. LineBisector(A, B) → n
  43. Mirror(i, n) → i'
  44. Mirror(Z, l) → Z'
  45. Intersect(j, l) → S
  46. Intersect(i', f') → R
  47. OrthogonalLine(K', f'_1) → q
  48. Mirror(N, l) → N'
  49. LineBisector(N, R) → a
  50. Intersect(p, h) → V
  51. Circle(U, V) → c
  52. Intersect(q, h) → W
  53. Circle(U, W) → d
  54. Intersect(c, h) → B_1, C_1
  55. Intersect(c, q) → D_1, E_1
  56. Polygon(R, K', D_1, C_1) → c2, r_1, k', d_1, c_1
  57. CurveCartesian(((1 - t)^(4) * K) + (((4 * (1 - t)^(3)) * t) * I_1) + (((6 * (1 - t)^(2)) * t^(2)) * F_1) + (((4 * (1 - t)) * t^(3)) * G_1) + (t^(4) * Z'), t, 0, 1) → e
  58. Intersect(p, t) → H_1
  59. Intersect(p, k) → J_1
  60. CurveCartesian(((1 - t)^(4) * N) + (((4 * (1 - t)^(3)) * t) * H_1) + (((6 * (1 - t)^(2)) * t^(2)) * J_1) + (((4 * (1 - t)) * t^(3)) * K_1) + (t^(4) * L_1), t, 0, 1) → w
  61. Polygon(L, L_1, N, K, Z') → polígono1, l_1, f_1, n_1, k_1, z'
  62. Mirror(w, l) → w'
  63. Mirror(L, l) → L'
  64. Mirror(L_1, l) → M_1
  65. Mirror(N, l) → N'_1
  66. Mirror(K, l) → K'_2
  67. Mirror(Z', l) → Z''
  68. Polygon(L', M_1, N'_1, K'_2, Z'') → polígono1', l', m_1, n'_1, k'_2, z''
  69. Mirror(e, l) → e'

AI Drawing Prompt Reference

Draw a geometric construction of the Kevin Durant logo using 2D vectors and transformations. Start by drawing a line segment and its perpendicular bisector, then use vectors and orthogonal vectors to build key geometric elements. Apply transformations like reflection, rotation, and mirroring, combined with circles and functions, to form the logo's shape. Highlight the relationships between vectors, circles, and transformations to show the application of 2D vectors in graphic design.
The prompt above was compiled from the original drawing commands and is for reference only.