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Bezier Surface by h.juratovich

Bezier Surface by h.juratovich
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2017-05-14 22:21
Coordinate GeometrySolid GeometryParametric Equation
This example demonstrates the construction of a Bezier surface. Key mathematical concepts include polynomial interpolation and surface geometry. Using GeoGebra commands such as Surface, Segment, and Point, complex surface shapes can be created. Suitable for high school or university geometry and computer graphics courses.

GeoGebra Commands & Parameters

  1. Surface((((1 - u)^(3) * (1 - v)^(3)) * A) + (((((1 - u)^(3) * 3) * v) * (1 - v)^(2)) * B) + (((((1 - u)^(3) * 3) * v^(2)) * (1 - v)) * C) + (((1 - u)^(3) * v^(3)) * D) + ((((3 * u) * (1 - u)^(2)) * (1 - v)^(3)) * E) + ((((((3 * u) * (1 - u)^(2)) * 3) * v) * (1 - v)^(2)) * F) + ((((((3 * u) * (1 - u)^(2)) * 3) * v^(2)) * (1 - v)) * G) + ((((3 * u) * (1 - u)^(2)) * v^(3)) * H) + ((((3 * u^(2)) * (1 - u)) * (1 - v)^(3)) * I) + ((((((3 * u^(2)) * (1 - u)) * 3) * v) * (1 - v)^(2)) * J) + ((((((3 * u^(2)) * (1 - u)) * 3) * v^(2)) * (1 - v)) * K) + ((((3 * u^(2)) * (1 - u)) * v^(3)) * L) + ((u^(3) * (1 - v)^(3)) * M) + ((((u^(3) * 3) * v) * (1 - v)^(2)) * N) + ((((u^(3) * 3) * v^(2)) * (1 - v)) * O) + ((u^(3) * v^(3)) * P), u, 0, 1, v, 0, 1) → a
  2. Segment(A, B) → f
  3. Segment(D, C) → g
  4. Segment(C, B) → h
  5. Segment(D, H) → i
  6. Segment(H, L) → j
  7. Segment(A, E) → k
  8. Segment(E, I) → l
  9. Segment(I, M) → m
  10. Segment(M, N) → n
  11. Segment(N, O) → p
  12. Segment(O, P) → q
  13. Segment(E, F) → r
  14. Segment(F, G) → s
  15. Segment(G, H) → t
  16. Segment(I, J) → b
  17. Segment(J, K) → c
  18. Segment(K, L) → d
  19. Segment(B, F) → e
  20. Segment(F, J) → f_1
  21. Point(n) → Q
  22. Segment(J, N) → g_1
  23. Segment(C, G) → h_1
  24. Segment(G, K) → i_1
  25. Segment(K, O) → j_1
  26. Segment(L, P) → k_1