MathPlotAI Logo MathPlotAI

Bezier Surface Construction Example

Bezier Surface Construction Example
Loading the math board and drawing, please wait…
2014-10-21 06:29
Solid GeometryTransformationGeometric Construction
In collections intersection: surface-surface, curve-curve
This example demonstrates constructing a solid using Bezier surfaces of degree 2. Key mathematical concepts include Bezier surfaces, plane intersections, and geometric transformations. Construction involves GeoGebra commands such as Cube, Line, Intersect, Plane, OrthogonalLine, Point, Bezier2, and IntersectPath. Suitable for high school students or college freshmen learning solid geometry and parametric curve drawing.

GeoGebra Commands & Parameters

  1. Cube(A, B, xOyPlane) → a, C, powierzchniaBCGF, powierzchniaCDHG, powierzchniaEFGH, krawędźAD, krawędźAB, krawędźBC, krawędźCD, krawędźAE, krawędźDH, krawędźEH, D, krawędźEF, krawędźBF, krawędźFG, krawędźCG, krawędźGH, E, F, G, H, powierzchniaABCD, powierzchniaADHE, powierzchniaABFE
  2. Line(A, G) → b
  3. Line(E, C) → c
  4. Line(F, D) → d
  5. Line(H, B) → e
  6. Intersect(c, xOyPlane) → I
  7. Plane(F, E, I) → f
  8. Intersect(d, c) → J
  9. Plane(H, G, J) → g
  10. Plane(H, E, J) → h
  11. Plane(F, J, G) → i
  12. OrthogonalLine(J, f) → j
  13. OrthogonalLine(J, g) → k
  14. OrthogonalLine(J, i) → l
  15. OrthogonalLine(J, krawędźFG, space) → m
  16. Point(d) → K
  17. Point(k) → L
  18. Point(c) → M
  19. Point(m) → N
  20. Point(l) → O
  21. Point(b) → P
  22. Point(j) → Q
  23. Point(e) → R
  24. OrthogonalLine(J, g) → n
  25. OrthogonalLine(J, xOyPlane) → p
  26. Point(p) → S
  27. PłatProstokątnyBezier2(K, L, M, N, S, O, P, Q, R) → q, r, g_1, h_1, o, s, t, a_1, b_1, c_1, d_1, e_1, f_1
  28. IntersectPath(i, h) → i_1
  29. OrthogonalLine(J, krawędźCG, space) → j_1
  30. OrthogonalLine(J, krawędźDH, space) → k_1
  31. Point(j_1) → T
  32. Point(i_1) → U
  33. Point(k_1) → V
  34. Point(c) → W
  35. Point(k) → Z
  36. Point(d) → A_1
  37. PłatProstokątnyBezier2(P, Q, R, T, U, V, W, Z, A_1) → l_1, m_1, c_2, d_2, u, n_1, p_1, q_1, r_1, s_1, t_1, a_2, b_2
  38. IntersectPath(f, g) → e_2
  39. Point(e_2) → B_1
  40. Point(j_1) → C_1
  41. Point(m) → D_1
  42. Point(b) → E_1
  43. PłatProstokątnyBezier2(R, O, M, V, B_1, C_1, A_1, D_1, E_1) → f_2, g_2, q_2, r_2, v, h_2, i_2, j_2, k_2, l_2, m_2, n_2, p_2
  44. Point(i_1) → F_1
  45. Point(k_1) → G_1
  46. Point(j) → H_1
  47. Point(e) → I_1
  48. PłatProstokątnyBezier2(M, L, K, C_1, F_1, G_1, E_1, H_1, I_1) → s_2, t_2, i_3, j_3, w, a_3, b_3, c_3, d_3, e_3, f_3, g_3, h_3
  49. Point(l) → J_1
  50. Point(e_2) → K_1
  51. PłatProstokątnyBezier2(K, N, P, G_1, K_1, T, I_1, J_1, W) → k_3, l_3, b_4, c_4, o_1, m_3, n_3, p_3, q_3, r_3, s_3, t_3, a_4
  52. Point(p) → L_1
  53. PłatProstokątnyBezier2(W, Z, A_1, J_1, L_1, D_1, I_1, H_1, E_1) → d_4, e_4, n_4, p_4, u_1, f_4, g_4, h_4, i_4, j_4, k_4, l_4, m_4

AI Drawing Prompt Reference

This graphic is a complex solid constructed using Bezier surfaces. It begins with a cube, defines several line segments and planes, and computes their intersections to obtain points. Then, perpendicular lines are constructed from these points, and more points are obtained by intersecting these lines with planes. Finally, a Bezier surface construction function is used to combine these points into multiple surface patches, which together form a continuous surface structure. The surface patches may join to create an overall solid, demonstrating the application of Bezier surfaces in geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.