MathPlotAI Logo MathPlotAI

Surfboard or Canoe Surface

Surfboard or Canoe Surface
Loading the math board and drawing, please wait…
2019-01-11 02:05
FunctionSolid GeometryGeometric Construction
This example demonstrates the geometric construction of a surfboard or canoe surface. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Point, Dilate, Surface, etc., the surface of a surfboard or canoe can be constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Point(ff) → A_2
  2. Point(ff) → B_2
  3. Dilate(Translate[Rotate[ff, Angle[B_2, A_2, A_2 + (1, 0)], A_2], Vector[(-A_2)]], 1 / Distance[A_2, B_2], (0, 0)) → cf
  4. Point(fp) → A_1
  5. Point(fp) → B_1
  6. Dilate(Translate[Rotate[fp, Angle[B_1, A_1, A_1 + (1, 0)], A_1], Vector[(-A_1)]], 1 / Distance[A_1, B_1], (0, 0)) → cp
  7. Point(fc) → A_3
  8. Point(fc) → B_3
  9. Dilate(Translate[Rotate[fc, Angle[B_3, A_3, A_3 + (1, 0)], A_3], Vector[(-A_3)]], 1 / Distance[A_3, B_3], (0, 0)) → cc
  10. Surface((u * Longueur / 2), 0, ((Longueur * (fpp(u) + fcc(u))) * (1 - v)) + (v * 0.2) + hv, u, -1, 1, v, 0, 1) → glop
  11. Surface((u * Longueur / 2), (v * fy((u * Longueur / 2))), ((Longueur * fff(u)) * sqrt(1 - (v / Largeur)^(2))) + (Longueur * fcc(u)), u, -1, (2 * LongueurMax / Longueur), v, -1, LargeurMax / Largeur) → sf
  12. Surface((u * Longueur / 2), (v * fy((u * Longueur / 2))), (Longueur * ((fpp(u) * sqrt(1 - (v / Largeur)^(2))) + fcc(u))), u, -1, (2 * LongueurMax / Longueur), v, -1, LargeurMax / Largeur) → sp