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Smiley Construction

Smiley Construction
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2020-04-30 05:02
FunctionCoordinate GeometrySolid GeometryParametric EquationGeometric Construction
This example demonstrates how to construct a smiley face using elements like spheres, kites, and function graphs. It involves core mathematical concepts including solid geometry (spheres), coordinate geometry (function graphs), parametric curves, and transformations. Key GeoGebra commands and objects used in the construction are Sphere, PointIn, Circle, Point, Ray, Intersect, Mirror, and Surface. It is suitable for high school students learning about solid geometry, coordinate geometry, and parametric equations, helping them understand spatial图形 construction and transformations.

GeoGebra Commands & Parameters

  1. Sphere(O, r2 + 0.0185) → e
  2. PointIn(Sphere[(0, 0, 0), 1]) → A
  3. Circle(A, r2 / 10, Vector[O, A]) → p
  4. Point(p) → B
  5. Ray(O, B) → h
  6. Intersect(h, e) → D,
  7. Mirror(A, Plane[xAxis, zAxis]) → A'
  8. Surface(((cos(u) * cos(v)) * f(v, u)), ((sin(u) * cos(v)) * f(v, u)), (sin(v) * f(v, u)), u, -3.14159, 3.141592653589793, v, -1.5708, 1.5708) → s
  9. Circle(A', r2 / 10, Vector[O, A']) → r
  10. Mirror(B, Plane[xAxis, zAxis]) → C
  11. Circle(A', r2 / 3.5, Vector[O, A']) → k
  12. Circle(A, r2 / 3.5, Vector[O, A]) → d
  13. Circle(C, r2 / 6, Vector[O, C]) → c_1
  14. Circle(B, r2 / 6, Vector[O, B]) → d_1
  15. Ray(O, C) → i
  16. Intersect(i, e) → E,
  17. Circle(E, r2 / 5.5, Vector[O, E]) → t
  18. Circle(D, r2 / 5.5, Vector[O, D]) → q
  19. Surface(((cos(u) * cos(v)) * f(v, u)), ((sin(u) * cos(v)) * f(v, u)), (sin(v) * f(v, u)), u, -0.65, 0.65, v, -0.5708, (b2 - 1) / 15) → j

AI Drawing Prompt Reference

Draw a smiley face with two large circular eyes, a small circular nose, a large circular mouth, and a small circular smile. Start by drawing two large circles for the eyes, then a small circle for the nose. Next, draw a large circular arc for the mouth and a small circle for the smile. Finally, use a sphere as the background and adjust the positions and sizes of each part through mirroring and transformations.
The prompt above was compiled from the original drawing commands and is for reference only.