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Dini's Surface (composed of 101*101 points)

Dini's Surface (composed of 101*101 points)
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2015-01-04 03:11
FunctionSolid GeometryTransformationParametric EquationGeometric Construction
This example demonstrates the 3D visualization of Dini's Surface constructed from 101*101 points. It involves core mathematical concepts such as surface, geometric transformations, reflection, perimeter, cone, and similarity transformation. The construction utilizes GeoGebra commands and objects like Sequence, Join, RemoveUndefined, Textfield, Max, Min, and Surface. Suitable for high school and above students to understand complex surface constructions and properties.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(u_{min} + (i * dx), v_{min} + (j * dy)), i, 0, Na], j, 0, Na) → l1a
  2. Join(l1a) → uv
  3. RemoveUndefined(X1) → X1E
  4. RemoveUndefined(Y1) → Y1E
  5. RemoveUndefined(Z1) → Z1E
  6. Textfield(X1) → inputBox1
  7. Textfield(Y1) → inputBox2
  8. Textfield(Z1) → inputBox3
  9. Max(X1E) → x1maxa
  10. Min(X1E) → x1mina
  11. Max(Y1E) → y1maxa
  12. Min(Y1E) → y1mina
  13. Max(Z1E) → z1maxa
  14. Min(Z1E) → z1mina
  15. Textfield(N) → inputBox6
  16. Surface(((5 * cos(u)) * sin(v)), ((r_Y * sin(u)) * sin(v)), (r_Z * (cos(v) + log(tan(v / 2)))) + (a * u), u, u_{min}, u_{max}, v, v_{min}, v_{max}) → h
  17. Textfield(h) → inputBox4

AI Drawing Prompt Reference

Draw Dini's surface using 101x101 points. First, create a sequence of points, then connect them to form the surface. Adjust parameters to change the shape and size of the surface, and finally display the X, Y, and Z ranges.
The prompt above was compiled from the original drawing commands and is for reference only.