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Intersection of Implicit and Explicit Surfaces by Roman Chijner (2)

Intersection of Implicit and Explicit Surfaces by Roman Chijner (2)
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2016-08-23 21:47
FunctionTrigonometrySolid Geometry
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the intersection between the implicit surface x^2*cos(x)+y^2*cos(y)+z^2*cos(z)=0 and the explicit surface z=x^2+y^2. Key mathematical concepts include implicit and explicit functions, trigonometric functions, and 3D geometry. GeoGebra commands used include If, Polygon, Textfield, Point, Zip, ImplicitCurve, and IntersectPath. Suitable for high school math education and students learning 3D geometry.

GeoGebra Commands & Parameters

  1. If(Length[RemoveUndefined[Join[Zip[Mirror[{Roots[f01(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, Sequence[x_{min} + ((x_{max} - x_{min}) / N_P * i), i, 0, N_P]]]]] ≟ 0, false, true) → lb1
  2. If(lb1, RemoveUndefined[Join[Zip[Mirror[{Roots[f01(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, Sequence[x_{min} + ((x_{max} - x_{min}) / N_P * i), i, 0, N_P]]]], Sequence[(10000, 10000), k, 1, 50]) → P1xxy
  3. If(lb1, RemoveUndefined[Join[Zip[Reverse[{Roots[f01(x, a), x_{min}, x_{max}]}] + (0, a), a, Sequence[y_{min} + ((y_{max} - y_{min}) / N_P * i), i, 0, N_P]]]], Sequence[(10000, 10000), k, 1, 50]) → P2yyx
  4. Polygon((x_{min}, y_{min}), (x_{max}, y_{min}), (x_{max}, y_{max}), (x_{min}, y_{max})) → poly1, b, c, d, e
  5. Textfield(x_{min}) → inputBox4
  6. Textfield(x_{max}) → inputBox5
  7. Textfield(y_{max}) → inputBox6
  8. Textfield(z_{max}) → inputBox7
  9. Textfield(y_{min}) → inputBox8
  10. Textfield(z_{min}) → inputBox9
  11. Textfield(N_P) → inputBox10
  12. Textfield(zoom_{3D}) → InputBox1
  13. Point(Pxy) → D
  14. Textfield(u) → InputBox4
  15. Textfield(f) → inputBox3
  16. Zip((x(a), y(a), u(x(a), y(a))), a, Join[{P1xxy, P2yyx}]) → list1
  17. ImplicitCurve(f01) → pp
  18. IntersectPath(Z_0, f(x, y, z0) + z0) → ic2z
  19. Textfield(t1) → InputBox2
  20. Textfield(t2) → InputBox3

AI Drawing Prompt Reference

Draw the intersection of an implicit surface x^2*cos(x)+y^2*cos(y)+z^2*cos(z)=0 and an explicit surface z=x^2+y^2 in 3D space. First, set the minimum and maximum values for x and y, and the value of N_P. Then, generate a series of points based on these values and use the ImplicitCurve and IntersectPath commands to draw the intersection of the two surfaces. Finally, adjust the 3D view's zoom level.
The prompt above was compiled from the original drawing commands and is for reference only.