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Color Surfaces (f(x,y) on the Cube)

Color Surfaces (f(x,y) on the Cube)
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2020-01-07 16:13
FunctionSolid GeometryParametric EquationGraphing
In collections Color 3D surfaces
This example demonstrates how to map a bivariate function f(x,y) onto the six faces of a cube, creating colorful 3D surfaces that wrap around the solid. The core mathematical concepts include multivariable functions, parametric surfaces, spatial coordinate transformations, and surface parameterization of polyhedra in solid geometry. Construction highlights: using GeoGebra commands such as Polygon and Cube to build the cube frame, Textfield for inputting the function expression, and Surface to generate colored surfaces on each face; a slider Speed controls dynamic animation. Objects include multiple faces (faceHIML, faceIMRN, etc.) and edges (arêteIM, arêteHI), along with auxiliary points, vectors, and function objects. Suitable for high school to university students learning multivariable function visualization, 3D surface plotting, or mathematical modeling, and for teachers demonstrating intuitive representations of functions in three-dimensional space.

GeoGebra Commands & Parameters

  1. Polygon(K, I, H, J) → poly1, k_2, i_1, h, j
  2. Cube(I, H, zAxis) → ff, L, faceHLQP, faceLMRQ, faceNPQR, arêteIM, arêteHI, arêteHL, arêteLM, arêteIN, arêteMR, arêteNR, M, arêteNP, arêteHP, arêtePQ, arêteLQ, arêteQR, N, P, Q, R, faceHIML, faceIMRN, faceHINP
  3. Textfield(f) → ChampTexte1
  4. Surface(x(G) + f(t, s - k), y(G) + s, z(G) + t, s, (-Length), Length, t, (-Length), Length) → i
  5. Surface(x(B) - f(t, s - k), y(B) + s, z(B) + t, s, (-Length), Length, t, (-Length), Length) → l
  6. Surface(x(E) + t, y(E) + s, z(E) - f(t, s - k), s, (-Length), Length, t, (-Length), Length) → c
  7. Surface(x(C) + t, y(C) - f(t, s - k), z(C) + s, t, (-Length), Length, s, (-Length), Length) → e
  8. Surface(x(D) + t, y(D) + f(t, s - k), z(D) + s, t, (-Length), Length, s, (-Length), Length) → d
  9. Surface(x(F) + t, y(F) + s, z(F) - f(t, s - k), s, (-Length), Length, t, (-Length), Length) → b

AI Drawing Prompt Reference

Create a 3D cube with six faces, each mapped with a colorful parametric surface generated by a bivariate function, wrapping around the solid. The cube consists of edges and faces, with each face having a surface whose height depends on the function value, animated by a speed slider. Include an input field for editing the function, plus auxiliary points and vectors. Build the cube frame first, then generate colored surfaces on each face, and finally add dynamic control.
The prompt above was compiled from the original drawing commands and is for reference only.