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Function Surface and Curve Mesh Demonstration

Function Surface and Curve Mesh Demonstration
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2013-10-16 03:37
FunctionSolid GeometryParametric Equation
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the 3D image of a function z=f(x,y) along with its corresponding curve mesh effect. The core mathematical concepts involved include functions, surfaces, parametric equations, and curve meshes. The construction utilizes GeoGebra commands such as Corner (corner points), Sequence (sequences), Join (joining), and Element (elements) to build complex surfaces and curve meshes. It is suitable for high school and above mathematics learners to understand the geometric representation of function images and the drawing of parametric curves.

GeoGebra Commands & Parameters

  1. Corner(1) → W01
  2. Corner(2) → W02
  3. Corner(4) → W04
  4. Sequence(y(C0 - yW * (j - 1)), j, 1, Ny) → my
  5. Sequence(x(C0 + xW * i), i, 0, Nx) → mx
  6. Join(Sequence[Sequence[{(Element[mx, i], Element[my, j]), (Element[mx, i + 1], Element[my, j])}, i, 1, Nx], j, 1, Ny]) → l1
  7. Element(l1, b) → z0
  8. Sequence(Text[i], i, 1, (Nx + 1) * Ny) → l2
  9. Element(l2, b) → z1
  10. Corner(3) → W03

AI Drawing Prompt Reference

Draw a 3D image of a function z=f(x,y) and add its corresponding curve mesh effect. First, determine four corner points, then generate grid lines in both x and y directions, and finally use these grid lines to draw the complex surface and curve mesh.
The prompt above was compiled from the original drawing commands and is for reference only.