Parametric Surfaces by Kyle Havens
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This example demonstrates the generation of parametric surfaces, which are defined by two parameter variables in a three-dimensional space. The Surface command is used in the construction. Suitable for high school and above students to learn about three-dimensional geometry and parametric equations.
GeoGebra Commands & Parameters
Surface((((1 - u) * (3 + cos(v))) * cos(((4 * π) * u))), (((1 - u) * (3 + cos(v))) * sin(((4 * π) * u))), (3 * u) + ((1 - u) * sin(v)), u, -2, 2, v, -2, 2) → a
AI Drawing Prompt Reference
Create a parametric surface using parameters u and v. The surface is defined by these expressions: x = (1 - u) * (3 + cos(v)) * cos(4πu), y = (1 - u) * (3 + cos(v)) * sin(4πu), z = 3u + (1 - u) * sin(v). The range for both u and v is from -2 to 2.
The prompt above was compiled from the original drawing commands and is for reference only.