“An Apple a Day...” 3D Solid Rendering in GeoGebra
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In collections
Surfaces
This example demonstrates how GeoGebra can produce a 3D, render-like visualization (fruits) by constructing and displaying a selected 3D surface. The key math/CS visualization ideas are solid/3D geometry visualization via surface construction, together with object-selection logic (choosing which surface from a set to render using an index). In the construction, it relies on the Surface command to generate the 3D surface geometry and uses SelectedIndex to select the active object from a list (e.g., parameters/objects such as a, b, ddMenu, is are used to drive which surface is targeted). It is suitable for middle school to early high school students learning 3D geometry and for GeoGebra users who want to understand how commands and object indexing work in advanced visualizations.
GeoGebra Commands & Parameters
Surface((cos(a) * (4 + (3.8 * cos(b)))), (sin(a) * (4 + (3.8 * cos(b)))), (((cos(b) + sin(b) - 1) * (1 + sin(b))) * ln(1 - (pi * b / 10))) + (7.5 * sin(b)), a, 0, 6.283185307179586, b, -3.141592653589793, 3.141592653589793) → aSurface((cos(a) * (4 + (3.8 * cos(b)))), (sin(a) * (4 + (3.8 * cos(b)))), (((((cos(b) - 3.5) * (1 + sin(b))) * ln(1 - (pi * b / 10))) + (10 * sin(b))) * (1 - ((0.4 * cos(b / 2)) * (1 + (0.2 * sin(b^(2))))))), a, 0, 6.283185307179586, b, -3.0402509550868966, 3.0402509550868966) → bSelectedIndex(ddMenu) → is
AI Drawing Prompt Reference
Create a 3D render-like closed surface that resembles a fruit. In 3D space, draw a parametric surface with x = cos(a)·(4 + 3.8·cos(b)), y = sin(a)·(4 + 3.8·cos(b)), and z given by a b-dependent combination expression. Let a vary from 0 to about 6.283185 and b vary continuously from about -3.141593 to 3.141593. Define two candidate surfaces that share the same x and y formulas but use different b-based z expressions, then select one candidate and display it as the final rendered surface.
The prompt above was compiled from the original drawing commands and is for reference only.