Function 3D Lab
Visualize a mathematical surface with an interactive three-dimensional graph.
Explore the lab
What you can explore
- Surface shape
Choose a preset or enter z=f(x,y) to compare bowls, saddles and oscillating surfaces.
- Domain and sampling
Change x/y bounds and sampling resolution to inspect a different region or surface detail.
- Spatial interpretation
Orbit the camera and toggle solid, wireframe or height coloring to connect z values with geometry.
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The model
Formula and underlying model
z = f(x,y); saddle example: z = x² − y²- x, y
- Independent coordinates in the chosen domain (abstract coordinate units)
- z
- Surface height (abstract coordinate units)
- f
- Preset or custom surface expression (depends on expression)
The surface and extrema are sampled estimates. Undefined expression values produce gaps; changing resolution changes the sampling detail.
The experiment
How it works
Choose a surface
Select a preset or use a custom expression with x and y.
Sample a domain
Set coordinate bounds and resolution to generate the mesh.
Inspect height
Rotate the view and compare surface shape with reported sampled values.
Learning outcomes
What you’ll learn
- Interpret a surface as a function of two inputs.
- Recognize a saddle from its cross-sections.
- Explain the effect of domain and resolution on a sampled mesh.
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Explore lab →Ready to experiment?
Explore Function 3D interactively
Open the lab, adjust the parameters, and see the results change in real time.