How 3D Graph Sampling Density Works
Sampling density is how many points per axis build the surface: more looks smoother but takes more browser work. It is fixed per page and shown in the status pill; narrow the x and y range for finer detail.
Use the interactive graph first, then connect the visual shape to the written rule.
Classroom check
Q: Why does the calculator cap sampling density?
A: Very high sampling can slow low-power devices without improving the lesson, so shared links are limited to 120 samples per axis.
Try it yourself
Use the interactive calculator below to experiment with this concept.
Related guides
Graph z=f(x,y)
Type a formula, choose x and y ranges, then rotate the result to inspect slices.
Saddle vs Minimum
A saddle curves up in one direction and down in another, unlike a true minimum.
Surface and Contours
Contours are horizontal slices of the 3D graph projected into 2D.
Teacher Setup
Use a locked view and teacher mode, which hides the answer until you reveal it, for classroom embeds.