Guides

3D graphing guides

Eleven written guides to the parts of a surface graph that are easy to misread: the domain, the contour map, the cross-section, the sampling grid, and the difference between an equation you can paste and a picture you can rotate. Every guide opens with a live calculator pointed at the surface it explains.

Start with the basics

The four guides that answer the questions people arrive with.

How to Graph z=f(x,y) Online

z = x^2 - y^2

Type a formula, choose x and y ranges, then rotate the result to inspect slices.

7 min read

Saddle Point vs Minimum in 3D Graphs

z = x^2 - y^2

A saddle curves up in one direction and down in another, unlike a true minimum.

6 min read

Surface Graph and Contour Map Relationship

z = x^2 + y^2

Contours are horizontal slices of the 3D graph projected into 2D.

6 min read

Cross Sections and Traces of a Surface

z = x^2 - y^2

A trace is the curve a plane leaves when it cuts a surface, and the cross-section panel draws that cut as a flat 2D curve you can read exactly.

6 min read

Classroom and publishing

Turn a graph into a lesson, a worksheet, or an embedded widget.

Best 3D Graphing Calculator Setup for Teachers

z = x^2 - y^2

Use a locked view and teacher mode, which hides the answer until you reveal it, for classroom embeds.

6 min read

How to Embed a 3D Graph in a Lesson

z = x^2 - y^2

Copy the iframe code and paste it into a blog, LMS, or course page.

6 min read

How to Export a 3D Graph as PNG

z = x^2 - y^2

Use the export button after rotating the graph to the desired angle.

6 min read

How to Copy LaTeX from a 3D Graph

z = x^2 - y^2

Copy the formula in LaTeX form for notes, worksheets, and articles.

6 min read

How the drawing works

Why a surface can look smooth, blocky, or partly missing.

How 3D Graph Sampling Density Works

z = sin(20 * x)

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.

7 min read

Why Is Part of My 3D Graph Missing?

z = sqrt(x^2 + y^2 - 9)

Missing patches on a 3D surface are usually the domain at work: points where the formula has no real value are left out instead of drawn at zero.

7 min read

Parametric Surface Equations Explained

z = sin(sqrt(x^2 + y^2))

A parametric surface maps two parameters u and v to a point in space, the only way to describe a torus, a helicoid, or a Möbius strip.

6 min read

Want the whole library?

Every surface on this site has its own page with the formula, a teaching note, and the live calculator.

Browse graph examples