surface example

3D Distance Field Surface Graph

A surface showing distance to the nearer of two points.

z = min(sqrt((x - 2)^2 + y^2), sqrt((x + 2)^2 + y^2))

Quick facts

  • Formula: z = min(sqrt((x - 2)^2 + y^2), sqrt((x + 2)^2 + y^2))
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The ridge marks where both points are equally near.

Where it appears in calculus

This connects geometry, optimization, and Voronoi regions.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. Click Formula or LaTeX to copy the equation for your notes

Embed this graph

Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.

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Teacher prompt

Question: What does the ridge represent?

Answer: The ridge is where the two source points are equally close.

Related graphs

Explore more surface examples and compare shapes, slices, and contour behavior.

Elliptic Gaussian

z = exp(-(x^2 / 8 + y^2 / 2))

A stretched bell surface with different widths by axis.

Anisotropic Paraboloid

z = x^2 / 4 + y^2

A bowl that curves more sharply along y than x.

Two Peak Surface

z = exp(-((x - 2)^2 + y^2)) + exp(-((x + 2)^2 + y^2))

Two smooth hills separated along the x-axis.

Basin and Ridge

z = x^2 - cos(3*y)

A parabolic basin crossed by repeated ridges.

Exponential Slope

z = exp(0.25*x) * cos(y)

A wave whose amplitude grows along x.

Ring Valley

z = (sqrt(x^2 + y^2) - 3)^2

A circular valley with a raised center and outside wall.

Explore more tools

Use these free browser tools to extend your graphing workflow.

3D Surface Plotter

Plot z=f(x,y), rotate, and export

Embed Builder

Create ready-to-use iframe embeds

Worksheet Export

Export graph images for classroom worksheets

How to Graph z=f(x,y)

Step-by-step guide for beginners