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))

Teacher prompt

What does the ridge represent?

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

min z 0.00max z 0.0056 samples

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.

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Related graphs

Open another surface page and compare shape, slices, and contour behavior.

Saddle Surface

z = x^2 - y^2

A saddle surface curves up in one direction and down in the perpendicular direction.

Gaussian Surface

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

A smooth bell-shaped surface centered at the origin.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.