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Click on the level set to place a tangent point.

Experiment with options in the sidebar to show the tangent line or plane, the gradient, and labels.

Switch between 2d and 3d modes.

You can enter standard custom functions in the text box.

Overview

∇φ is perpendicular to level sets of the form φ(r) = c.

Given a point r₀ on the level set, set the normal vector N to be some multiple of the gradient: N = k ∇φ(r₀)

Given a generic point r on the tangent, we see that:

N • (r-r₀) = 0      
      ⇒ N • r = N • r₀

Thus we have an equation for the tangent line or plane!

In 2d:       N₁ x + N₂ y = N₁ x₀ + N₂ y₀
In 3d:       N₁ x + N₂ y + N₃ z = N₁ x₀ + N₂ y₀ + N₃ z₀