# Distance estimation

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A distance estimate is a function that gives bounds (typically expressed as a multiplicative factor) on how far away the nearest element of a set is from a specific point. Analytic distance estimates are typically calculated using derivatives. Numeric distance estimates are needed when analytic derivatives are not available.

Distance estimates can be used for colouring fine details in 2D escape-time fractals, or for ray marching in 3D.

## See Also

Original Page by Claude