Minimum Distance Between a Point and a Curve

Minimum Distance Between a Point and a Curve

For a point:

$$(x_0,y_0)$$

and a curve:

$$y=f(x)$$

the squared distance from the point to a point $$(x,f(x))$$ on the curve is:

$$D^2=(x-x_0)^2+(f(x)-y_0)^2$$

Usage

- Minimizing $$D^2$$ instead of $$d$$ simplifies distance optimization problems.

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