Re: Algorithm for distance from point to function

The minimum distance is the length of the shortest line from the point
x1y1 to a tangent to the line y=f(x). The equation of the tangent is a
line whose slope is the first derivative at x2y2. The point x2,y2
satisfying the function and at the shortest distance is the
intersection of a line through x1y1 which is perpendicular to the
tangent at x2,y2 and therefore has a slope of the inverse of the tanget
(or the reciprocal of the first derivative at that point).
Then the distance is just the normal Gausian square rooot of the sum of
the squares of the differences between each coordinate of the pair
x1,y1; x2,y2
Searching by closer approximations is the best technique.

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