Is there an easy way of finding the shortest distance from a point to a polynomial?
18 views (last 30 days)
Show older comments
With access to the point and the coefficients of the polynomial, is there an easy way of getting the perpendicular distance? Currently I'm having to find the distance from the point to every point in the curve and find the shortest manually, and its sloooooow.
0 Comments
Accepted Answer
Matt J
on 3 Jul 2013
Edited: Matt J
on 3 Jul 2013
The analytical solution boils down to finding the roots of another polynomial. If your fixed point is (x,y) and your polynomial is p(t), then the distance squared is
f(t) = (t-x)^2 +(p(t)-y)^2
Setting the derivative of f(t) to zero leads to
(t-x)+ (p(t)-y)*dp/dt = 0
which is just a problem of finding the roots of the polynomial on the left hand side. Once you find its roots using the ROOTS command, you then test f(t) at the real roots for the minimum distance.
More Answers (0)
See Also
Categories
Find more on Polynomials in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!