Learning OpenCV, 2nd Edition

);

Given a cubic polynomial in the form of a three- or four-element vector coeffs, cv::solveCubic()

will compute the real roots of that polynomial. If coeffs has four elements, the roots of the following

polynomial are computed:

coeffs

0

x

3

+ coeffs

1

x

2

+ coeffs

2

x + coeffs

3

= 0

If coeffs has only three elements, the roots of the following polynomial are computed:

x

3

+ coeffs

0

x

2

+ coeffs

1

x + coeffs

2

= 0

The results are stored in the array roots, which will have either one or three elements, depending on how

may real roots the polynomial has.

A word of warning about cv::solveCubic() and cv::solvePoly(): the order

of the coefficients in the seemingly analogous input arrays coeffs is opposite in the

two routines. In cv::solveCubic(), the highest order coefficients come first, while

in cv::solvePoly() the highest order coefficients come last.

cv::solvePoly()

int cv::solvePoly (

cv::InputArray coeffs,

cv::OutputArray roots // n complex roots (2-channels)

int maxIters = 300 // maximum iterations for solver

);

Given a polynomial of any order in the form of a vector of coefficients coeffs, cv::solvePoly()

will attempt to compute the roots of that polynomial. Given the array of coefficients coeffs, the roots of

the following polynomial are computed:

coeffs

n

x

n

+ coeffs

n−1

x

n−1

+ ! + coeffs

1

x + coeffs

0

= 0.

These roots are not guaranteed to be real. For an order-n polynomial ...