Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.
Break the given line by building a piecewise linear function constituted by two branches:
- one branch stands for the parent polynomial p;
- and another branch stands for the perpendicular line, r, to p that passes by the point P (see figure below).
Given (P, p), find
- R, the breaking point;
- r, the 1×2 array that represents the perpendicular line. If r violates the definition of a function, return r = ''.
input: (P, p)
output: (R, r)
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Running into numerical precision issues again, some testcases are using isequal instead of isapprox :)
As claimed, I fixed by using isapprox to allow for numerical errors whenever they are to be expected. I apologize if I failed to achieve that. It is really very difficult for me to accept wrong numbers as correct answers (especially, integer numbers or rational numbers with finite decimal part), because this violates my rule: To be or not to be.
@Luisa if you feel ill at ease with using isapprox in such cases, keep in mind that many rational numbers with finite decimal part are not perfectly representable as IEEE 754 floats on a computer. 0.8 and 0.6 from test case 2 are such numbers, so R_correct isn't actually correct either there.
Thank you, @Christian Schröder.