Find the coordinates of a point lying on the bisector of the angle formed by two vectors, knowing their coordinates
Given 2 vectors a and b, coming from point A, it is necessary to find the coordinates of point B. The distance AB is calculated, AB divides the angle formed by the vectors in half. I assume to move the coordinates of T. A to search in:
В = (Ах + АВ * Соs Alpha; Аy + АВ * Sin Alpha)
Then I build a vector from A to Ox:
e = {100; 0}
I find the angles between a, e and b, e:
cos Betta = a * e / |a| * |e| ; cos Gamma = a * e / |a| * |e|
And now, to search for Alpha, there are two possible conditions:
Alpha = (Betta - Gamma) / 2
Or
Alpha = (Betta - Gamma) / 2 + min(Betta, Gamma)
Tell me, are my judgments correct? And what is the condition should it be for Alpha search?
1 answers
A point lying on the bisector of the angle
Do you know how many points there are on the bisector? Millions!
Everything is much simpler. Reduce the vectors а and b to a single (or any equal) length and add (vector-wise, of course). Add the coordinates of their sum to the coordinates of the point А - this will be the point B. And AB is the diagonal of a rhombus constructed on reduced vectors of equal length. If the condition has a requirement for the length of |AB|, give the result vector AB to this length.