问题
Suppose I have two sets of points, A and B, in 2D space. I want to know if there exists a single straight line that will have all points of A on one side and all points of B on the other, and if possible, find one such line. I found this question while searching but it is more of a "line of best fit" problem.
Intuitively, I feel like it is a question regarding cross-products but I can't figure out how it can be done.
回答1:
You could find the convex hull for each set of points, and then follow the procedure in this question to determine if they intersect (and return a dividing line if they don't):
How do I determine if two convex polygons intersect?
回答2:
In machine learning, the classical solution to this is the Support Vector Machine (SVM). It will generalize to N dimensions, find a best approximation in case there's no solution, and if there are multiple solutions it will optimize the margins left and right of the divider. Possibly overkill for you then, but there are multiple implementations already available. (E.g. OpenCV)
来源：https://stackoverflow.com/questions/25836565/dividing-two-sets-of-points-using-a-straight-line