Given two lines on a plane, how to find integer points closest to their interseciton?

Posted by Lukasz Lew on Stack Overflow See other posts from Stack Overflow or by Lukasz Lew
Published on 2010-04-25T14:50:27Z Indexed on 2010/04/25 15:13 UTC
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algorithm

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problem-solving

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project-euler

I can't solve it:

You are given 8 integers:

A, B, C representing a line on a plane with equation A*x + B*y = C
a, b, c representing another line
x, y representing a point on a plane

The two lines are not parallel therefore divide plane into 4 pieces. Point (x, y) lies inside of one these pieces.

Problem:
Write a fast algorithm that will find a point with integer coordinates in the same piece as (x,y) that is closest to the cross point of the two given lines.

Note:
This is not a homework, this is old Euler-type task that I have absolutely no idea how to approach.

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