c# - how to move point a given distance d (and get a new coordinates)?

Question

I was wondering if there is any efficent way to calculating coordinates of point (which was moved distance d from it's original location). Let's say I have a point P(0.3,0.5) and I need to move that point random direction with distance d. So far I did it by random picking new x and y coordinates and I was checking if distance between old and new point equals d. I do realize that is't too eficient way to do that. How would You do it ??

Answer 1

Let's assume that the new position is M(x, y). If you consider P being the center of a circle with radius d, then M can be any point on this circle. The equation of this circle will be (x-0.3)² + (y-0.5)² = d². Then pick any random value for x, greater or equal to (0.3-d) and less or equal to (0.3+d). In this way, by using the above formula, you will be able to calculate the correct value for y, thus, the position of M. In C# the square root is Math.Sqrt().