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

Question

Hi 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

Given a point (x1, y1), we want to find a "random" point (x2, y2) at a distance d from it.

Pick a random angle theta. Then:

x2 = x1 + d * cos(theta)
y2 = y1 + d * sin(theta)

This will be a random point on a circle of radius d centered at (x1, y1)

Proof:

Distance between (x1, y1) and (x2, y2)
= sqrt ( (x2 - x1) ^ 2 + (y2 - y1) ^ 2)
= sqrt ( d^2 * (sin^2 (theta) + cos^2 (theta) ) )
= d

You might want to look at:

• Polar coordinate system
• Distance Formula
• Pythagorean trigonometric identity