Fastest way to put a point on the circumference of a circle My goal is to take a point that is inside of a circle with a given radius and put it on the circumference.

Recently I have been normalizing the vector between the point and the center of the circle then multiplying that by the radius.  However I need (if possible) a less computationally expensive method because the distance formula is expensive.

Another thought I had was to use "atan2" to get the angle between the two points and then use sine and cosine multiplied by the radius to get the point on the circumference.

Which method do you think would be faster for the computer to process? Can you think of a faster method.

Details about the simulation
This is an ios application written in swift.

Basically there are a bunch of particles moving around randomly. And the user is putting down fingers. Each finger is a circle with a radius that grows as time goes on. The part that is inneficent is that if the dot is ever inside of any of the circles (attached to touchscreen touches) that it goes on the circumference of the circle.
Before focusing on optimising the individual process of moving a point, consider how many points are being processed this way. This is likely to give a much more significant speed up if it hasn't yet been addressed.

For example, if every point on the screen is being tested against every circle, then most of the points are being checked needlessly.

If instead you divide the screen into a grid, with each grid cell keeping a list of all points currently within it, then each circle only needs to be checked against the points that appear in the grid cells which that circle overlaps. This allows checking a few tens of points, instead of hundreds or thousands.

This is a much bigger speed up than you can hope to achieve by optimising the circumference calculation, and after this you may find that further optimisation is not needed.