Find point with vector projection

Question

I am trying to work this out in java with LatLng point

I was looking at this post here Circle line-segment collision detection algorithm?

I have a method to find distance between 2 point. The instruction says

Project the vector AC onto AB. The projected vector, AD, gives the new point D. If the distance between D and C is smaller than (or equal to) R we have an intersection.

I don't have knowledge about vector, could anyone help me how to find point D here ?

Thanks in advance

Answer 1

If you really need D point coordinates - let's vectors
AB = (B.X-A.X, B.Y-A.Y)
AC = (C.X-A.X, C.Y-A.Y)
then the simplest (I believe) form of projection of C to AB is:

AD = AB * (AB.dot.AC) / (AB.dot.AB);
In coordinates:

CF=((B.X-A.X)*(C.X-A.X)+(B.Y-A.Y)*(C.Y-A.Y))/((B.X-A.X)^2+(B.Y-A.Y)^2)
D.X=A.X+(B.X-A.X)*CF
D.Y=A.Y+(B.Y-A.Y)*CF

Distance CD, as David Wallace has already written, is
|CD| = |AC x AB|/|AB| (x = cross product)