Hi, I am wondering if there is a better way to my problem as the solution I found seems not optimal.

Looking at the picture, I need to know the 3d position of E and F.

Here's what I do know:

B is my camera position.

A and D are known and moving in world space, so I also know AB and AD.

I also know the radius of each spheres.

Here the solution I found:

I compute angle alpha knowing AB and AC.

Then I compute the angle BAD with the dot product of the two vector... This is the part I'm not sure as it is suppose to give me the cos of BAD I hope.

Then I compute CAE doing the difference between BAD and alpha.

Then knowing CAE I can compute the hypothenuse AE.

Repeat the operation for the second sphere and I finally get F.

Any better, clever way ?

Thanks to all you maths guys.