I need some help doing calculations on ellipses. Note that this is for

a bit-mapped graphics screen, in pixel coordinates. What I am doing

is looking at spheres in 3-d space, projecting them onto the screen and

drawing them. What I haven't figured out is as follows: I have three

spheres. Their centers define a triangle. I want to draw in the section

of the plane defined by the three centers which lies outside the (assumed

opaque) spheres, as hidden by the front two spheres. I have been unable

to come up with a simple(not involving trig functions) method of

determining the equation of the line connecting the triangle with the

surface of the sphere, which is a section of an ellipse. Has anybody

solved this problem? (I need something fast, as I need to do this at least

4 times per second on an ordinary IBM-PC. Without the fillrd in triangle

I am getting about six per second.)