## Sphere-plane intersection

### Sphere-plane intersection

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.)

I've found and interesting CAM problem that appears to boil down to
intersecting a sphere with two perpindicular planes. Is there any
reference to this kind of thing before I break down and re-invent the
wheel?