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From: mcdonald@uxe.cso.uiuc.edu
Newsgroups: comp.graphics
Subject: Sphere-plane intersection
Message-ID: <46900009@uxe.cso.uiuc.edu>
Date: 28 Jan 88 15:35:00 GMT
Lines: 16
Nf-ID: #N:uxe.cso.uiuc.edu:46900009:000:922
Nf-From: uxe.cso.uiuc.edu!mcdonald    Jan 28 09:35:00 1988


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.)

Doug McDonald  (mcdonald@uiucuxe)