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From: 3ksnn64@cidmac.ecn.purdue.edu (Joe Cychosz)
Newsgroups: comp.graphics
Subject: Re: intersecting planes and spheres
Message-ID: <1991May24.214306.16919@noose.ecn.purdue.edu>
Date: 24 May 91 21:43:06 GMT
References: <1991May23.205708.9746@hellgate.utah.edu> <1991May24.180454.10744@noose.ecn.purdue.edu>
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In article <1991May24.180454.10744@noose.ecn.purdue.edu> 3ksnn64@cidmac.ecn.purdue.edu (Joe Cychosz) writes:
>In article <1991May23.205708.9746@hellgate.utah.edu> mblum%asylum.utah.edu@cs.utah.edu (Michael Blum) writes:
>>HI!
>>
>>I'm trying to figure out how to find whether a sphere intersects a plane.
>>Actually, I need to know whether a sphere intersects a cube, and
>>if so which side of the cube.  I imagine this is a simple extension
>>to the general intersection problem, but I'm not exactly sure
>>how to approach the problem.  Any ideas?  please e-mail at
>>mblum@asylum.utah.edu
>>
>
>1. Compute the perpendicular distance the center of the sphere is from the
>   plane.
>
>2. The dot product of the plane normal with the vector formed by the the
>   line from the plane through the center of the sphere tells you what
>   side of the plane the sphere is on. The dot product should be 1 or -1.
>
>3. If the perpendicular distance is less than the radius, the sphere
>   intersects the plane.
>
>4. For the cube case you can treat the plane pairs together and the
>   distance to the second plane = the distance between the planes -
>   dot product (step 2) * distance (step 1).
>
>5. Count the number of cases where the sphere is between the plane pairs
>   or intersects one of the planes.  If the answer is 3, the sphere is
>   within or intersects the cube.  Assumption: the normal of the 6 planes
>   all point outward of the cube.

As has been pointed out to me.  It is possible for a sphere to intersect
the plane pairs and still not intersect the cube.  At the moment I do not
have a correction for the algorithm.

	A sphere may be "between" all three plane pairs and still not
	intersect the cube. As an example consider the cube  defined by
	0<= x <= 1; 0 <= y <= 1; 0 <= z <= 1 and the sphere centred at
	(-2, -2, 0) and passing through (-1, .5, 0).