Hi,

How would I go about determining whether a point P is enclosed by a tetrahedron A,B,C,D?

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- September 11th 2006, 04:26 AMscorpion007Point in Tetrahedron test
Hi,

How would I go about determining whether a point P is enclosed by a tetrahedron A,B,C,D? - September 11th 2006, 09:24 AMThePerfectHacker
This is what I do not understand.

You are given a tetrahedron and asked to determine if a point is inside?

You cannot, because it can be inside or outside.

~~~~

Or are you given a certain tetrahedron surface defined as,

f(x,y,z)=C

And you are given P(x_0,y_0,z_0)

And asked to determine if P is inside f?

If so,

It looks very similar to that polygon test (whatever it is called) for 2-d. - September 11th 2006, 09:45 AMCaptainBlack
You are given a tetrahedron with vertices A, B, C, D, and you want to know

if the point P is inside the tetrahedron.

one way of doing this is given at PNPOLY - Point Inclusion in Polygon Test - WR Franklin (WRF)

RonL - September 11th 2006, 09:48 AMThePerfectHacker
- September 11th 2006, 07:45 PMscorpion007
I guess I'm looking for a way to determine this using simple vector calculations (cross/dot products).

What if point P was always (0, 0, 0) would that make the calculation easier? - September 12th 2006, 03:09 AMQuick
- September 12th 2006, 06:00 AMCaptainBlack
Choose and arbitary unit vector

**u**and consider the ray P+a**u**, if this meets

the faces at only one internal point (of a face) for positive a then P is an

internal point of the tetrahedron, if it meets an edge or a vertex, then

perturb the unit vector to avoid this.

(Such a ray from an external point will meet the faces either twice or zero

times)

RonL - September 17th 2006, 10:38 PMmalaygoel