Hi,
How would I go about determining whether a point P is enclosed by a tetrahedron A,B,C,D?
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Hi,
How would I go about determining whether a point P is enclosed by a tetrahedron A,B,C,D?
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.
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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.
You are given a tetrahedron with vertices A, B, C, D, and you want to knowQuote:
Originally Posted by ThePerfectHacker
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
I do not have a general method to do this.Quote:
Originally Posted by CaptainBlack
But I would create 4 linear inequalities involving x,y,z
And see if P satisfies all 4.
Again this is not a general method.
You need to adjust it to problem to problem.
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?
If that's the case, then all you have to do is see if the vertices are in different quadrants.Quote:
Originally Posted by scorpion007
Choose and arbitary unit vector u and consider the ray P+a u, if this meetsQuote:
Originally Posted by scorpion007
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
Are the points given in a coordinate system?Quote:
Originally Posted by scorpion007