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Math Help - Point in Tetrahedron test

  1. #1
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    Question Point in Tetrahedron test

    Hi,

    How would I go about determining whether a point P is enclosed by a tetrahedron A,B,C,D?
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    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.
    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
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  4. #4
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    Quote Originally Posted by CaptainBlack View Post
    You are given a tetrahedron with vertices A, B, C, D, and you want to know
    if the point P is inside the tetrahedron.
    I do not have a general method to do this.
    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.
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  5. #5
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    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?
    Last edited by scorpion007; September 12th 2006 at 01:39 AM.
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  6. #6
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    Quote Originally Posted by scorpion007 View Post

    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.
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  7. #7
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    Quote Originally Posted by scorpion007 View Post
    Hi,

    How would I go about determining whether a point P is enclosed by a tetrahedron A,B,C,D?
    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
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  8. #8
    Super Member malaygoel's Avatar
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    Quote Originally Posted by scorpion007 View Post
    Hi,

    How would I go about determining whether a point P is enclosed by a tetrahedron A,B,C,D?
    Are the points given in a coordinate system?
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