Subject:
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RE: need Help finding a co-ordinate
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Newsgroups:
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lugnet.cad
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Date:
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Mon, 11 Sep 2000 16:46:47 GMT
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Viewed:
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463 times
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> Does anyone have a program or an algorithm that does the following:
>
> Given four points in three dimension space (four corners of a quad,) and an
> (X,Y) co-ordinate on the quad, calculate the Z co-ordinate so the fifth point
> is on the quad.
>
> In other words, how do I find a point that is on a quad?
Ummm, if you mean co-planar, there is no guarantee that
4 points are coplanar in 3-space. however, 3 points are always
coplanar.
If the 4 points ARE coplanar, then
throw out one of the points and figure out the equation of
the plane described by the three points. This can be
found in any decent algebra text.
If you then specify the x,y pair for your desired point,
you can easily solve for z.
Hope this helps....
Cheers,
Ralph Hempel - P.Eng
--------------------------------------------------------
Check out pbFORTH for LEGO Mindstorms at:
<http://www.hempeldesigngroup.com/lego/pbFORTH>
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Reply to: rhempel at bmts dot com
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Message has 1 Reply:
 | | RE: need Help finding a co-ordinate
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| (...) And in case you don't have a text handy... lets call our points A=(a1,a2,a3), B, and C. Find the cross product of AB x AC = N = <n1,n2,n3> to get the normal vector to the plane. Then n1(x-a1) + n2(y-a2) + n3(z-a3) = 0 is the equation of the (...) (24 years ago, 11-Sep-00, to lugnet.cad)
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Message is in Reply To:
| | need Help finding a co-ordinate
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| Does anyone have a program or an algorithm that does the following: Given four points in three dimension space (four corners of a quad,) and an (X,Y) co-ordinate on the quad, calculate the Z co-ordinate so the fifth point is on the quad. In other (...) (24 years ago, 11-Sep-00, to lugnet.cad)
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