Subject:
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Re: Math Problem Again
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Newsgroups:
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lugnet.cad.dev
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Date:
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Fri, 14 Nov 2003 01:08:21 GMT
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Viewed:
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1866 times
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In lugnet.cad.dev, Tore Eriksson wrote:
> You are given three 3d cooridates.
> This makes a triangle in 3d space. The z values may all be three different, so
> it may be rotated in almost*) any direction.
>
> I am just interested of the plane; the surface it makes.
>
> Now, we have a forth point, with only x and y values given. I wish to calculate
> the z value where this line meets the plane from the triangle (* -> they will
> meet, but not necesserily within the triangle)
>
> If possible, I would like an Excel spreadsheet, but just the formula will do.
>
> TIA,
> /Tore
http://astronomy.swin.edu.au/~pbourke/geometry/planeeq/
tells you how to derive the equation of
a plane passing thru the three points
(x1,y1,z1)
(x2,y2,z2)
(x3,y3,z3)
The standard equation of a plane in 3 space is
A.x + B.y + C.z + D = 0 (where the "." means times)
So given three points in space
(x1,y1,z1),
(x2,y2,z2),
(x3,y3,z3)
you can work out the the equation of the plane through
these points (on which your triangle lies) by working out some
matrix determinants which, if this means nothing to you, boils down to
this -
Calculate A,B,C,D from these equations,
A = y1 .(z2 - z3) + y2 .(z3 - z1) + y3 .(z1 - z2)
B = z1 .(x2 - x3) + z2 .(x3 - x1) + z3 .(x1 - x2)
C = x1 .(y2 - y3) + x2 .(y3 - y1) + x3 .(y1 - y2)
- D = x1 .(y2.z3 - y3.z2) + x2.(y3.z1 - y1.z3) + x3.(y1.z2 - y2.z1)
Having worked these out (i.e. this has given you the A,B,C,D in
A.x + B.y + C.z + D = 0) just plug in your fourth point's x and y co-ords
(say x4 and y4) into this equation i.e. let x=x4 and let y=y4
This gives you the equation for z4 that you are looking for viz.
A.x4 + B.y4 +C.z4 +D =0 (where now the only thing you don't know is z4)
rearranging this is just
z4=(-D -A.x4 - B.x4)/C
Then again, it's late :)
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Message has 2 Replies:
 | | Re: Math Problem Again
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| In lugnet.cad.dev, Ronan Webb wrote: 8<------ (...) Yes, it's very late. I'd better get myself some sleep first, and have a look at it tomorrow. Thanks a lot! /Tore (20 years ago, 14-Nov-03, to lugnet.cad.dev)
| | | Re: Math Problem Again
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| (...) Hey! cool! where was this info when I wrote my calculator program? It would have made it alot easier. The calculator grew into a slightly different purpose though. it was for helping determine where to trim lines and quads at intersection (...) (20 years ago, 14-Nov-03, to lugnet.cad.dev)
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Message is in Reply To:
| | Math Problem Again
|
| You are given three 3d cooridates. This makes a triangle in 3d space. The z values may all be three different, so it may be rotated in almost*) any direction. I am just interested of the plane; the surface it makes. Now, we have a forth point, with (...) (20 years ago, 13-Nov-03, to lugnet.cad.dev)
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