Subject:
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Re: Finding a rotation matrix for a triangle
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Newsgroups:
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lugnet.cad
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Date:
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Mon, 28 Nov 2005 18:11:27 GMT
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Viewed:
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1364 times
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What I mean is:
In MLCad, you can take a part, and rotate it via a vector command like turn 45
degrees around y axis clockwise. Or more complex rotations based on more axes.
What I would like to know is: How do I find the rotation vector of a plane
(defined by three coordinates)?
Back in the math class years ago, one of the possible definitions of a plane was
a vector starting in some point on the plane, standing out at a 90 degrees angle
to it. That way you would know the 3d angle of the plane from the vector.¬
Now, if I could get the 3d rotations of such a vector corresponding to my
triangle, I would be able to place any primitive precisely on it at the right
angle.
I know there's formulas that would enable me to find that vector, and yet other
and more complex formulas that would give me the angles - I would just like to
know if there was some program out there that can do it for me.
It would probably not be too hard to make some sort of excel sheet, where you
could enter the coordinates of the triangle, (and preferably the point where you
would like to add the primitive), and get the rotation vector values out in the
other end - IF you have the formulas to find the vector, and the formulas that
will give you the correct, complex, rotation vector value.
I might be able to do the first part if I hadn't had to return the books when I
finished school, but I'm not sure how that rotation vector thingie works when
stuff is turned at more than one angle at a time: It seem to get really complex.
So I was kinda hoping that someone had made a clever program already, or that
somebody. that remembers a lot more of3D coordinate system and understand Ldraw
and/or Mlcad much better than I. would whip it up.
It would really be a great help when working with parts - like I said, I've
already got 2 parts I need this sort of program for: One that's stucked/halted
in the PT: <http://www.ldraw.org/cgi-bin/ptdetail.cgi?f=parts/s/6153s01.dat>¬
and one I've nearly finished, but got stucked with at least 7 months ago:
<http://peeron.com/inv/parts/6032>
I can't be the only one that could use such a program...
Cheers NB
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Message has 2 Replies:
 | | Re: Finding a rotation matrix for a triangle
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| (...) Hi Niels, I think you are getting two things a little crossed here but I will try to answer you questions. Firstly, you must remember that a plane can be defined meaningfully by a normal vector (one perpendicular to the plane) and a vector (...) (19 years ago, 28-Nov-05, to lugnet.cad, FTX)
| | | Re: Finding a rotation matrix for a triangle
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| (...) You take the cross product of two of the sides of the triangle, this will give the vector perpendicular to the triangle plane: (URL) will point either upwars or downwards. Unless your triangle is in a known winding state there's no way to (...) (19 years ago, 28-Nov-05, to lugnet.cad)
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Message is in Reply To:
| | Re: Finding a rotation matrix for a triangle
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| (...) Hi Niels, I'm not sure exactly what you mean by the rotation vector of a triangle? There isn't really one as a triangle is defined by three points (9 components) whereas a rotation matrix/vector is defined by only 1 point (3 components). A (...) (19 years ago, 27-Nov-05, to lugnet.cad)
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