Subject:
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Re: 3D geometry question
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Newsgroups:
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lugnet.cad
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Date:
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Wed, 13 Oct 1999 13:08:54 GMT
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Viewed:
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658 times
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"Jacob Sparre Andersen" <sparre@cats.nbi.dk> writes:
> Fredrik Glöckner:
>
> > Say I have a vector v with length normalized to 1. For
> > simplicity, picture this vector as starting in the origin.
>
> Vectors don't start anywhere. A vector is just a direction
> and a length.
Sure. But to picture the vector as starting in the origin makes it
easier to understand what I want in the paragraph below:
> > o If I rotate a part with one edge going from (0,0,0) to
> > (0,-1,0) (i.e., pointing upwards), this edge should
> > coincide with the vector v after the transformation
> There are infinitely many solutions to the problem. When you
> have one solution, any rotation around v is also a solution.
In fact, for my application, any of these solutions would suffice.
> We have to solve
>
> v = M e
>
> with respect to M, with the additional constraint
>
> det(M) = 1
>
> Hmmm? 9 variables and 4 equations. - That can't be sufficient
> constraints to ensure M is a rotation matrix.
I think we also need some constraints on M to ensure that there is no
scaling:
m11² + m12² + m13² = 1
m21² + m22² + m23² = 1
m31² + m32² + m33² = 1
But do the rows also need to be normalized, i.e, like this?
m11² + m21² + m31² = 1
m12² + m22² + m32² = 1
m13² + m23² + m33² = 1
> Lets try something else...
>
> Any direction in three-dimensional space can be constructed
> by one rotation around the x axis followed one rotation
> around the y axis:
Thank you for your suggestion, but I'm not too happy with this solution,
as I think there is a simpler solution along your original suggestion.
I'm familiar with the approach of rotation around the x and y axis, but
I was hoping that someone here has experience with a simpler solution.
Fredrik
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Message is in Reply To:
 | | Re: 3D geometry question
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| Fredrik Glöckner: (...) Vectors don't start anywhere. A vector is just a direction and a length. (...) Lets call the vector along the edge e. (...) There are infinitely many solutions to the problem. When you have one solution, any rotation around v (...) (25 years ago, 13-Oct-99, to lugnet.cad)
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