Re: Newbie Joint question

>On Wed, 24 Nov 2004, Jon Kleiser wrote:
>
>>  Thanks. I've got the "set-relative-rotation" method working, but it
>>  may be somewhat limited as to what it can do with the orientation of
>>  the connected parts. I suspect that "set-relative-rotation-matrix"
>>  could be a more powerful solution, but I can't find much info on how
>>  to figure out the suitable values to use in such a matrix. I've made
>>  a web page that describes what I try to do, including a snapshot, if
>>  you care to take a look:
>
>The set-relative-rotation should be capable of every rotation that
>the matrix method is capable of, though depending on what you're
>after, one method might be easier than the other.
>
>The way you describe the problem, you're trying to get a structure
>with the image you're showing using only one shape, but with different
>transformations.
>
>I'll give an example by looking looking at the yellow and purple shapes,
>and finding the transformation matrix to build it using only one shape. 
>If you're using just the purple shape, you'll see that the shape will
>need to be joined at the points (-1, 5, -1) and (5, -1, -1).  They
>can't both be joined at the same two points (-1, 5, -1), because then the
>z "point" of the shape would be facing the wrong direction.
>
>So if you connect these points together, you'll see that the object is
>not joined at the desired angle -- it's off by 90 degrees.  You'll also
>note that you want the Z face to stay pointed in the same direction,
>while the X and Y axis will both need to be rotated.  In other words,
>you want a 90 degree rotation about the Z axis, using this line before
>joining the links:
>
>	joint set-relative-rotation around-axis (0, 0, -1) by -3.14/2.0.
>
>If you want to use the rotation matrix, look at the initial uncorrected
>position, and think about the desired rotation: you'll want the X axis
>to point down (0, -1, 0), the Y axis to point to the right (1, 0, 0)
>and the Z axis to remain as it is (0, 0, 1).  These three vectors
>correspond to the columns of the 3x3 rotation matrix, so the result is:
>
>     joint set-relative-rotation-matrix to
>         [ (0, -1, 0),
>           (1,  0, 0),
>           (0,  0, 1) ].
>
>Both of these methods should produce the same results.  You should be
>able to follow the same logic for adding new links to your chain.
>
>- jon klein

Thanks a lot! That was very helpful. I have now updated my page at 
<http://folk.uio.no/jkleiser/breve/pyramids.html>.

Does breve/steve have a constant pi that I can use instead of 3.14?
One possibility is of course to use 2*asin(1).

/Jon
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