Le 09/08/2010 14:36, davidafisher a écrit :
> result in a parallelogram and not a
> rhomboid?

Houston, we got a problem.

Traditionally, in two-dimensional geometry, a rhomboid is a
parallelogram in which adjacent sides are of unequal lengths and angles
are oblique.

Please check
http://en.wikipedia.org/wiki/Rhomboid

Do they need to change the wiki ?

You want a specific matrix transform which will keep the length of the
side your square while changing the angle ? (but then the result would
not be a rhomboid, just an exceptional rhombus (and a rhombus is not a
rhomboid, so your question was wrong in first place ?))

A parallelogram is either:
 * a square (same length, right angle)
 * a rhombus (same length, not right angle)
 * a rectangle (not same length, right angle)
 * a rhomboid (all others)


Now, you do not provide the length of the original square size. (HINT:
you implied a 2D figure by writing about a square!)

You do not provide the length of the diagonals of the resulting rhomboid
(or the new coordinate/displacement of the corner opposite to the origin
corner [ "say 3 degres" is not a precise value, which direction ? and
what is the main plane of the original mesh ? ]), nor the length of its
sides. (for a rhombus, the length of the diagonals are enough, not for a
rhomboid as they are not intersecting at a right angle anymore: at least
one side is also needed, and the fourth length can be computed ( (sum of
squared sides = sum of squared diagonals, as the diagonals intersect at
their middle, their is no delta of 4*square distance between the middle
of the diagonal)**

So, yes, you have work on the computation of the 12 matrix's values to
get what you want, but so far I'm afraid we cannot help more with the
current data.

If you meant a rhombic prism (a 3D figure), it would still be a matrix
transform, just a bit more complex to set.


** formula for a convex quadrilateral ABCD : AB²+BC²+CD²+DA² =
AC²+BD²+4IJ² (where I,J middle of AC,BD), on parallelogram IJ=0.
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