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Simon Lemieux <lem### [at] yahoo com> wrote:
> just finished my session and learned quite a few interesting things...
such as
> 2D rotations, where in radians (0 <= r <= 2pi):
> x = cos(rad);
> y = sin(rad);
>
> Now, I was wondering how to add the Z coordinate? Is it possible? I guess
a
> better use would be to have different angles, rotating around a given axis
and
> use the cos&sin functions just like for x&y but substituting x&z for a
yAxis
> rotation, etc...
>
> Is there any better math out there to help about rotations? Except for
> matrixes...
All transformations in POV-Ray are ultimately represented as matrices,
because they offer the most general and compact form of the transformations
available in POV-Ray. But POV-script is designed to be written and read by
people, not just computers, and the rotate, translate and scale commands
offer a much more intuitive way of performing transformations. In other
words, don't feel obliged to learn matrices if the other three functions
allow you to do what you wish.
Regarding rotations - they are indeed performed, like you describe, as 2D
rotations about each of the three orthogonal axes, x, y, and z. For
example, rotate <40, -20, 165> is interpreted as rotating 40 degrees about
the x-axis, followed by -20 degrees around the y-axis, followed by 165
degrees around the z-axis. If you want to rotate around the y-axis, then
around the x-axis, you have to use two rotate commands, e.g. rotate y*45
rotate x*-90.
Another common method of expressing rotations in 3D space are quaternions -
these are rotations around arbitratry axes, rather than just the x, y, and z
axes. For example, you might want to spin an object around the diagonal
axis <1, 1, 1>. Quaternions are often used when interpolating objects from
one orientation to another, as they provide a smoother result than limiting
yourself to the x, y, and z rotational axes.
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